Class Notes Economics in the Digital Age
Week 1 pre recorded video
What is Economics?
-
economics is a social science concerned with description and analysis of the
production, distribution, and consumption of goods and services.
- How to allocate and use resources?
- Which products and services should be produced?
- Who should be producing and consuming goods and services? Who
can be the most efficient producer and who should be allowed to
consume
Scarcity
- using a resource means it cannot be used for another purpose
- Limiting factors: money, resources, time, energy
- Every choice involves important elements of scarcity
- SHould you buy a new laptop?
- should you watch another movie on netflix?
- should you run another km after that 10 you just ran?
If you had an infinite life with infinite resources, Economics would be irrelevant
because scarcity which drives economics would be irrelevant.
Economic way of thinking
- Systematic, clear, and precise way of answering questions related to decision
making under scarcity.
- This is much more challenging than we think:
- You might have incomplete information. Ex: a product didnt give you as
much benefit as you thought
- You might make mistakes in estimating benefits and costs
- You might be biased in your decision making.
Example: How much are you willing to pay for a bag of popcorn in the cinema?
50
- Most people end up at around 35 dkk, which is around the price it costs in the
cinema.
- Average markup of movie theater popcorn is 1275%
- It costs the cinema 2.5 dkk to produce the popcorn. Most people don't know
this which means we make decisions under incomplete information
- If you will buy it now it is still based on the benefit you receive from the
product in relation to the price.
Common Criticism of Economics
- People are likely to not approach decisions with economic theory in mind
- Nevertheless, economic theory turns out to be extremely helpful in predicting
human decision making.
- We optimize our decision making by trial, moving closer to what economists
consider optimal decision making. We become more rational in trial and also
gather more information over time. More rational behaviour
-
Behavior also often differ from predictions of economic models
- People lack the expertise to act rationally
- Nevertheless, economic models can in this case help us to make better
decisions
- EX: which costs and benefits do really matter when making
decisions?
Cost-Benefit Approach to Decisions
Should I do Activity X?
If B(x) > C(x), do x, otherwise don’t
- x is the activity
- B(x) are the benefits of activity x
- C(x) are the costs of activity x
-
Conducting this equation we need the same unit of measurement for costs
and benefits
Often this is monetary
- B(x) is the maximum price your willing to pay for activity x
Reservation Price
The reservation price of activity x is the price at which a person would be indifferent
between doing x and not doing x. The exact point where it doesn't really matter to
the person whether they conduct the activity or don't.
- Also called valuation or maximum willingness to pay.
- If costs are lower than the reservation price than the activity will make sense
to do and vice versa if the cost is higher than the benefit/reservation price.
B(x) is equal to the maximum willingness to pay / the reservation price
- These values differ between individuals
Example: Iphone introduced a new iphone in 2018 with a higher price. This iPhone
sold worse than the previous iphone, so it seems they introduced a price higher than
many previous buyers' reservation prices. I.E B(x) < C(x) for many people.
1. 500 is the reservation price - at this price the benefits and costs are the same,
making the consumer indifferent to conducting the activity.
2. somewhere above 60 to 80
- 60€ < reservation price <= 80€
Opportunity Costs
Opportunity cost of an activity(x) is the value of all that must be sacrificed in order
to do the activity
- Many people make bad decisions because they tend to ignore the value of
such foregone opportunities. Looking at an activity in an isolated manner
instead of comparing it to activities that are excluded because of consumption
of activity x
Our question then becomes: Should I do activity x or y?
- y is the highest valued alternative activity to x
- not “should i do activity x”
Example:
Studying at CBS means that you cannot study at Harvard.
You should choose x over y if the net benefit of x is bigger than the net benefit
of y:
B(x) - C(x) > B(y) - C(y)
3.
a) B(guitar) - C(guitar) = 500 - 400 = 100
B(concert) - C(concert) = 180 - 100 =80
B(guitar) - C(guitar) > B(concert) - C(concert) = 100 - 80 = 20
b) B(guitar) - C(guitar) = 500 - 400 = 100
B(concert) - C(concert) = 220 - 100 = 120
B(concert) - C(concert) = 120 > B(guitar) - C(guitar) = 100
-
B(concert) - C(concert) = 180 - 100 = 80
B(work) - C(work) = 120 - 70 = 50
-
B(concert) - C(concert) = 80 > B(work) - C(work) = 50
Sunk Costs
-
Sunk Costs are costs that are beyond recovery at a time a decision is made
and should therefore be ignored in the decision making.
Sunk cost fallacy - Considering sunk costs in decision making as actual costs
1. C(1) = 0 (transportation and lodging are sunk cost)
2. C(2) = 20 * 2 + 25 * 2 = 90
3. C(3) = 75
b) C(3rd day skiing) = B(Econ 1 day) - C(Econ 1 day)
Failure to understand the Average-Marginal Distinction
-
Previous examples related to Yes/No decisions - should you do x or not. Often
the question is:
- Should I increase the level by which I am currently engaging in
activity x?
- EX: should you eat a fourth pizza slice?
-
Marginal Cost: the increase in total cost that results from carrying out one
additional unit of activity
Marginal Benefit: the increase in total benefit that results from carrying out
one additional unit of the activity
-
Decision Rule: Increase consumption if Marginal Cost < Marginal benefit
-
It is common to have decrease in marginal benefit the more you have of a
resource or the more you carry out an activity
Homo Economicus
-
The stereotypical decision maker in the self interest model is given the label
Homo Economicus, or economic man
Homo economicus only cares about personal material costs and benefits
-
He makes rational decisions based on Benefit and takes into account the right
costs
Self interest is one of the most important human motives, but it is not the only
important motive’
Homo Economicus Challenged - Unselfish behaviour
- Why do people help friends?
- Why do people donate to charities?
- Why do people return a wallet full of cash?
- Why do people teach refugees in denmark?
-
Because these activities provide benefits that are higher than the costs.
These benefits are difficult to quantify in monetary values, but they exist.
Next to that, people receive social benefits, e.g spend time with friends, be
recommended for a job, receive help in return etc
Positive vs Normative Economic Questions &
Microeconomics vs Macroeconomics
Positive vs Normative Economic Questions
Positive Questions = a question about the consequences of specific policies or
institutional arrangements
- e.g what is the effect of a beer tax on beer consumption?
Normative Questions = a question about what policies or institutional arrangements
lead to the best solution?
- e.g should there be a tax on beer?
By itself, economics cannot answer normative questions, but provide valuable
information to make decisions. The positive question could help answer the
normative question, however norms would be the basis for the answer.
Microeconomics vs Macroeconomics
- Microeconomics: the study of individual choices and the study of group
behaviour in individual markets
- e.g should you buy a house or not, demand and supply for rental
apartments in copenhagen
-
Macroeconomics: The study of broader aggregations of markets
- eg. national unemployment rate, total value output
- Microeconomics can help inform macroeconomic questions
Additional Reading:
The 4 things it takes to succeed in the digital economy
1. Customer Expectations: Increased service expectations of customers, e.g
preventive car maintenance
2. Product Enhancements: Complementary products and services, providing
solutions. e.g Playstation 4 VR headset
3. Collaborative Innovation: Allow third parties to innovate on your platform,
e.g Apple App store
4. Organizational Forms: Flat hierarchies with data based (automated)
decision making. e.g UBER’s dynamic pricing algorithm
Week 2 Pre Recorded Class
Markets
-
A market consists of the buyers and sellers of a good or service. Some
markets are confined to a single specific time and location. Others are not
Examples: Auctions, Stock Exchanges, eCommerce for shoes in Denmark.
Definition of markets depends on purpose: Global, local, regional
How we define markets will always be a simplification of a very complicated
world - but very helpful to generate insights.
This illustrates a simple demand curve. How much of the good will be demanded at
different prices of the good
The market equilibrium, where the curve intersects tells us the price at which the
product will be traded, 2.5 given that we have a horizontal supply curve, and as well
at this price the demand will be 6 units. As 6 students want to buy, but can only buy 1
each
Consumer surplus: The sum of all individuals net benefits
Exogenous shock
The demand curve does not change, however the quantity demanded does change.
-
-
Here the demand curve shifts, as well as the quantity demanded.
We only speak of a change in demand if we have a shift in the demand curve,
if the demand curve is not moving the demand is not changing however there
may be a change in the quantity demanded as the supply curve intersects
with the demand curve at a different point.
Exogenous shocks causes either the demand curve or supply curve to shift.
Demand
-
The demand curve of a product tells us how much buyers want to purchase
for each possible price. Key properties:
- Downward sloped (less demand with higher price)
- Gives demand at various possible prices holding all else constant.
-
Real Price = real price of a product is the price of the product relative to the
prices of all other products and services. Current prices and value of money
today.
Practically: We could ask for the willingness to pay of every market participant
on the demand side and sort them according to their willingness to pay
(reservation price) and then draw a demand curve
-
Horizontal Interpretation = start with the price. At a specific price we can see how
many tulips will be purchased on the market. ex: price 8 cents would result in 4000
sold tulips
Inverse Demand Curve = start with the quantity, find marginal buyer's reservation
price. Ex: 4000 tulips are being sold in the market, then we know that the last buyers
reservation price would be 8 cents for a tulip.
Law of demand
- Law of demand is the empirical observation that when the price of a product
falls, people demand larger quantities of it
Drivers:
- People switch to substitutes at higher prices. Ex: if the price of coca cola
increases then some consumers would switch to pepsi assuming it hasn't
risen in price
- People are not able to buy as much when the prices are higher, money is a
scarce resource.
Supply
The Supply Curve of a product is the quantity that sellers are willing to supply at any
possible price
Law of Supply: the empirical observation that when the price of a product rises,
firms offer more of it for sale.
- The upward slope of the supply curve reflects the fact that costs tend to rise
when producers expand production in the short run.
-
-
This is because the supplier uses the best/cheapest resources first and
if they want to produce more they have to move to worse/more
expensive production resources.
If the price of a good decreases, producers will substitute to another
good that they produce. At lower prices the supplier can be more
profitable by producing a different good and leave the market. if prices
of goods are increasing, new producers will enter the market as the
price is higher here.
Horizontal Interpretation: start with price, at 8 cents per tulips the suppliers will be
able to supply 2000 tulips
Vertical Interpretation: Start with quantity, find the marginal cost of last product
produced, for example at 5000 tulips per day, the last tulip produced would cost 20
cents
Shifting Demand and Supply
Change in demand / supply means a shift of the entire demand / supply curve.
Change in quantity demanded / supplied means a movement along the demand /
supply curve.
Increase in demand:
- an increase in demand will lead to an increase in both equilibrium price and
equilibrium quantity demanded/supplied
Decrease in demand:
- A decrease in demand will lead to both a decrease in equilibrium price and
the equilibrium quantity supplied/demanded
Increase in Supply:
- an increase in supply will lead to an decrease in the equilibrium price and an
increase in the equilibrium quantity supplied/demanded
Decrease in Supply:
- a decrease in supply will lead to an increase in the equilibrium price and a
decrease in the equilibrium quantity demanded/supplied
The Algebra of Supply and Demand
-
The Q gives us the slope in the curves, positive for supply, negative for
demand.
Equilibrium Quantity and Price
Equilibrium quantity and price = the price-quantity pair at which both buyers and
sellers are satisfied. This is where the demand and supply curve intersect.
In the equilibrium, market participants have no incentives to change their behaviours.
Excess supply: the amount by which quantity supplied exceeds quantity demanded.
The length of the golden line
Excess demand: the amount by which quantity demand exceed quantity supplied,
the length of the green line
In excess supply: sellers would rationally reduce price, resulting in downward
pressure toward equilibrium price until the supplier sell all their supply
In excess demand: buyers that are dissatisfied, and are not able to get the product
and start outbidding each other, resulting in a upward pressure on price until the
price reaches the equilibrium price
Some Welfare properties of Equilibrium
- If price and quantity take anything other than their equilibrium values, it will
always be possible to reallocate to make at least some people better off
without harming others.
- Therefore, the equilibrium outcome is said to be Pareto Efficient.
-
an outcome is pareto efficient if it is not possible to make some person better
off without harming another person.
Ex: with excess supply, they can reduce their price with 2 KR and which would
result in a consumer surplus for the consumer and the supplier.
Example Equilibrium Price.
Comparative statics - is the comparison of two different economic outcomes,
before and after a change in some underlying exogenous parameter while all other
parameters are held constant
Market Interventions
-
Pareto efficiency is an economic state where resources can not be reallocated
to make one individual better of without making another person worse of
Pareto efficiency implies resources are allocated in the most efficient way
possible, but not fairly
Efficiency simply means that given the low income of the poor, free exchange
enables them to do the best they can.
It may still be desirable to redistribute wealth within society.
-
Governments sometimes intervene in the market to redistribute wealth and
make it more fair, these often have harmful consequences however.
Rent Controls
- A price ceiling for rents is a level beyond which rents are not permitted to rise.
- A price ceiling below the equilibrium price will create excess demand.
- A price above the equilibrium price will have no effect.
-
What is likely to happen here is that there sellers would cut on maintenance
because there is double the demand than supply.
People will use bribes, as there are people willing to pay 800 and not 400.
Suppliers will convert their apartments to other types of property to circumvent
the regulation.
Price Support
- A price support or Price Floor keeps prices above their equilibrium levels.
- This leads to excess supply as suppliers produces more than is demanded
- A price support requires the government to become an active buyer in the
market to purchase the excess supply
- FOr example: the purpose of farm price supports is to ensure prices high
enough to provide adequate incomes for farm families.
- The intervention is problematic:
- What to do with the surplus produced?
- with agricultural price floors, the products are often wasted
- The intervention helps especially large producers, not in need of the
support
- Price of these products increases for all consumers. Both finished
products and products where the price floor product is used as input.
The Rationing and Allocative Functions of Price
Prices serve two important functions:
1. Rationing Function of Price: equilibrium prices ration scarce supplies to the
users who place the highest value on them.
- People that are the most willing to pay for products should be
the ones who get them as they get the most value from them.
2. Allocative function of price: signals to direct productive resources among
different sectors of the economy
- for example, if a certain industry sector is especially profitable
with high demand, the price will increase and suppliers will move
to this market instead.
Market interventions undermine both functions of the price mechanism
Factor that shift supply and demand
Type of Goods
-
Substitute Goods - are two alternative goods that could be used for the
same purpose, Tea and Coffe
Complementary Goods - complements are products that are used together,
socker and milk. Consols and video games
Inferior Goods - for inferior goods an increase in income causes a fall in
demand as consumer switch to the better substitute
For Normal Goods an increase in income leads to an increase in demand
Factors that shift the demand curve
Incomes
- Normal Goods - the quantity demanded at any price rises with increases in
income
- Inferior Goods - the quantity demanded at any price falls with increases in
income
Tastes
- Tastes can change, if a product becomes fashionable it will increase demand
Price of Substitutes and Complementaries
- Complements - an increase in the price of one good decreases the demand
for the other good, because they go together and the increased price of the
one product will decrease the demand of that product
- Substitutes - an increase in the price of one will tend to increase the demand
for the other
Expectations
- If people expect that the price of something will increase the demand will
increase to avoid the higher price
Population Size
- As the population increases demand increase.
Factors that shift the Supply Curve
Technology
- A cost-saving invention increases supply as cost drops.
Factor Prices
- Input factors, An increase in factor prices results in a decrease in supply
The Number of Suppliers
- More suppliers, right shift of the supply curve, decrease in equilibrium price
and increase in equilibrium quantity
Expectations
- If Prices are expected to increase in the future there may be a decrease in
supply as suppliers hold their supply
Weather
- Important for agriculture
Case Example recapped: Apple Iphone
-
Apple could have estimated the demand curve wrong, that the demand curve
was flatter in reality than expected. This would lead to the increase in Price
resulting in a larger decrease in the quantity of demand
Additional Reading: Integrating Supply and Demand
Week 3 Pre-recorded Class
Theory of Rational Consumer Choice
Rational COnsumer Choice
- Individual consumption decisions that add up to the demand curves
Assumptions in rational consumer choice theory:
- Consumers enter the market with well defined preferences. Consumers know
what products they like and to what extent
- Prices are taken as given. This is the price compared to the price of all other
goods
- Consumers need to allocate their incomes to best serve their preferences:
step 1: which combination of goods can the consumer buy given the
budget constraints and prices of goods
step 2: select the combination of these available goods that is prefered
by the consumer. I.e the bundles with the highest net benefit
The Budget Constraint
Bundle
- a bundle: a particular combination of two (or more) goods.
- EX: food and shelter.
-
On a more general level we denote good one as x1 and good 2 as x2. With x1
on the horizontal axis and x2 on the vertical axis. Shelter x1, food x2
Notation for bundles (S0, F0)
Measured as flows: consumption per time unit (per week in this case but can
be any other time measure)
Budget Constraint
The Budget Constraint represents the set of all bundles that exactly exhausts the
consumers income at given prices
- Its slope is the negative of the price ratio of the two goods
-
The opportunity cost of 1 additional square meter of shelter is 0.5 kg of food
Affordable Set/feasible set: bundles on or below the budget constraint. All of
the bundles the consumer can afford.
-
(For the budget constraint to be expressed we need to have a bundle that
exhausts our budget constraint)
-
Notation:
- On the Axis we have the goods (e.g shelter or food) and units of goods
(e.g m2 / week, or kg/week)
- All bundles beneath the budget line are affordable for the consumer
- The budget constraint is the line that includes all combinations of the
goods X1 and X2 that exhaust the consumer's budget
our budget constraint can be derived by:
X2 = (M / P2) - ((P1 / P2) * X1)
Properties of the Budget Constraint
-
-
The slope of the budget constraint equals:
– P1 / P2
and expresses the opportunity cost of good 1 in units of good 2: How
much of good 2 does the consumer need to give up to get one more unit of
good 1?
For example: –P1/P2 = –2, the consumer needs to give up 2 units of good 2 if
she wants to get 1 more unit of good 1
If there is an exogenous shock that shifts the budget constraint upwards, and
the newly affordable bundles include the former budget constraint, the
consumer is better off (i.e an increase in affordable bundles)
Budget Constraints Involving More Than Two Goods
- Usually consumers need to choose between more than only two goods.
- When we want to draw a consumer’s budget constraint for three goods we
need to draw a plane (3-dimensions)
- When we look at a consumer’s budget constraint for more than 3 goods (N>3)
we are looking at a hyperplane / multi dimensional plane. This is very difficult
Instead we look at a consumer choice between X and a composite good Y
Composite Good
-
A Composite Good combines all other goods than X (focal good) that a
consumer needs to choose from
By convention, the composite good has a price of €1 per unit
The amount of the composite good represents the amount of income the consumer
has left to spend after buying a certain amount of the good X.
-
If we consumed X2 units of X we would have the amount of Y2 left of our
budget/left to spend on the composite good
Preference Ordering
Budget Allocation
Step 1: Which combination of goods can the consumer buy given the budget
restrictions and prices of goods
Step 2: Select the combination that is preferred by the consumer. The best
bundle given the consumer's budget constraint and th preferences
- To do this we need to look at the Preference Ordering
Preference Ordering
- Enables consumer to rank pairs of bundles
- But does not allow the consumer to quantify by how much he likes a bundle
A over bundle B
- Can be visualized as Indifference Curves / map
- The preference ordering follows certain properties that allow us to describe
preferences and clearly define which bundles of goods consumers prefer
Indifference Curve
- The indifference curve is the collection of all bundles between which the
consumer is indifferent – consumer regards them of equal value.
Bundle A and B are equally attractive to the consumer, at D the consumer would be
worse off, at C the more-is-better property applies and the consumer would be better
off/be at a higher indifference curve.
Construction of Indifference Curve
- Mark an arbitrary bundle in the coordinate system
- Change the amount of X1, with a small amount of ∆X1
- Ask: By how much does the amount of X1 need to change (∆X2) so that the
consumer is indifferent between (X1, X2) and (X1 + ∆X1, X2 + ∆X2)
- Mark that new point at the indifference curve (B) and repeat the process.
- Connect the dots to create the indifference curve.
Properties of Preference Orderings
-
assumptions made in relation to preference orderings
Properties of Preference
Orderings for Rational Consumers
1. Completeness: the consumer is able to rank all possible combinations of
goods and services
- E.G I know that I like coffee more than water and water more than tea
– I also know which drink I prefer (or equally like - indifferent) for all
other available drinks
2. Transitivity: for any three bundles A, B and C, if a consumer prefers A to B
and prefers B to C, then he always prefers A to C.
- E.G I like coffee more than water, and water more than tea, therefore I
also like coffee more than tea
3. More-Is-Better: all other things equal, more of a good is preferred to less.
- e.g I prefer 2 cups of coffee over 1 cup of coffee
Why two indifference Curves (for the same individual) Do Not cross
Indifference Curves
Indifference Curves: a set of bundles among which the consumer is indifferent.
Indifference Map: a representative sample of the set of a consumer’s
indifference curves, used as a graphical summary of her preference ordering.
Indifference Map
Properties of Preference Ordering
1. Completeness: the consumer is able to rank all possible combinations of
goods and services
- E.G I know that I like coffee more than water and water more than tea
– I also know which drink I prefer (or equally like - indifferent) for all
other available drinks
2. Transitivity: for any three bundles A, B and C, if a consumer prefers A to B
and prefers B to C, then he always prefers A to C.
- E.G I like coffee more than water, and water more than tea, therefore I
also like coffee more than tea
3. More-Is-Better: all other things equal, more of a good is preferred to less.
- e.g I prefer 2 cups of coffee over 1 cup of coffee
4. Continuity: small changes in the bundle should not lead to a jump in
preferences.
5. Convexity: mixtures of goods are preferable to extremes
Based on the properties of the indifference curve we can make certain statements:
- Indifference Curves are ubiquitous: Any bundle has an indifference curve
passing through it because our preferences are complete.
- Indifference curves are downward sloping (This comes from the
more-is-better property
- Indifference curves cannot cross (This comes from the combination of the
Transitivity and More-Is-Better properties)
- Indifference Curves become less steep as we move downward and to
the right along them (this is implied by the convexity property of
preferences) people prefer balanced combinations that a lot of one good and
litle of the other
People with Different Tastes / Indifference Maps
-
Different consumers will likely have different preferences regarding the same
good
Special Type of Preferences
Perfect Substitutes Indifference Curves
-
The consumer is willing to trade the goods at a constant rate.
This could mean 1 to 1 but it could as well mean 1 to 2, the important part is
that it is constant
This Violates the convexity principle - the consumer is willing to trade the
goods at a constant rate
Indifference Maps for Perfect Complements
-
-
The consumer wants to always consume the goods at a constant ration.
In this case the consumers want to consume 1 computer for 1 operating
system vice versa and would not be better of with 2 operating systems and 1
computer
This violates the More-Is-Better Property, as the consumer is not better of with
100 operating systems and 1 computer than 1 computer and 1 operating
system
The Marginal Rate Of Substitution
Trade-Offs between goods
Marginal Rate of Substitution (MRS): The rate at which the consumer is willing to
exchange the good measured along the vertical axis for the good measured along
the horizontal axis.
- Equal to the absolute value of the slope of the indifference curve at that point.
The slope of the Budget Constraint tells us the rate at which we can substitute
good X2 with good X1 without changing total expenditure
The MRS tells us the rate at which we can substitute good X2 with good X1 without
changing total satisfaction
-
If the preference properties are fulfilled, the MRS is negative per definition
- The MRS for perfect substitutes is constant
- For perfect complements, the MRS is either 0, minus infinity, or not
defined (at the 90* angle)
- For convex preferences, the absolute value of the MRS decreases with
an increase in X1. The more the consumer has of good 1, the less she
is willing to give up units of good 2 to get units of good 1
-
This is what we call: Law of diminishing marginal rates of substitution
The marginal Rates of substitution
-
The marginal rate of substitution is the slope of the indifference curve at the
respective point of the bundle we look at.
Best Affordable Bundle
Budget Allocation
-
Step 1: Which combination of good can the consumer buy given the budget
restrictions and price of goods
Step 2: Select the combination that is preferred by the consumer
- Preference Ordering:
- Enables consumer to rank pairs of bundles
-
But does not allow the consumer to quantify by how much he/she likes
bundle A over bundle B
The Best Affordable Bundle
Consumers Goal: to choose the best affordable bundle, given the consumer's
budget restriction
- The same thing as reaching the highest indifference curve the consumer can,
given the budget constraint.
- The best bundle may lie at the point of tangency between the highest
indifference curve and the budget constraint.
- or, there may be a corner solution where she consumers zero of one of the
goods
EX: the best affordable bundle in regards to shelter and food.
-
-
The best affordable bundle here, F, where we have tangency between the
indifference curve and the budget constraint, and the MRS of the indifference
curve is the same as the slope of the budget constraint.
The best affordable bundle must lie on the budget constraint and not inside.
Because this would imply a bundle of less of the goods than possible.
A is not the best affordable bundle despite it is on the budget constraint
because it is at the same indifference curve as D and D is less than F
The Condition For The Best Affordable Bundle
If there is an Interior Solution the condition that must be satisfied is:
If there is a Corner Solution, there is no point on the preference curve that has the
same slope as the budget constraint.
For all points on the indifference curves
Tangency Condition: The slope of the indifference curve, measured by the Marginal
Rate of Substitution, must be the same as the slope of the budget constraint
measured by –P1 / P2
What if MRS != P1/P2
-
Assume that MRS = 2 and P1 / P2 = 1
- The consumer is willing to give up 2 units of good 2 for 1 unit of good
1 at point A (indifference curve)
- At a price ratio of 1, she would only need to give up 1 unit of good 1 for
1 unit of good 2 (budget constraint)
- so she would be better of by making this trade (because more is
better), therefore we know that this is not the best affordable bundle as
the MRS is higher than the slope of the budget constraint
-
Assume that MRS = 1 and P1 / P2 = 2
- The consumer is willing to trade good 1 and good 2 in the ratio 1:1
- At the price ratio of 2, the consumer only need to give up 1 unit of
good 1 for 2 units of good 2 – so she would be better of making this
trade, meaning point A is not the best affordable bundle and she
should could move to a higher indifference curve
-
An unrestricted grant would correspond to the budget B1 in the diagram
B2 is the restricted budget constraint
On B1 the university would want to spend more than 2 million on the secular
activities anyway, so the restriction will have no effect.
In relation to similar government policies regarding rent support, we can see
that if people spend more money on rent than they receive in grants anyway
then the restriction that it can only be used for rent serves no purpose and
only creates unnecessary byrochrasy
Corner Solutions
-
Corner solutions are solutions in which a consumer is best off by only
consuming 1 of the two goods in a two dimensional table.
-
-
-
-
The best affordable bundle in this case is A where the consumer only
purchases food and no shelter.
This is the case if there is no point where the Marginal Rate of Substitution
(MRS) is equal to the price ratio
In this case the MRS is always smaller than the the budget constraint or price
ratio, which is why the consumer is best of using a corner solution and only 1
of the two goods
Another situation where the best affordable bundle is a corner solution is for
perfect substitutes. (if the slope of the indifference curve isnt equal to the
slope of the budget constraint because then there would be an indifference
curve that overlap the budget constraint along the whole curve
Perfect substitutes is a bundle where the consumer is willing to trade them at
a constant rate where MRS is constant. In these cases the MRS is never the
same as the P1/P2 (price ratio)
In this case MRS is larger than P1/P2.
Interior Solution
In a choice between two goods, a case in which the consumer consumes a positive
amount of both goods is what we call an interior solution
- But, it is actually not the most common solution
- However, it is more interesting and more informative to analyze
External Reading: Defeating Future Fatigue
Utility Functions
- Utility functions yield a ‘number’ that represents the amount of satisfaction
provided by the consumption of a bundle
- U(X1, X2) = aX1 + bX2
- The utility of consuming good X1, and X2 as a function of their
respective quantities consumed.
-
Measured in utils (arbitrary units)
Not about the actual number of utils but it is the ranking of bundles
based on utils that matters
Reading: Defeating Feature Fatigue
- Manufacturers tend to include more and more features in their products that
increase products’ capabilities but negatively influence the products usability
Consumers Value both:
- A products capability
- A products usability
Consumer's utility function for Product A:
-
Prior to consumption, consumers value capability higher than usability a > B
(should be the alpha and beta sign)
Post consumption, consumers value usability higher than capability : a < B
consumers do not know their actual utility of a product before using it. They can only
form an expectation of the utility of a product:
1. more is better and completeness
2. Technology products and utility products
Question 2
- The issue is especially prevalent for complicated products that are difficult to
assess prior to consumption. E.g Cars, X-Ray equipment
We often distinguish between 2 categories of goods. For experience good,
pre-consumption utility assessment is particularly dificult
- Search Goods possess attributes that can be evaluated prior to purchase or
consumption. E.g a toaster, fridge, vacuum cleaner (consumer electronics)
- Experience Goods can be accurately evaluated only after the product has
been purchased and experienced. E.g visiting a concert, playing a computer
game, books
Week 4 - Pre Recorded Video: Individual and Market
Demand
Deriving The Individual Demand Curve
The Individual Demand Curve
Price-consumption curve (PCC): for a good X is the set of optimal bundles traced
on an indifference map as the price of X varies (holding income and the price of all
other goods constant)
Individual Demand Curve : is a relationship that tells how much the consumer
wants to purchase at different prices
- With the budget constraint and
the indifference curves we find the
bundle providing the highest value given
the budget restriction – the bundle a
rational consumer should choose
- The Demand Curve shows which
quantity is demanded at a given price
From optimal bundles to demand curve:
- We look at the indifference map
for a good q1, and the composite good
q2
- Now we change the price for q1,
p1 , holding the budget m, price p2 for
q2, and preferences constant, which
rotates the budget constraint
-
If we plot the price-quantity combinations into the coordinate system for the
demand curve, p1(q1), we arrive at the individual demand curve for the
focal consumer.
B1: Y = 24 - 3Q
B2: Y = 24 - 2Q
B3: Y = 24 - Q
Bundle 1: Q = 4, P = 3
Bundle 2: Q = 6, P = 2
Bundle 3: Q = 8, P = 1
equation:
slope = (y2 - y1) / (X2 - X1) = (2 - 1) / (6 - 8) = -1 / 2 = –(½)Q
P(5) = Q0
P = 5 – (½)Qx
Qx = 10 – 2P
Solution: Exercise – Individual Demand
Changes In Income
The Effects of Changes in Income
Income-Consumption Curve (ICC): for a good X is the set of optimal bundles
traced on an indifference map as income varies (holding the prices of X1 and X2 and
preference constant).
Engel Curve: curve that plots the relationship between the quantity of X consumed
and income.
-
-
-
Here we have the composite good at the Y-axis and shelter in sq.m / wk on
the X-axis.
we look at the best affordable bundle of a consumer that wants to consume
shelter, holding preferences and price constant.
at bundle 2 (from left to right) we have a budget of €60 and after consuming 3
sq.m / wk of shelter we have 30€ left of our composite good
bundle 3 we have a budget of 100€ and choose to consume 5 sq.m /wk of
shelter leaving us with €50 left of the composite good, etc for the 4 different
budgets.
When we trace the points we get our ICC - income consumption curve
Here the ICC is linear, but it doesn't have to be, we get it by tracing our best
affordable bundles
If we take this combination of different budget and the quantities from the best
affordable bundles we reach the engle curve
Here we have the combinations of how much a rational consumer would
consume given that a certain budget is available
-
ICC vertical axis: shows the amount the consumer spends each week on all
goods other than shelter (composite good)
Engel Curve vertical axis: shows the consumer’s total weekly income. The
engel curve shows us how quantity demanded varies with the income a
consumer has at his disposal.
Normal and Inferior Goods
The Effects of Change in Income
Normal Good: a good whose quantity demanded rises as income rises
Inferior Good: a good whose quantity demanded falls as income rises
What are examples of normal goods and inferior goods?
-
The prototypical inferior good is one with several strongly preferred, but more
expensive substitutes
Strictly speaking, these examples represent examples only for the
preferences of a certain consumer – for other consumers, preferences might
look different
-
-
Here we can see that as the income rises, the quantity consumed of a normal
good, a tenderloin, increases. This shows by an upward sloping engel
curve
For the inferior good, the hamburger, the quantity consumed decreases as the
income rises. This in turn leads to a downward sloping engel curve
Substitution and Income Effects
-
what we do here is a systematic analysis of the effect of a change in price of a
good (P1) on the demand for this good (X1)
A change in price has two effects:
1. The Substitution Effect
- The ratio at which you can exchange the good (X1) with another good
(X2) changes
2. The Income Effect
- The purchasing power of the consumer (holding her income constant)
changes
Substitution effect: results from the associated change in the relative attractiveness
of other goods
- e.g if Cola becomes more expensive, consumers substitute to pepsi
Income effect: results from the associated change in purchasing power
- e.g as the consumer has less real income (less purchasing power), she will be
able to buy less cola.
Total effect: the sum of the substitution and income effects
Example:
- what we observe here is the optimal bundles to consume for a consumer that
wants to consume shelter on the X-axis and the composite good on the Y-axis
- what is happening here is that the price increases from 6/sq. m to 24/sq. m.
our budget M is constant at 120€. The budget constraint however rotates
inwards.
- With the price increase we move from the optimal bundle A to D
- The shift in the quantity consumed, from 10 to 2 (or A to D) is the total effect
-
After the change in price, the rotation of the budget constraint, we do the
following steps
1. Create a hypothetical budget constraint that allows us to stay on the original
budget constraint, we increase our budget until we find a tangency point with
the original indifference curve. this is B’ in the picture
- How much Income would the consumer need to reach his original
indifference curve (I0) after the increase in the price of shelter?
- The slope of our new budget constraint needs to be the same as the
budget constraint after the price change, B1, as were looking at the
new price ratio
- After creating our hypothetical budget constraint B’ we can see that we
reach a new bundle C on our first indifference curve
2. The point C at B’ and I0 shows that if the consumer would face this price ratio
and get at the same indifference curve he would purchase bundle C
- The distance between the quantity demanded in the original bundle, A,
and the hypothetical bundle where we could reach the same
indifference curve with B’ is what we call the Substitution effect
- Substitution effect - The shift in quantity demanded originating from
the decrease in relative attractives of shelter given the increase in
price.
3. The movement from bundle C on B’, to D on B1, the optimal bundle given the
new price and our budget constraint, is what we call Income Effect
- Income Effect - a reduction in purchasing power as the price of shelter
increases.
Income and Substitution effects
-
The Substitution effect always causes the quantity consumed to move in the
opposite direction as the change in price
The direction of the Income Effect depends on whether the good is normal or
inferior
- For normal goods, the income effect works in the same direction as
the substitution effect
- so if we have an increase in the price and we have a normal
good than the income effect will reduce the quantity consumed
of the good
- For inferior goods, by contrast, the income and substitution effects
work against one another
- example below
-
-
Here we have the inferior good, the hamburger, it’s quantity demanded is
denoted on the X-axis. On the Y-axis we have our composite good
B1 illustrates an increase in price, an inwards rotation of budget constraint
D on I1 is our new best affordable bundle.
The distance between A and D is our total effect.
To decompose this we create a hypothetical budget constraint B’ which is
parallel to the new budget constraint and it is at a point of tangency with the
original indifference curve
This illustrates the hypothetical optimal bundle of C
The distance between C and A is the substitution effect, the change in
quantity demanded caused by the change in relative price of the hamburger
The distance from C to D, caused by our decreased purchasing power, works
in the opposite direction, subtracting the substitution effect causing the total
effect to be smaller than the substitution effect
-
Skis and bindings are perfect complements, we always want to consume
them in the constant ratio 1:1
When the price of bindings doubles we can no longer reach our old
indifference curve, the budget constraint rotates inwards
Our hypothetical budget constraint, that allows us to reach our old indifference
curve reaches a point of tangency as the original optimal bundle, C = A
This means that, for perfect complements the substitution effect is zero, there
is no difference between C and A
This means that the total effect is equal to the income effect
Aggregating Market Demand
Market Demand Curves
Market demand Curve: the horizontal summation of the individual demand curves
- This is what we see bellow, we look at different prices of shelter, and see how
many quantities, sq. m / wk these consumers consume
- At a price of 12, only one consumer purchases shelter, which is the only
consumption illustrated in the horizontal summation
- The second consumer only has a demand after P=8€ so here the demand
curve of the horizontal summation changes
Algebra of Market Demand Curves
-
If each consumer i has a demand curve of:
-
Because we ad quantities and not prices we would have to rearrange this to
-
Then, the market demand for all consumers, n, is given by the sum of all
individual demand curves:
Note: We can only add demand curves for price levels at which all consumers
demand the focal good. We can not ad a demand curve of a consumer, who for say,
has a demand at P=100€ if no one else has a demand here
1
P1 = 16 - 2Q1
Q1 = 8 – 0.5P
2
P = 8 - 2Q2
Q2 = 4 - 0.5P
3 (horizontal summation)
For 16>=P>8:
P = 16 - 2Q
For 8>=P>=0:
P = 12 - Q
Summation For 8>=P>=0:
Q = Q1 + Q2 = 8 - 0.5P + 4 - 0.5P = 12 - P
P = 12 - Q
-
-
If we want to add these two individual demand curves in the market, we have
to careful to look at these price ranges
At a price of 8 and higher, consumer 2 will not demand any shelter, this
means for 16>=P>=8, we simply have the demand of consumer 1:
P = 16 - 0.5P
As soon as P is smaller than 8, we need to aggregate the demand and sum
up the 2 individual demand curves, using horizontal summation, to create
the market demand curve.
Algebra of Market Demand Curves
-
if n consumers each have the same demand curve
-
Rearrange to give:
-
Then, we could simply multiply the individual demand curve with n given that
all the individual consumers would have the exact same demand curve, and
the market demand is given by:
-
Rearranging we get:
Price Elasticity of Demand
Price elasticity of demand: the percentage change in the quantity of a good
demanded that result from a 1% change in its price
-
Elastic: if the quantity demanded changes more than 1% (–1%)
Unit elastic: if the quantity demanded changes 1% (–1%)
-
Inelastic: if the quantity demanded changes between 1 - 0% (–1 - 0%)
Table: Price Elasticity estimates for Selected Products:
-
-
Green peas are elastic, and have a price elasticity of –2.8 which is higher than
-1. meaning that at a 1% increase in price, many people would substitute it for
other vegetables.
Cigarettes however is inelastic, meaning if the price would increase by 1% the
demand wouldn’t decrease by that much
The Price elasticity of demand at current price and quantity is algebraically defined
as:
It may be derived using the slope of the demand curve:
slope = ∆P / ∆Q = (0 – 16) / (8 – 0) = –16 / 8 = – 2
PA = 12
QA = 2
= (12 / 2) * (1 / –2) = 6 * (1 / –2) = –3
P = 40 – Q
slope = – Q or (– 1)
32 = 40 – Q
Q=8
epsilon = (32 / 8) * (1 / –1) = 4 * –1 = –4
-
-
The price elasticity of demand is inversely related to the slope of the demand
curve.
The steeper the demand curve, the less elastic is demand at any point along
the demand curve
with a horizontal demand curve, a perfectly elastic demand curve,
e=–∞
with a vertical demand curve we have inelastic demand
e=0
-
-
-
another important thing to understand in relation to the price elasticity of
demand depends not only on the slope, but also on the position on the
demand curve
Therefore, there will be different values of price elasticity of demand on
different points of the demand curve, with different price / quantity values
In the above picture you can see that we have a slope of the demand curve
that is constant. But as we have different points on the demand curve we
have different values of price elasticity of demand
Also, note that we usually write the absolute value of price elasticity of
demand and therefor remove “–”, i.e 1 and not –1
Determinants of Price Elasticity of Demand
Substitution Possibilities: the substitution effect of a price change tends to be
small for goods with no close substitutes.
- We have a more stable demand, low price elasticity of demand, if there are
few substitution possibilities, they cant switch products
- a good with many substitutes have a high price elasticity of demand
Budget Share: the larger the share of total expenditures accounted for by the
product, the more important will be the income effect of a price change
Direction of income effect: a normal good will have a higher price elasticity than an
inferior good
Time: demand for a good will be more responsive to price in the long run than in the
short run as it may take time for people to find substitutes
- Higher price elasticity for a longer time period
External Reading: A refresher on price Elasticity
In the reading the author uses some other definitions for price elasticity
Product have different price elasticities of demand
- Perfectly elastic: very small change in price results in a very large change in
the quantity demanded. E.g “pure commodities”
- Relatively Elastic: small change in price cause large changes in the quantity
demanded. E.g Beef
- Unit Elastic: change in price is matched by an equal change in quantity
demanded
- Relatively Inelastic: large changes in price cause small changes in demand.
E.g Gasoline “products with stronger brands tend to be more inelastic”
- Perfectly inelastic: quantity demanded does not change when price
changes. E.g Fee for new passport, or medicine
Our definition:
a) Iphone – apple
b) Inelastic or unit elastic, the demand has pretty much stayed the same during
recent years, or dropped a bit, while the price has increased.
c) They could try to create a stronger brand, as this would differentiate them
from other products and create additional value for the customers. Thy could
market the features that differentiate them, or a lifestyle representing the
product that differentiate them that decreases the customer perceived
substitution possibilities.
d) Other competitors could create features or a brand image that is different and
similarly attractive as the iphone to increase the perceived substitution
possibilities or try to emulate the features and brand to make them more
similar and thereby also increase perceived substitution possibilities among
customers’
Week 5 Pre-recorded video – Consumer Surplus and
Elasticity
-
To calculate the cross price elasticity of demand we use comparative statics.
We hold the price of our focal good P1, and our income M constant, changing
the price P2 of another good X2
-
In this situation the demand curve rotates on the vertical axis, we have the
same income and the price of X1 is the same
The price of P2 changes however and is now P2’ and the quantity we can
afford of X2 is now lower.
We can now not reach the old indifference curve but only reach a lower one,
where the new optimal bundle is
-
Demand of X depending on the Price of Z?
-
The demand of X depends also on the price of another good Z
here we distinguish between two types of goods
Complements - An increase in the price of good 2 leads to a decrease in demand
for good 1
- This is because these goods are consumed together. If the price of one
increases the consumption of the other decreases
Substitutes – An increase in the price of good 2 leads to an increase in the demand
for good 1 (focal good).
- This is because the relative attractiveness of good 2 in relation to good 1
decreases as the price of good 2 increases as they fulfill the same need.
Cross Price Elasticity of Demand
Cross-price elasticity of demand - the percentage change in the quantity
demanded of one good caused by a 1% change in the price of the other good
eXZ = (∆Qx / Qx) / (∆Pz / Pz)
The cross-price elasticity of demand for any two goods X and Z is:
- You can also make use of the point slope method:
eXY = (PY / QX) * (1/slope)
-
-
-
if eXZ < 0. X and Z are complements
- if cross price elasticity is smaller than 0, X and Z are complements
meaning if the price of Z increases the consumption of X decreases
if eXZ > 0. X and Z are substitutes
- If the price of Z increases, the demand for good X increases
Butter and margarine are substitutes, because as the price of Margarine
increases, the demand for butter increase
Entertainment and food are compliments, as the cross price elasticity is
negative. If the price of food increases, the quantity consumed of
entertainment decreases
a)
Identify the relevant information to solve the exercise:
2017:
2018:
-
QX = 400
PY = 10
QX = 300
PY = 12
The price of PX is constant (PX=3) and all other factors that might influence
QX are constant as well
The exercise tells us that we can assume that the change in quantity
demanded (∆QX) is cause by a change in PY
-
Slope :
(Y2 – Y1) / (X2 – X1)
(12 - 10) / (300 - 400) = 2 / -100 = -1/50
-
Function for PY = A – 1/50QX
Find A by replacing PY an QX with the coordinates of one of the point, e.g
(400, 10)
10 = A – 1/50*400
10 = A – 8
18 = A
A = 18
PY = 18 – 1/50QX
-
When we have this equation we can calculate the cross price elasticity.
-
Calculating the cross-price elasticity for the point QX = 400, PY=10 and the
relationship PY = 18 – 1/50QX
Formula:
-
eXY = (10 / 400) * (1/(-1/50)
eXY = (1/40) * -50
eXY = – 1.25
- When the price of Y increases by 1% the quantity demand for X decreases by
1.25%. This means the goods are complements
- We can also use the other method:
b)
b) An example could be that X represents video games for sony playstation and Y
the sony playstation game console. The games are useless without the console –
when people buy less consoles due to an increase in price, they will also buy less
games
Taxes and Subsidies
-
Taxes: fees levied on consumers or firms by a government entity (local,
regional or national) in order to finance government activities.
-
Taxes fall on whoever pays the burden of the tax, independent of whether
this is the entity being taxed.
E.g Value added tax (VAT)
-
-
Subsidies: benefits given to consumers or firms usually by the
government. Subsidies are commonly transferred in the form of a cash
payments or a tax reduction
E.g unemployment benefits
Taxes – Burden on the seller
-
-
-
A per unit Tax of T=10 Levied on the seller shifts the supply curve upward by
T units
Now suppliers need to charge a higher price in order to still be able to
produce the good, and be able to operate profitably
Here P0 at Qo is 25 and P1 at Q0 is 35
Looking now at a graph with the demand curve as well.
We can see the the equilibrium price moves from P* to P1* and the quantity
from Q* to Q1* when the seller needs to pay a tax of T=10 to the government
Importantly, even though the seller pay a tax of T on each product purchased,
the total amount the seller receives (equilibrium price) lies less than T (10)
above the old supply curve
The old Equilibrium price was P* the new equilibrium price is P1* is not the 10
monetary units above the original equilibrium price as the quantity demanded
decreases.
-
Note also that even though the tax is collected from the sellers its effect is to
increase the price paid by buyers
This means that the burden of the tax (T) is divided between the buyers and
the seller, this is what we call Tax Incidence
Tax Incidence
-
Even if the tax is collected from the seller, its effect is to increase the price
paid by buyers. The burden of the tax (T) is thus divided between the buyer
and the seller.
Calculating the sellers share of the tax, ts:
ts = (P* – (P*1 – T)) / T
- We can also see the seller's share of the tax in the green square.
Calculating the Buyers share of the tax, tb:
-
the amount of the tax that the buyers pay
This is also shown in the blue square
-
The distance between P1* and P1* – 10, is the total amount of the tax, 10
Taxes – Burden on the buyer
-
Here the tax, T=10, is being placed on the buyers.
We can see that that the demand curve shifts downward by T=10
The new equilibrium price is then P2* but the buyer would need to pay the
equilibrium price P2* + 10, the 10 goes to the government
The demand curve shifts left, from equilibrium P* to P2*
Legal and Economic Incidence of Tax
We distinguish between the legal and the economic incidence of tax
-
Legal Incidence of the tax: describes whether the buyer or seller is
responsible is responsible for paying the tax to the government
The legal incidence has no effect on the economic incidence of the tax
-
Economic Incidence of the tax: tells us the respective share of the tax
borne by buyers and sellers through the tax’s effect on the price of the good
The share of Tax on the buyers and sellers depends on Elasticity of
demand
-
-
-
One aspect of the demand curve that is heavily influencing who is bearing the
economic burden of the tax is the elasticity of Demand
(a) is a less elastic demand curve meaning the demand does not react very
much in an increase in price
(b) is more elastic meaning the demand decreases substantially as price
increases.
In both the curves there is a tax of T=10 placed on the seller, but the effect of
the tax is very different
If buyers have no substitute to turn to, with a low price elasticity of demand,
they will carry the major burden on of the tax that was imposed on the seller
which we can see in figure (b)
With a more elastic demand, a smaller slope, the burden will mainly be placed
on the seller.
The burden tends to fall on the side of the market that can least escape it (has
no substitutes)
a) P* = 5
P1* = 6
T=2
- sellers share:
ts = (5 - (6 - 2)) / 2
ts = 1 / 2
ts = 0.5
-
Buyers share
tb = (P1* - P*) / T
tb = (6 - 5) / 2
tb = 1 / 2
Absolute term:
buyers pay:
- Absolute terms: 0.5 * 2 = 1
- percentage terms 50%
sellers pay:
- absolute terms: 0.5 * 2 = 1
- percentage: 50%
b) P* = 5
P1* = 4
T=2
-
Total tax: Q1* * T = 4 * 2 = 8
½ means 50% so 0.5 * 8 = 4, both sides pay 4 each
-
The tax shares of the suppliers and consumers Always add up to 1. Meaning
if we have the tax share of the buyers we know the tax share of the suppliers.
(1 - buyers share)
-
The calculation of the economic incidence of the tax is in this case symmetric
independent of whether the legal incidence of the tax is levied on the supplier
or consumer - Economic Incidence of the tax
Consumer Surplus
Consumer Surplus - a measure of the extent to which a consumer benefits from
participating in a transaction
- In a graph -> area between demand curve and price
-
In the figure above, a demand curve is depicted.
if the units of good X were small, that staircase function would be a
continuous function
the gross benefit (B(X) for the consumption of X1 is simply the area under the
inverse demand curve from 0 to X1
At a price of zero the green area equals the consumer surplus
-
-
-
Here we see a demand curve which tells us the willingness to pay for either a
single consumer if it is an individual demand curve or for all the consumers if it
is is a market demand curve
Consumers are willing to purchase more of the focal good, here X1, until their
marginal benefit is lower than the marginal cost of the next unit, therefore we
know where the market equilibrium is
It as well means we can find the consumer surplus, which is the net
benefit/consumer suplus (B(X) – C(X) for the consumption of X1. Here the
consumer surplus is the area between the inverse demand curve from 0 to
X1, minus the rectangle below, which is the cost of the consumers
Application of Consumer surplus: Cost-Benefit Analysis
-
-
for all economic decision we compare costs with benefits
This becomes difficult when several consumers are affected by an economic
decision
In such cases the consumer surplus is an important measure to consider
The Consumer Surplus tells us: By how much is the willingness to pay of the
consumers (their benefit from consuming the goods) bigger than the price
they need to pay (the costs of consuming the goods)
considering consumer surplus can help us make political decisions.
E.g Should we build a new highway?
- A good way for the government to decide whether tax money should be
allocated to building this highway is to think about what the consumer
surplus of using this highway is. Then we would look at a price of 0 for
the consumers and see how much they would benefit from the highway
and if it is larger than the costs for the government to build the highway.
Consumer surplus before the tax:
P = 10 – Q
P=2
2 = 10 – Q
Q=8
Consumer surplus:
((10 - 2) * 8) / 2 = 32
Consumer surplus after the tax:
P = 10 – Q
P = 2 * 1.5 = 3
3 = 10 – Q
Q=7
consumer surplus:
((10 – 3) * 7) / 2 = 49 / 2 = 24.5
difference:
32 – 24.5 = 7.5 €
External Reading: The frontier of Price Optimization
Maximize Revenue by setting the price of your product optimally.
Steps to go through:
1. Forecast:
- Based on historical data from related products the relationship between
demand and price is being predicted
2. Learn
- The prediction is being applied in practice and updated based on actual
performance
3. Optimize
- After the learning period the price optimization is rolled out over
hundreds of products
A)
-
You can optimize your revenue at a price elasticity of demand of -1 (unit
elasticity)
- At this point, price elasticity of -1, you maximize your revenue in relation to
price
Why is –1 price elasticity optimal?
- Revenue = P * Q
- Price Elasticity of Demand tells us by how much (in percent) the quantity
demanded changes when we increase the price by 1%
- Inelastic Demand (e = – 0.8), what happens if we increase the price of
1 %?
- Revenue = 1.01P * 0.992 Q = 1.002 PQ
- The revenue increases when increasing the price, although the
demand decreases
-
Elastic Demand (e = 1.2) increase P by 1%
- Revenue = 1.01P * 0.988Q = 0.998 PQ
-
The revenue decreases when increasing the price as the loss of
demand is outweighing the revenue gained from the price increase. We
should then decrease the price
The point we want to be at is e= -1 as we optimize price here
b) Why is price optimization challenging in practise?
- Even though we understand the mechanism behind how the quantity
demanded reacts to changes in price, in practise, we commonly do not know
how price elastic demand for a product is. This type of data is difficult to
collect and can often only be approximated
c) Think about an example firm that could benefit from such an optimization
and explain why
- Companies that have a large product portfolio with differentiated products, e.g
fashion retailers, consumer electronic stores
- These types of suppliers need to set a lot of prices and the demand for every
product is likely to be different. Therefore, an automated optimization can offer
a big potential to increase revenue
Week 6 - Production
The Production Function
Production: Any activity that creates current or future utility
- This can be a car or Daniels micro videos
Production Function: The relationship that describes how input (e.g labor, capital,
resources, intermediate products) are transformed into output (e.g Cars, Holiday
Packages, Game Consoles,..)
For example:
Q = F (K, L)
-
Q = Amount of output
K = Capital
L = Labour
How much output do we generate from a certain amount of Capital and
Labour
As economists we are primarily interested in the mathematical relationship of
how much output we can generate from a certain amount of input
Short and Long Run Production
Short Run: the longest periods of time during which at least one of the inputs used
in a production process cannot be varied. (at least not economically feasible)
- A firm cannot adjust its production facilities in the short run but the firm can
hire more workers in the short run
How long is “short run”? That depends on how much time it takes to change all input
factors
Long run: the shortest period of time required to alter the amounts of all inputs used
in a production process.
- In the long run there are no fixed input factors
Variable input: an input that can be varied in the short run.
Fixed input: an input that can not be varied in the short run
Short-run Production Function
Three commonly observed properties:
1. It passes through the origin
- without any input factors we are not able to produce any output
2. Initially the addition of variable inputs augments output at an increasing rate
(convex)
- Initially when we increase our variable inputs we will increase our
output at an increase rate.
3. Beyond some point, additional units of the variable input give rise to smaller
and smaller increments in output (concave)
-
Here we have a short term production function. With output being meals per
week
We are looking at how the quantity of output changes as we vary the variable
input of Labour.
K0 indicates that this variable is fixed and cannot be altered in the short run
Firstly we see that the slope of the curve increases to the point of Q=4 after
which the slope decreases
-
-
In the line to the left we can see that the first unit of labour increases output by
4, the second unit of labour increases output by 10, the 3rd by 13, the 4th by
16 and then after the 4th output decreases in relation to an additional unit of
variable input, with the 5th unit of labour producing 15 units of output, 1 less
than the 4th one.
At this point (L=4) the slope of our curve decreases continuously.
-
The curve goes through the origin
The curve increases until L=4
At the inflection point of L=4 the slope of the curve decreases.
Law of diminishing return: if inputs are fixed, the increase in output from an
increase in the variable input must eventually decline.
Example: Software company - writing software for a client
- A programmer can write code for 8h/day.
- In order to finish the development phase before the deadline, the company
could hire more employees (variable input)
- We assume that other input factors (computers, office space) cannot be
changed in the short run (fixed input)
- Programmers can work in 3 shifts to fully occupy computers (we assume they
are indifferent towards the time of day they work)
- We can let programmer work in pairs (pair programming)
- If we add more programmers to the team they will start to compete for
computers and office space (other fixed input factors). Be in each other's way
- Furthermore, having more programmers in the team will make coordination
and communication increasingly difficult.
a) A nuclear power plant.
- Variable inputs, would be Labour, possibly uranium and other materials
needed
- Fixed inputs would be plant/machine capacity. These would be reactors
and other machines like the cooling system etc. The maximum capacity
of these would not be possible to vary in the short run
b) Initially you could increase variable input factors such as labour and material,
by working in shifts 24/h per day and producing at maximum capacity at all
times. After the point of 24/7 maximum capacity, increasing variable input
factors would not lead to an increase in output (energy), as the capacity of the
reactors and other machines are being exhausted increasing labour and
materials would not lead to an increase in output, the workers would only be
in each others way, and all the material would not be used and would have to
be stored or thrown away
Answer:
Short-run Production Function
Total Product Curve: a curve showing the amount of output as a function of the
amount of variable input (e.g Q as a function of L with K0 (fixed))
Marginal Product: change in total product due to a 1-unit change in the variable
input
Average product: total output divided by the quantity of the variable input
-
In this example, we look at how much we on average produce of output Q in
relation to the amount of variable input, Labour we have used.
Graphical Representation of the short-run Production Function
-
In the top graph the Y-axis is Q (meals/wk) and on the X-axis we have Labour
in person hr/wk
- The top graph illustrates the total product curve. At different levels of variable
input factor L we can produce different levels of output Q
Marginal Product curve
- At different levels of L, how much extra output, Q, do we generate when we
add an extra unit of Labour (X)
-
-
We do this by calculating the slope of the total product curve at different
points
In the graph we can see this in MPL, which is calculated 2 times.
MPL = 12/1 = 12 & MPL = 16/1 = 16
We can plot these points to create a marginal product curve, where we have
the marginal product at different quantities of input. The marginal product
curve is shown in the bottom graph
The marginal product curve is the first derivative of our total product
curve and our production function. Giving us the increase in output at a
certain amount of Q if we add an additional unit of labour.
Some important point to note in the graphs:
- Q=4 is our inflection point – the point from where we move toward diminishing
returns. If we add an an additional unit of labour after L=4 our increase in
output will be less than the time before
- If we move from L=4 -> L=5 we will have a smaller increase in output than
when we moved from L=3 -> L=4
- The inflection point is the maximum point of the Marginal Product curve,
in the bottom graph.
-
-
At L=8 we are at the maximum of the total product curve, after where the total
product starts decreasing. Here we move from a positive slope of the total
product curve to a negative one
In the Marginal Product Curve this is the point where the Marginal Product
Curve intersects with the X-axis
After L=8, an additional unit of Labour will decrease the total output.
Production Function
-
Q = F(K, L) gives the total output at point (K0, L)
-
MPL gives the marginal product at point (K0, L). How much more output can
the firm produce when increasing labor with 1 unit point (K0, L)
-
APL gives the average product of input L at a point (K0, L). How many units
of output was the firm able to produce per unit of labour at point (K0, L)? The
average productivity.
Average Product
-
-
-
-
-
At the top we first have our total product curve and at the bottom we first have
the Marginal Product Curve.
To draw our Average Product we look at a certain point, in this case L=2,
where we have Q=14, where we input 2 units of labour and the output is 14
meals/wk
To get the average product we draw a ray from the origin through the specific
point. Using rise over run, we calculate 14/2=7. Now we know that on average
we can generate 7 units of output from one unit of labour at this specific point.
Drawing several rays from the origin that intersect with the total product curve
we can generate the Average Product Curve which is depicted by the green
curve in the bottom graph
At input L=6 and output Q=72, the ray from the origin through this point is at a
point of tangency with the total product curve. As we know, the Marginal
Product is the slope of the curve at any point of the total product curve, this
means that when the ray is tangent to the total product curve, The marginal
product and the Average Product are equal.
This is as well illustrated in the bottom panel where the curve intersects. At
the point of input L=6 the marginal product and average product intersect
When the ray of the average product is tangent to the total product curve
the marginal product and average product is equal
Relationships between Total, Marginal and Average Product Curves
-
When the marginal product curve lies above the average product curve ,
the average product curve must be rising
- The marginal product gives us the change in output if we add another
unit of input (L). If the Marginal product is above the Average product,
i.e if the additional output produced from an additional unit of input is
more than the average product, then it means that the average product
will rise.
- EX: if you have gpa of 3 and get a 4 the gpa will increase
-
When the marginal product curve lies below the average product curve, the
average product curve must be falling.
The marginal product curve and the average product curve intersect at the
maximum value of the Average Product Curve
-
Exercise:
a) MP1 (X5) = 10
MP2 (X5) = 15
If the farmer had an extra unit of fertilizer he should apply it to the second field
(red) as the marginal product is higher here.
b) at the optimal optimal point MP1 = MP2 (except for corner solution)
The optimal point would be
Solution:
-
The general rule for allocating an input efficiently in such cases:
Allocate the next unit of the input to the production activity where its marginal
product is highest.
Production in The Long Run
-
-
-
-
In the long run, all input is variable
- In the long run we are not only able to increase variable input by, for
example hiring more workers, but as well increase fixed input by
building factories for example
A certain amount of output Q0, can oftentimes be reached with different
combinations of the input factors.
- Ex. produce a car with 4 machines and 10 workers or a car with 1
machine and 30 workers.
Isoquant: all combinations of variable inputs that yield a given level of output
Here we see a production function of a product with 2 input factors, Capital
(K) and labour (L)
- The first step to produce isoquants is to fix one/several amounts of output.
- In this case we have the amounts of output fixed at Q 16, 32 and 64
Production Function:
Q = F(K, L) = 2KL
Drawing the isoquant for Q=16:
16 = 2KL
K = 16/2L
K = 8/L
- To draw the isoquant, we input different values of L to see which amount of K
wee need to produce Q=16 given that we use the amount of L
- For instance, if we use 8 units of Labour, we need 1 unit of capital (K)
to produce 16 units of output
- To produce the other Isoquants, we fix the Quantities of output that we want to
produce and then solve the equation for Capital (K) to as K is depicted on the
Y-axis
Isoquants
Isoquants possess similar properties as indifference curves:
- We have a map of isoquants that cannot intersect
- They cannot intersect as we have different fixed quantities of output for
different isoquants
- The slope of the isoquants is the marginal rate of technical substitution:
how many units of input factor 2 are needed to compensate for a 1 unit
reduction of input factor 1
-
In a more generalized notation we use X1 and X2 to describe two input
factors that are needed to produce Q
The Marginal Rate of Technical substitution
Marginal rate of technical substitution (MRTS): the rate at which one input factor
can be exchanged for another without altering the total level of output
- Depends on current level of inputs as we have this convex curve
-
It is essentially the slope of the isoquant at a certain capital and labour
combination in this case
Examples of Production Functions (in the long-run)
Q = 4X1 + 2X2
- A production function where the output Q is dependent on 2 input factors X1
and X2. As we are in the long-run, all the input factors are variable
How can we draw isoquants for this production function?
- We fix Q to certain amounts of output that we are interested in and then we
solve the production function for either X1 or X2 dependent on which input
factor we want drawn on the y-axis
- We solve for the factor we want on the y-axis, this is most often X2
- In this case we decide to solve for X2
Q = 4X1 + 2X2
Q - 4X1 = 2X2
X2 = 0.5Q – 2X1
- Fix Q at a value and draw the curve (20, 60, 80)
These input factors are Perfect Substitutes:
- MRTS is constant: replace 1 unit of X1 with 2 units of X2 to produce the
same Q
- We can as well see that in the equation where our slope is – 2
- The isoquants we have drawn here are for 20, 60 and 80 Q
Example 2
-
This is a Leontief, or Fixed Proportions Production Function
Q is equal to the minimum of X1 and 4X2
We fix Q at a value and draw the curve (4, 8, 12), which is shown in the graph below
-
-
-
Here we have X2 on the y-axis and X1 on the X-axis
In this case we need 4 times as many units of X1 than X2 to produce a
quantity of Q
- For example for Q=4, X1 = 4 and X2 = 1, for Q=12 we need, X1=12
and X2 = 3
We plugg in the amounts of the input factors and then we look at what the
minimum is. If we use 4 units of X1 and 1 unit of X2, then we have the
minimum of {4, 4}
If we used less units of X1 for example 3 units of X1 and 1 unit of X2, then we
would have minimum {3, 4} which means we can only produce 3 output units
These type of production functions are for Perfect Complements, where we
need to use our input factors in a certain constant ratio, in this case 4:1, 4
times as much of X1 than X2
Example 3:
Q = 3X1X2
- Cobb-Douglas-Production Function
-
Again, to be able to create a graphical representation we need to solve the
equation for X2:
X2 = Q / (3X1)
Fix Q at a value and draw the curve (in this example 15):
X2 = 15 / (3X1)
X2 = 5 / X1
In the picture, Isoquants are plotted for Q = (3, 15 , & 30)
- Moving northeast on the Isoquant map, the Quantity of output increases
Returns to Scale
Returns to scale is an inherently long-run concept
- we multiply (increase) all input factors with the same number
- EX. if we have a production function that is contingent on the input of labour
and capital. To see how our returns to scale look like we would multiply these
factors with the same fixed factor for instance 3, and then we would see what
happens to our output
Increasing returns to scale describe the property of a production process whereby
a proportional increase in every input yields a more than proportional increase in
output.
- ex. multiplying all input factors with 3 resulting in an increase of output of 4x
Constant returns to scale describes the property of a production process whereby
a proportional increase in every input factors yields an equal proportional increase in
output
- Increasing input factors with a factor of 3 yields an increase in output of
3*output
Decreasing returns to scale describes the property of a production process
whereby a proportional increase in every input yields a less than proportional
increase in output
- Increasing input 3X and output increases with 2X
Returns to scale Mathematically
What happens when you multiply F(X1, X2) with a constant c and c needs to be
larger than 1 (c>1)
-
Increasing returns: F(cX1, cX2) > cF(X1, X2)
Constant returns: F(cX1, cX2) = cF(X1, X2)
Decreasing returns: F(cX1, cX2) < cF(X1, X2)
Examples:
a) Q = 5X1 + 3X2
5cX1 + 3cX2 = c(5X1 + 3X2) = cQ
- we multiply both our input factors with c which we then can pull out resulting in
c(5X1 + 3X2). We can see that we have the initial production function
multiplied by c, which is ofcourse equal to c multiplied with Q.
- We have constant returns to scale
b) Q = X1 * 5X2
cX1 * 5cX2 = c^2(X1 * 5X2) > cQ
- Here we have increasing returns to scale, because we have c squared
multiplied with the production function which is larger than c multiplied by the
quantity of output
Exercise:
a) Q = 4X1 + X2
-
4*cX1 + cX2 = c(4X1 + X2) = cQ
constant returns to scale
b) Q = 3X1*X2
c
3*cX1*cX2 = c^2(3X1 * X2) > cQ
- Increasing returns to scale
c) Q = 3X^0.3 * X2^0.7
3*cX^0.3 * cX2^0.7 = c^2(3X1^0.3 * X2^0.7) > cQ
d) Q =
Solution:
a)
b) -
c) -
d) -
Distinction between Diminishing Returns and Decreasing Returns
to Scale
-
Decreasing returns to scale - describes the situation when all inputs are
multiplied by a given factor and the output grows by a smaller factor.
- Ex. Car production where we need machines and workers. If we
increase both input factors by 3X and the output only increase by 2X,
we have decreasing returns to scale
-
Law of Diminishing Returns - refers to the case in which one input varies
while all others are held constant. The increase in output from an increase in
the variable input must eventually decline.
- ex Car. If we increase workers while holding machines constant, there
will come a point where the output decreases as the workers will be in
each other's way and be hard to organize.
-
why do decreasing returns to scale exist if we can just increase our input (K
and L) and replicate our production?
Q = F(K, L)
---> Unmeasured input factor
e.g Organization and Communication do not scale well beyond a certain size of a
firm. Because after some point of increasing the size of the organization it becomes
very hard to coordinate and communicate leading to decreasing returns to scale
External Reading: The End of Scale
-
-
-
Traditionally, economies of scale, for which firms divide their fixed costs such
as factories and machinery over a large number of output units, have offered
large corporations a competitive advantage.
Economies of scale: Average costs decrease with increase in output
Increasing returns to scale: Output grows over-proportionally to
increase in input
economies of scale focus on cost while increasing returns to scale focus on
output
Platform based business models have challenged this advantage, by focusing
on niche markets and being more flexible in their production
- e.g Dollar Shave Club delivers shaving gear without distribution to
retailers and not owning production, UBER does not own any cars
Three ways to unscale large companies:
1. Become a platform: Rent out your capabilities, allow 3rd parties to make use
of these capabilities
2. Install an absolute product focus: Focus on making the best product that fits a
consumer’s preferences and outsource non-core activities
3. Grow through dynamic product bundling: Understand the consumer and offer
the product she wants
a) By only providing a platform, 3rd parties can utilize the platform to sell or do
business. This means that the platform only needs to provide the forum /
platform and not own any production resources. This means that input factors
like factories either are rented or provided by the 3rd party seller making them
easily scalable and a variable input factor.
Answers:
a) Platform-based business models reduce the amount of capital (K) that is used
in the production by renting capital intensive assets
b) AirBnB uses consumers apartments, Netflix is renting online storage from
Amazon instead of having own server farms
c) Examples:
- Hotel Industry, Input: Service staff, hotel facilities.
while Marriot need to build new hotels to increase its production, AirBnB can
more flexibly list/unlist apartments of consumers
-
Entertainment Industry, Input: Infrastructure, content, management. Netflix
does not need to build its own data centers but can simply rent data centers
from Amazon AWS and scale its service up and down on demand
Week 7: Costs
Costs in the Short Run
Fixed Cost (FC): cost that does not vary with level of output in the short run (the
cost of all fixed factors of production).
FC = rK0
(K0 is capital at a fixed level of units, r is the rental price per unit)
Variable cost (VC): Cost that varies with the level of output in the short run (the cost
of all variable factors of production)
Total cost (TC): all costs of production: the sum of variable cost and fixed cost.
Visualizing Cost Functions
In this case we start by looking at our production function Q = F(K0, L)
-
The production function tells us how many units of output we can produce
when we vary the variable input factor of labour
At L=4 is our inflection point, where the marginal output starts decreasing.
From here we have diminishing returns to Labour
-
-
The first type of cost listed in the figure is fixed cost. Fixed cost to the fixed
input factor, in this case Capital. The fixed cost does not vary in the short run,
i.e it does not vary with different values of output or variable input factors.
The second cost Variable Cost varies, varies with the amount of Labour that
we use.
The last cost, Total Cost is the sum of the Fixed COst and Variable Cost at
different values of L (or Q)
Visualizing the Costs
-
-
-
As the Fixed Cost is constant in the short run it is a horizontal line at the
value of the fixed cost (nr of units * rental value). In this case it is constant at
30. and not dependent of output, Q, in the short run
Variable Cost Curve
- The variable cost goes through the origin, if we do not produce
anything we don't have any variable cost as it is dependent on L
- The second point is the inflection point, up until this point the slope of
our variable cost curve is decreasing, the marginal cost is decreasing.
- Up until this point we have increasing returns of labour to our output.
After the inflection point the slope of the Variable Cost curve increases,
meaning our marginal cost is increasing. After the inflection point we
have decreasing returns on variable input factors to our output, and
have to use more labour to produce additional units of our output
Total Cost Curve
- To arrive at the total cost curve we add the variable and fixed cost
curves which result in a parallel shift of the variable cost curve of 30
units, i.e our fixed cost. Our Total cost curve then starts where the fixed
cost curve intersects with the y-axis, in this case at 30
Average & Marginal Costs in the Short Run
Average fixed Cost (AFC): fixed cost divided by the quantity of output
Average Variable Cost (AVC): variable cost divided by the quantity of output:
Average Total Cost (ATC): total cost divided by the quantity of output:
Marginal Cost: the change in total cost that results from a 1-unit change in output:
-
the marginal cost in the short run is the same for both the total cost and the
variable cost because the fixed cost does not change. (it is the same in the
long run as well because here all input factors are variable.
The Marginal, Average Total, Average Variable, and Average Fixed
Cost Curves
-
In the top graph we have the Variable Cost, the Fixed Cost which is constant
and added together we get the Total Cost
- On the X-axis we have the Quantity of Output and on the y-axis we have the
cost in Euros/hour
Average Fixed Cost:
- The average fixed cost is shown by the light blue slope in the bottom graph
which is downward sloping. This is because it is constant and thereby
decreases as the Quantity decreases, it moves towards 0 as we produce
more units of output because it will be spread out on more units of output.
Average Total Cost:
- Geometrically we derive the total cost curve by drawing rays that start from
the origin and intersect with the Total Cost Curve. The slope of the ray will
then give us the Average Total Cost at different values of Q.
- Geometrically, average total cost (ATC) / average variable cost (AVC) at any
level of output Q may be interpreted as the slope of a ray to the total / variable
cost curve at Q. Which is the same as the cost divided by the quantity.
Marginal Cost Curve:
- The yellow curve in the bottom graph is the marginal cost curve. The marginal
cost curve is the derivative of the total cost curve. I.e the slope of the total
cost curve at any point of Q.
- This is why we have the minimum value of Marginal Cost at Q1. If we look at
the total cost curve at Q1 we see that this is the inflection point. Up until this
point our cost per unit is decreasing and after the inflection point it is
increasing
- The next interesting point is where the Marginal Cost and Average Total Cost
intersect at level Q3.
- Why do these curves intersect here? Another way to express what the
marginal cost curve is telling us is by looking into the tangent rays to our total
cost. We see that the slope of the ray which is tangent to our total cost at Q3
is equal to the slope of the total cost curve as it is tangent. We therefore know
that the Marginal Cost curve and Average Cost curve at this point Q3 must be
equal and therefore intersect.
Average Variable Cost Curve:
- The average variable cost curve is the navy blue curve in the bottom figure.
- Geometrically deriving the Average variable cost curve is done the same way
as the Average Total Cost Curve, drawing a ray from the origin that intersects
at different points of the Variable Cost Curve. This Slope of the ray is then the
Average Variable Cost at that value of Q
- The Average Variable Cost curve and the Average Total Cost curve are
moving closer together as we increase Q. This is because the the difference
is the Average Fixed Cost which is slowly converging towards 0, decreasing
with higher values of Q
-
Another important thing to notice is that we have different units on the two
y-axis.
- In the top graph we have €/hr on the y-axis
- In the bottom graph we have €/unit of output on the y-axis
- This is the case because we either divide our top curves with Q or take
the derivative of them
Exercise
1. Fixed Cost (FC):
- 5
2. Average Fixed Cost (AVC):
- 5/Q
3. Variable Costs (VC):
- VC = 3Q^2 + Q
4. Average Variable Cost (AVC):
- VC/Q = (3Q^2 + Q) / Q
- AVC = 3Q + 1
5. Average Total Cost:
- TC/Q = (3Q^2 + Q + 5) / Q
- ATC = AVC + AFC = 3Q + 1 + 5/Q
6. Marginal Cost:
- dVC = 6Q + 1
- MC = 6Q + 1
Answer:
Marginal Cost
-
Marginal Cost is the same as the cost of expanding output by 1 unit at a
certain level of Q (or the savings from contracting)
It is by far the most important of the seven cost curves as it allows the firm to
decide whether to expand or contract production to minimize costs
Geometrically, at any level of output, marginal cost may be interpreted as the
slope of the total cost curve at that level of output.
- This is why it can be derived by taking the derivative of the total cost
curve.
- Since the total cost and variable cost curves are parallel, marginal cost
is also equal to the slope of the variable cost curve
Marginal and Average Cost
-
When marginal cost is less than average cost (either ATC or AVC), the
average cost must be decreasing with output.
- We can see this in the blue area for values below Q3 (for AVC it is for
values below Q2). Here the slopes of the Average cost curves turn
upwards sloping
- Ex: if my average grade is 4 and I get a 3 it will decrease
-
When marginal Cost is greater than average cost, average cost must be
increasing with output.
- This is shown by the green area, where the Marginal cost has
exceeded the ATC and so now the ATC starts increasing with higher
values of Q
- Here an additional unit costs more than the average cost of a unit.
The Marginal Cost Curve Intersects with both the ATC and AVC curves at their
minimum
Cost Minimization Algebraically
We look at the case of a production function with 2 inputs (X1, X2). The price of input
1 is P1 the price of input 2 is P2. We assume that the predefined amount of output
Q0 should be produced at minimum cost.
The cost minimization problem that we are facing can be described by minimizing
the cost equation:
-
-
this expression represents our cost. How can we minimize the amount of our
input factors to be able to produce the quantity Q0 at the lowest possible cost.
The prices P1 and P2 are not given so we cant change these, what we are
interested in is to find the best combination of our input factors X1 and X2
What we want to minimize is C, the cost of our function
1. The Cost minimization problem is to some extent similar to the utility
maximization of consumers
- For consumers the budget constraint is given, and we look for the
highest reachable indifference curve
- For cost minimization the isoquant is given, and we look for the lowest
possible isocost line.
2. If the slope of the isocost line is always larger (or smaller) than the slope of
the isoquant, we can have a corner solution (only one input is used)
3. If both inputs are used (interior solution) the lowest reachable isocost line is
tangent to the isoquant
4. At minimal costs:
- The price ratio is equal to the Marginal Ratio Of Technical substitution
That means that the absolute value of the MRTS must be equal to the ratio of the
input prices. Why?
Assume p1/P2 = 2 and MRTS = 1
- if the firm uses 1 less of input 1 it can buy 2 units of input 2
- As the absolute value of the MRTS is 1, it only needs 1 unit of input 2 to
replace the missing unit of input 1. The costs for the second unit of input 2 can
be saved
- This means the firm had not minimized its costs at this point
Exercise:
Cost Minimization
Pay attention to the type of input factors used in the production:
- Perfect Substitutes
- Input factors are substitutable and the firm only uses one input that
allows for cheaper production
- In these case we will have a corner solution
-
Perfect Complements
-
Input factors need to be used in a predefined combination: any other
combination will lead to a waste of one input
The relationship between marginal products and marginal rate of technical
substitution:
In the cost minimum:
Therefore we can also find the cost minimum with the condition:
We can cross-multiply this equation:
The extra output we get from the last euro spent on an input must be the same for all
inputs in this optimal point when we minimize cost
Output Expansion Path
The Relationship Between Optimal Input Choice and Long-Run Costs
Output Expansion Path:
The Locus of tangencies (minimum cost input combinations) traced out by an isocost
line of a given slope as it shifts outwards into the isoquant map for a production
process
-
-
-
Essentially, we look into the case where we have fixed prices for our input
factors and we increase our output, which we see in the isoquants (the higher
the isoquants the higher the output)
Then we trace the optimal cost minimizing combinations of our input factors
and we get to this output expansion path which is denoted by EE in this
case.
We always find the optimal combinations of input factors that minimizes cost
by looking at these points where the isocost line is tangent to our respective
isoquant.
-
-
-
-
We can use this information to construct our Long-Run Total Cost Curve.
Essentially we plot the relevant quantity–cost pairs from the output expansion
path to get to LTC (long run total cost curve)
In the Long-Run, there is no need to distinguish between total, fixed and
variable costs, since all costs are variable.
- We can now change all of our input factors which means that if we are
not producing anything we will not have any costs because we simply
don't use any of our input factors
Again the long run marginal cost curve (LMC) intersects with the long run
average cost curve (LAC) at its minimum. The LMC is the first derivative of
our LTC
The Long Run Total Cost goes through the origin, as all inputs can be
liquidated in the long run
External Reading: Winning the Race With Ever-Smarter
Machines
-
Computers become better and cheaper at tasks that were previously
conducted by humans and previously not thought to be able to be conducted
by computers
- Self-Driving Cars
- Chatbots to service customers
- Vacuum Robots
-
Still, humans can offer their creativity and emotional understanding and
coordinate machines
- This in many cases result in better results than solely solving the task
with computers or solving it by humans
Win the race WITH machines not against them
-
We have introduced the concept of production functions, for which the output
is a function of input factors. Let's assume capital K encompasses
investments in technology/computers and L represents labour
We have also introduced the isocost line:
Where Pk and PL are the prices for capital and labour respectively
a) Production Function
-
Production is becoming relatively more capital and less labor intensive (we
assume investments in technology are captured by K). Relatively more capital
in relation to labor
-
The functional form of the production function is changing
- With less capital and labor, we can produce the same output, increase
in productivity
- Computers start to take over tasks that needed to be conducted by
humans previously.
b) Isocost line:
-
-
PK is decreasing as technological development makes capital intensive
assets cheaper (e.g compare the costs for the same computer 4 years ago
and today, its cheaper)
PL is increasing. Firms need to hire less employees (L decreases) but better
educated ones that are higher paid, w increases
The same products can now be produced at a lower cost:
- Decrease in PK
- Increase in K (in the long run we might probably see a decrease as
computers become more powerful)
- Increase in PL
- Decrease in L
–>If the costs for production would not decrease, firms would not adopt new
technology as firms maximize their profit by minimizing costs
–> If the cost of production is lower, the profits available at a given price will
increase, and producers will produce more
–> With more produced at every price, the supply curve will shift to the right meaning
an increase in supply and a decrease in prices
Derivatives Rules
The Basic Rules For Derivatives
The Power Rule
The Product Rule
The Quotient Rule
The Chain Rule
Week 8 - Perfect Competition
Week 7 Recap
Week 8 Objectives
Perfect Competition Definitions and Conditions
Main Assumption: Profit Maximization
Economists assume that the goal of firms is to maximize economic profit
- Economic Profit: the difference between total revenue and total cost where
total cost includes all costs – both explicit and implicit – associated with
resources used by the firm.
- Opportunity cost is included
- Accounting Profit: Is simply total revenue less all explicit costs incurred.
- Does not subtract implicit cost, no opportunity cost
The 4 Conditions for Perfect Competition
1. Firms sell a Standardized Product
- The product sold by one firm is assumed to be a perfect substitute for
the product sold by any other competitor, products are homogenous.
- This condition is rarely observed, however if we define the market
narrowly enough we can define products as perfect substitutes.
- EX: different sellers of crude oil.
2. Firms Are Price Takers
- The individual firm treats the market price of the product as given.
- Here we assume that firms/producers in the market can not
influence the price which the product is sold
- Later on regarding monopoly we will see that there are market
constellations where firms can influence the price at which
products are traded
3. Free Entry and Exit
- Perfectly mobile factors of production in the long run that allow market
access.
- Every firm that wants to enter the market can do so in the long
run as all input factors are available in the long run
4. Firms and Consumers Have Perfect Information
- Both firms and consumers have full information that allows them to
maximize their profit or net utility respectively.
- For firms: maximization of profit, for consumers: maximization of
net utility
- Perfect information means that actors have the necessary
information to make the best decisions in the market.
- It can be knowing the price of input factors or for consumers, the
prices of products.
- The information access has increased with the internet as there
are tools like price comparison web sites as well as easier
information accessible to firms regarding global suppliers
Exercise: The 4 conditions for perfect competition
1. For basically any product, except for some unprocessed goods, there will be
differences in the features such as price quality etc, which make product not
perfectly substitutable.
2. Through marketing and positioning, firms try and set the price and create a
demand.
3. Many input factors such as knowledge and relations may not always be
possible to acquire from scratch
4. For some products it is not possible to know the utility of the product before
purchase, further there will almost always be asymmetries in information
Answers:
-
For experience goods it is close to impossible to know how much the product
will be worth to us before consumption
Profit Maximization in the Short Run
-
To maximize economic profit, the firm will choose that level of output for which
the difference between total revenue and total cost is largest
-
In the top panel, on the y-axis is total revenue and total cost in euros/wk. On
the x-axis is Quantity produced
The firm is interested in maximizing the distance between the total revenue
curve and the total cost curve.
The total revenue is derived multiplying the fixed price of the good by the
quantity it sells, in this case the price is €18 and so the TR = 18Q
Because the firm cannot influence the price, they are price takers, they have a
fixed price which they sell their goods at. This is why the total revenue curve
is linear.
-
-
-
Looking at the total cost curve we see the commonly occurring shape where
there is first increasing returns of output to its variable input, the slope of the
TC-curve is decreasing, and then decreasing returns to input when the slope
is increasing and the firms need more variable input to produce a quantity of
output. The slope of the curve is first concave and then convex
The TC-curve intersects with the y-axis at 30, indicating that we are in the
short run, as there is a fixed cost of 30
-
-
The total cost curve intersects with the total revenue at Q = 4,7 & 8.7. At
these points the firm make no economic profit, an economic profit of 0. This is
because the revenue is the same as the Total cost.
At Q=7.4 the distance between TC and TR is the largest, which amounts to
12.6 € per week
The Short-run Condition For Profit Maximization
To maximize profits, the firm should produce a level of output for which marginal
revenue is equal to marginal cost on the rising portion of the MC curve.
-
Marginal Revenue is the change in total revenue that occurs as a result of a
1-unit change in sales.
-
Looking at the graphical representation we see that the Marginal Revenue is
simply a horizontal line at P0=18. For every additional unit we sell of the good,
we will earn an additional 18€ of revenue.
The point Q=7.4 is where the Marginal Cost curve intersect with the marginal
revenue curve, which is the profit maximizing quantity of production.
This is dependent on the fact that the Marginal Revenue Curve lies
above the minimum value of the Average Variable Costs Curve
-
-
Provided that marginal revenue is larger than the minimum value of the
average variable cost, the firm should produce a level of output for
which marginal revenue equals marginal cost on the rising portion of
the marginal cost curve
-
Why should we only produce if we are at a price level above Average Variable
Cost? That is because if we produce at a level below average variable cost it
would make more sense to shut down our production.
-
-
Now assume that the market price is €18, why should we produce Q=7.4 and
not Q1 where the price of the good is higher than our marginal cost? If we
produced a good at Q1 we could produce it at a price that is lower than what
we can sell it for on the market, so that means we still can generate an
economic profit.
At Q2 the marginal cost is larger than the price the good can be sold for,
leading to an economic loss.
The Shutdown Condition
Shutdown condition: if the price P0 lies below the minimum of average variable
cost, the firm should shut down in the short run.
the short-run supply curve of the perfectly competitive firm is the rising portion of
the short-run marginal cost curve that lies above the minimum value of the average
variable cost curve
-
On the y-axis we have euros/unit of output, on the x-axis we have Quantity
produced, the output
Here we have no given price, but ask the question: at what price should the
firm start producing output?
The firm should produce output from the point where the marginal cost
exceeds the average variable cost.
As we see in the graph, this may be a point where the Marginal Cost lies
below the Average Total Cost, for example, at a price of 14 the firm should
produce despite the price being below the ATC meaning that they would
produce at a loss, as the revenue cant cover the cost of all the inputs required
for producing at that output.
-
-
-
-
-
This is the case because, at a price above AVC, the firm can cover some of
the cost of the Fixed Cost, which cannot be recovered by shutting down in the
short run.
The distance between the Average Variable Cost and the Average Total
Cost is the Average Fixed Cost. This is why the ATC and the AVC curves
move closer with output.
If the price lies between the AVC and the ATC it still makes sense for the firm
to produce, because the firm is able to cover all of its Variable Cost, and as
well it can cover some of the fixed cost, which can not be recovered in the
short run by shutting down
If the firm would choose not to produce when the price lies between the ATC
and the AVC they would have a larger economic loss than if they chose to
produce as the revenue would cover some of the fixed cost.
The generates economic profit at price levels which lie above the average
total cost curve.
The Short-run Competitive Industry/market Supply
-
-
-
Again, the short run supply curve of the perfectly competitive firm, is the rising
portion of the the Marginal Cost Curve that lies above the minimum value of
the Average Variable Cost curve (AVC)
To derive the industry supply curve we use horizontal summation.
To use horizontal summation we need to solve the supply curves for Q and
then add the amounts that the firms are willing to supply at the different price
levels.
In the example below we can see that from a price level of 2, firm 1 is willing
to supply the good, at P=2 firm 2 is not willing to supply the product.
-
-
Looking at the Industry Supply curve we can see that from P=2 to P=3 the
industry supply curve consists only of firm 1
From P=3, Firm 2 is as well willing to supply the product and from this point
we need to add up the quantities that the 2 firms are willing to supply
at P=3, Firm 1 is willing to supply 3 units, Firm 2 is willing to supply 4 units,
adding these amounts up we get Q=7 which is shown in the Industry Supply
Curve
At P=7, Firm 1 is willing to supply 7 units, Firm 2 is willing to supply 8 units
resulting in an industry supply of 15 Quantities (the horizontal sum)
The Short-Run Competitive Industry Supply
-
-
-
On the left hand side is a figure representing the market and on the right a
focal individual firm is represented, with MC, ATC and AVC
In perfect competition we know that the price of a product is determined in the
market, it is determined where the Demand Curve and Supply Curve
Intersects.
In the figure we can see that the equilibrium price is P*=20, producing a q of
Q*.
In a market of perfect competition we know that the individual firm is a price
taker, meaning that the price is determined on the market and the individual
firm needs to figure out how much it should produce at this given price.
Knowing the Price, we can derive the Marginal Revenue Curve, a horizontal
curve at P=20 in this case.
-
Further, we know that the firm should produce the quantity where the Marginal
Cost curve intersects with the Price curve (Marginal Revenue Curve),
contingent on the point of intersecting being at a price larger than the Average
Variable Cost Curve at this point.
-
Given that we have this information we can calculate how much economic
profit the firm generates at this point
-
-
-
We know that the intersection of P (MR) and MC will be at Q=80. And we
have our ATC curve as well, leading us to be able to determine that our
economic profit will be 8 * 80 (Q) = 640€.
We can calculate this as we see that the ATC curve is at a point of P=12 at
Q=80 leading to costs equaling to 80*12 = 960 (red square). Our revenue is
equal to price multiplied by quantity leading to 20*80 = 1600
Total Revenue – Total Cost = 1600 – 960 = 640€
The individual firm's demand curve is a horizontal line at P=20
- The firm cannot affect the market price, it is a price taker in this
situation of perfect competition
Short-Run Price and Output Determination under Pure Competition
-
Even though the market demand curve is downwards sloping, the demand
curve facing the individual firm is perfectly elastic.
-
Breakeven Point: the point at which price equal to the minimum of average
total cost.
- The lowest point at which the firm will not suffer negative profits in the
short run
-
The firm should produce if the price is higher than the minimum of the
average variable cost (AVC)
In the picture above the price determined is €10 per unit of output which leads
to a situation where the price intersects with the marginal cost at a point which
is higher than the AVC but lower than the ATC, resulting in the firm taking an
economic loss.
Nonetheless the firm should still supply the product as its loss is smaller than
TFC, meaning if the firm did not produce the loss incurred would have been
larger than the loss incurred if they produced at P=10
-
-
Exercise
Solution:
- Short run profit maximization at P = MC, given that P>min AVC. Otherwise the
firm should shut down
-
With P = 12
MC = MR
2Q = 12
Q=6
- P=12 > min AVC = 0
- We can express profits: π = P*Q – AVC*Q – FC
With fixed costs factored out as: π = (P–AVC)Q – FC
-
since the average variable cost is AVC = Q = 6, the firm would earn profits of:
π = (12 – 6)6 – FC = 36 – FC
Thus with fixed costs FC = 36, the firm would earn zero profits
The Efficiency of Short-Run Competitive Equilibrium
-
There are 2 types of efficiencies
Allocative efficiency: all possible gains from exchange are realized
Pareto efficient: It is only possible to make one person better of at the expense of
another.
-
-
There is no possibility for a private exchange at a price other than €10
Consumer would be happy to pay less than €10 for an additional unit of output
but producers need to pay MC = €10 for the next unit and are not interested in
such a transaction
Firms are happy to produce another unit for a price higher than €10, but there
are no consumers left that are willing to pay more than €10 (with 100 000
units on the market). All of the consumers that have a willingness to pay at
P=10 have already purchased the good, and the consumers not willing to pay
of course will not pay a higher price larger than 10 euros
Producer Surplus
-
Now that we have derived both the individual firm's supply curve as well as
the industry/market supply curve we can look at Welfare Measures
We have gone through consumer surplus in previous lectures and will now
look into Producer Surplus
Producer Surplus
-
-
-
-
A competitive market is efficient when it maximizes the net benefits to its
participants
Producer Surplus: The euro amount by which a firm benefits by producing a
profit-maximizing level of output.
We can visualize the producer surplus in two ways.
On the left hand side, we see that the market price is given at P* and that MC
intersects with P* at Q*i.
To establish the producer surplus in this case we look at the AVC at the
equilibrium quantity of Q*I and multiply is by Qi*, then we look at the market
price and multiply it by Q*i. And lastly subtract AVC from the price * Q*i to get:
Producer Surplus = (AVC * Q*i) – (P* * Q*i)
Another way to depict the producer surplus is shown to the right.
We know that variable cost at any level of output is equal to the area under
the Marginal Cost Curve because we can simply add up the marginal cost for
every next unit to get the total sum of our Variable Cost.
We therefore subtract the variable cost from the revenue that is achieved, and
this gives us the producer surplus as well.
-
Producer surplus is the sum of economic profit and fixed cost
Producer surplus is the same as economic profit in the long-run as all costs
are variable
-
If we look into the market perspective, we have depicted here the industry
demand curve and the industry supply curve, which is the sum of the marginal
cost curves (above the lowest point of AVC).
The curves intersect, giving us the equilibrium price and Quantity.
-
-
-
-
We have established how to derive the consumer surplus in a market called
aggregate consumer surplus
very similarly we can derive the aggregate producer surplus
The supply curve tells us, of all the suppliers in the market, for the next unit
that is supplied how much would they at least need to be payed to be willing
to supply this good.
As long as the price is higher/equal to the necessary compensation needed
for firms to supply the good they will.
Therefore the distance between the marginal cost of the next unit and the
price that can be achieved is the producer surplus in an aggregate form.
We can also then define the total welfare which is equal to consumer surplus
+ producer surplus
Total Welfare = Consumer Surplus + Producer Surplus
Terminologies:
Total Welfare = Economic Surplus = Total Surplus
- These terms are used interchangeably
Exercise:
Equilibrium price and quantity:
Pd = 30 – 0.001Q
Ps = 10 + 0.001Q
30 – 0.001Q* = 10 + 0.001Q*
20 = 0.002Q*
Q* = 10 000
P* = 30 – (0.001 * 10 000)
P* = 20
Consumer surplus:
((Pd0 – P*) * Q*) / 2 = ((30 – 20)* 10 000) / 2
CS = 50 000
Producer Surplus:
((P* – Ps0) * Q) / 2 = ((20 – 10) * 10 000) / 2
PS = 50 000
total welfare = Aggregate Consumer Surplus + Aggregate Producer surplus
Total Welfare = 50 000 + 50 00
Total Welfare = 100 000
Answer:
Consumers have a demand curve of:
P = 30 – 0.001Q
Producers have a supply curve of:
P = 10 + 0.001Q
Steps:
1. Find the equilibrium price and quantity by finding where demand and supply
intersect, set demand and supply equal:
2.
-
Calculate the welfare measures:
Consumer Surplus = ½ * 10 000 * (30-20) = 50 000
Producer Surplus = ½ * 10 000 * (30-20) = 50 000
Total Welfare = Consumer Surplus + Producer Surplus = 100 000
Adjustments in the Long Run
Profit Maximization in the Long Run
-
The firm’s objective in the long-run is the same as in the short run_ to earn the
highest economic profit it can.
- There are two things firms can do in the long-run that they cannot do in the
short run:
1. Change fixed inputs which will change the short-run marginal costs and
therefore the short-run supply curve
2. Leave the industry or decide to enter a new industry which will change the
industry supply curve
-
This means we are facing a different situation than in the short run.
Adjustments in the Long-run
-
Positive economic profit creates an incentive for outsiders to enter the
industry
- As additional firms enter the industry, the industry supply curve shifts to the
right
- This adjustment will continue until these two conditions are met:
1. Price reaches the minimum point on the LAC curve.
2. All firms have moved to the capital stock size that gives rise to a short run
average total cost curve that is tangent to the LAC curve at its minimum point
-
-
On the left side of the figure below is our market demand and supply curve,
intersecting at P= 10
On the right side we see the situation of the individual firm.
Because we are looking at a situation of perfect competition, the firm is a price
taker facing a horizontal demand curve. The firm can only adjust its output to
the price it is facing in the market
The individual firm is producing its profit maximizing amount of Q = 200,
where the horizontal demand of P=10 intersects with the SMC1
This price exceed the ATC at Q=200, meaning the firms earn an economic
profit (π = 600)
- ATC at Q = 200: 7 * 200 = 1400
- TR = P* * 200 = 10 * 200 = 2000
- π = 2000 – 1400 = 600
-
As there is potential to generate economic profit in this market, other firms are
attracted to enter the market which we will now look at
-
We can see that when other firms enter the market we have a rightward shift
of the market supply curve.
The new market supply curve results in a decrease in the equilibrium price
from P* = 10 to P*1 = 8.50
The firm is still a price taker in the market of perfect competition meaning at
the lower price of P*1 = 8.50 we will intersect the short run marginal cost
curve at a different position.
The decrease in the equilibrium price leads to an adjustment of the output
level for the existing firm as the new price intersects with the SMC1 at a
different level of Q. As we can see it will produce a quantity of Q = 190
-
-
-
-
Still, this price exceeds the ATC1 at Q=190, leading the existing firm to earn
an economic profit of π=304 (which is depicted by the gold area) and keeping
the market attractive for entrants (as they are earning an economic profit).
This is the first adjustment taking place as we see the supply curve shifting to
the left but as we are in the long run there is another adjustment happening.
-
-
-
-
-
At lower output level the existing firm is interested in reducing its quantity of
fixed inputs (this is possible in the long-run, because fixed inputs become
variable in the long run)
The adjustment lead to a shift in ATC and SMC. The existing firm contracts its
output but can earn more profit (π = 378) by adjusting its capital stock. The
market remains attractive for entrants
The contracting of the capital stock leads to a slight shift of the market supply,
with the right shift from entering firms dominates the left shift originating in the
adjustment of fixed inputs
- Despite the contraction of output from the firms that have been in the
market, the right shift is dominating the left shift resulting in a neto right
shift
This adjustment continues until firms in the market do not earn economic
profit anymore:
- Price has reached the minimum on the LAC curve
- Firms have adjusted their fixed input factors leading to an ATC curve
tangent to the LAC curve at its minimum
Now there is no incentive for new firms to enter the market anymore
The Invisible Hand
Why are competitive markets attractive from the perspective of society as a whole?
- Price equal to Marginal Cost
- The last unit of output consumed is worth exactly the same to the
buyer as the resources required to produce it.
- Price is equal to the minimum point on the long-run average cost curve.
- There is no less costly way of producing the product.
- When firms have adjusted their capital stock there is no less costly way
of producing the focal good
- All producers earn only a normal rate of profit
- The public pays not a cent more than what it costs the firms to serve
them
External Reading: How Competition is Driving AI’s Rapid
Adoption
-
Artificial Intelligence (AI) is a major driver of economic growth
-
AI adoption (the share of firms that use AI) and absorption (the degree to
which firms can extract value from AI) could be more rapid than adoption of
previous technologies:
1. Breadth of ways in which AI can be used - can be used in a lot of different
ways
2. Promising large returns for ‘front runners’ - companies that adopt the
technology early on can collect larger returns than followers
-
Nonetheless, it takes time until investment in AI yields benefits
Exercise:
a) Firms can reduce costs with the help of AI by making the production more
efficient and earn short-run economic profits. The different cost structure also
influences the firm’s marginal cost curve, making it cheaper to produce
additional output units. Taking the price as given this will mean that the firm
will increase its output in the short run (MC = P). As revenue is a function of
the quantity and price (which the firm cannot influence in perfect competition)
the short run revenue will also increase as a consequence of the increase in
produced quantity. In the long run, other firms will adjust their production
(adopt AI) or other firms will enter the market driving the economic profit to 0.
Given that we have perfect information, all firms will be able to implement AI
and copy their competitors
b) If AI is reducing the costs in a market, new companies can suddenly become
able to enter the market. This is especially the case if these companies have
capabilities in AI that existing firms in the market do not have
c) (self-driving) cars are an example. While the car industry was for a long time
dominated by large car manufacturers, we now see Technology companies
such as google and Tesla entering the market. This is driven by both
advanced capabilities in how these firms can use technology (e.g AI) but also
the fact that the market for self-driving cars is different from the market for
traditional cars
Monopoly
What is a Monopoly?
Monopoly: a market structure in which a single seller of a product with no close
substitutes serves the market.
- A monopolist has significant control over the price it charges
- In contrast, a competitive firm is a price taker and therefore can only control
the amount it produces.
5 Sources of Monopoly
1. Exclusive control over Important Inputs
- Exclusive control over a crucial input factor will keep other firms from entering
the market. Leading to a tendency of monopoly
2. Economies of Scale
- When the long-run average cost curve is downward sloping, the least costly
way to serve the market is to concentrate production to one firm (natural
monopoly)
- The most efficient way is to be served by 1 firm as the costs here are
the smallest
3. Patents
- Typically confers the right to exclusive benefit from all exchanges involving the
invention to which the patent applies
- Also an incentive for firms to innovate
4. Network Economies
- On the demand side, a product becomes more valuable as greater numbers
of consumers use it
- A typical example is social media, the more people using a platform the
more valuable the platform becomes as it means the consumer can
interact with more friends.
5. Government Licenses or Franchises
- A typical example is public transport, where firms only license out the
market to one firm, excluding all other firms
The Profit-Maximizing Monopolist
The monopolist's goal is to maximize economic profit
- In the short run this means choosing the level of output for which the
difference between total revenue and short-run total cost is the greatest
Importantly, the monopolist is not a price taker!
- The monopolist’s output quantity determines the price on the downward
sloping demand curve.
- Contingent on how much output the monopolist chooses to produce,
this will determine how much quantity is available on the market
because the monopolist is the only supplier on the market, and
therefore this will automatically determine the price of which the
product is being traded on the market
- Therefore, the monopolist’s total revenue TR is not a linear function of Q with
fixed P but varies with both Q and P.
-
For a perfectly competitive firm P does not vary but is always at P* and the
firms act as price takers
Revenue for Monopolist
As price falls, total revenue for the monopolist does not rise linearly with output.
- Instead, it reaches a maximum value at the quantity corresponding to the
midpoint of the demand curve, after which revenue begins to fall
- Total revenue reaches its maximum value when the price elasticity of demand
is unity (1).
Demand, Total Revenue and Elasticity
-
We know that the total revenue is the highest at unit elasticity -1, to the left of
unit elasticity we have higher price elasticity of demand meaning a decrease
in price is beneficial, to the right of unit elasticity we have lower elasticity than
unit elasticity meaning an increase in the price results in higher revenue.
-
As the monopolist is the only actor serving the market, the total expenditure
represents the monopolist's total revenue in the market
The revenue is highest at unit elasticity, -1, which is at Q=200, at the mid point
of the demand curve
Total Cost, Revenue and Profit Curves for a Monopolist
-
Maximum profit is achieved when Total Revenue and Total Cost are parallel
(have the same slope/derivative)
Optimality Condition: Marginal Revenue (MR) = Marginal Cost (MC)
-
-
-
The revenue generated from the next unit of output is equal to the cost of
producing it.
In the top panel we can see that if we would move further to the right than
Q=175, we would increase marginal cost, but we have a decrease in marginal
revenue. We would move to a point where it would cost more to produce an
additional unit than we would get in marginal revenue
To the left the marginal cost is lower than the marginal revenue meaning it is
preferable to increase the quantity as the marginal revenue is larger than the
marginal cost
Only at the point of Q=175 where the marginal revenue is equal to marginal
cost can we maximize revenue
The profit Maximizing Monopolist
optimality condition for a monopolist:
A monopolist maximizes profit by choosing the level of output Q where the marginal
revenue equals marginal cost.
-
Marginal revenue can also be expressed as the first derivative of total
revenue:
-
Provided that marginal revenue intersects marginal cost from above. Marginal
revenue
- Marginal cost up until this point needs to be smaller than marginal
revenue, meaning, up until the curves intersect, it would cost less to
produce the product than the revenue from the unit
- If it could be the other way around, the marginal cost would be higher
than the marginal revenue which would not be in the firms interest as
this would lead to an economic loss
-
The general formula for the demand curve is:
-
The corresponding marginal revenue curve is:
-
The same curve but with twice the slope
Marginal Revenue and Position on the Demand Curve
-
-
-
-
What we see in the figure above is the marginal revenue and the position on
the demand curve
What we can look into is what happens when the monopolist decides to
produce different levels of output Q
For example, in the first case, the monopolist goes from producing Q0 to
Q0+∆Q. And we see that we move from the higher red circle to the lower one.
Now we are trading the product at a lower price, the loss in revenue from the
decrease in price is depicted by the area A
The gain in revenue is depicted by the area B which we see is larger than A,
meaning the increase in quantity sold at the lower price is larger than the loss
in revenue from the price decrease
This will be the case for all prices that are above our unit elasticity point (-1),
MR = 0. When we decrease price above the unit elasticity point we will
increase our revenue and this is why the marginal revenue is larger than 0.
If we are at a point lower than M, we have a marginal revenue smaller than 0,
meaning an increase in output would result in lower revenue.
This can be seen in the green circles, where the loss from increase in quantity
(or decrease in price), area C, is larger than than the gain, area D
Marginal Revenue can be seen as:
- The gain in revenue from new sales (increase in Q)
- Minus the loss in revenue from selling the previous output level at the new,
lower price (decrease in P)
The demand Curve and Corresponding Marginal Revenue Curve
-
above we have depicted our demand curve and our marginal revenue curve.
The marginal revenue becomes 0 at the point of unit elasticity
Demand:
P = 80 – 0.2Q
Marginal Revenue:
P = 80 – 0.4Q
-
At the level of Q where we have unit elasticity, our marginal revenue is 0. That
means that this is the point where the MR intersects with the x-axis, the axis
where we depict units of output, Q
Exercise
Solution:
Demand: P = 100 – 2Q
Total Cost: TC = 640 + 20Q
a) Find the MC (the first derivative of total cost):
MC = 20
Find the Marginal Revenue Curve, which we have learned is the same as the
demand curve but with 2x the slope:
P = 100 – 4Q
For the maximum profit level we need to set marginal revenue equal to marginal
cost. MR = MC:
20 = 100 – 4Q
Q* = 20
b) To find the price we put Q* in the market demand curve:
P* = 100 – 2Q
P* = 100 – 40
P* = 60
c) Calculate the monopolist's total revenue, total cost and profit in the short run
Total Cost: TC = FC + (20 * Q*).
TC(20) = 640 + 20 * 20 = 1040
Total Revenue: optimal quantity * optimal price = P* x Q*
TR = 20 * 60 = 1200
Profit: TR – TC:
TR – TC = 1200 – 1040 = 160
-
-
Below we see the graphical representation
We find the optimal output level (Q) by looking at what level of output Q does
the Marginal Revenue Curve intersect with the Marginal Cost curve, which is
at Q=20
Inserting Q=20 to our demand curve we can see what price we will reach
which in this case is P=60
Also depicted is the Average Total Cost Curve, enabling us to derive the total
profit
π = (60 – 52) * 20 = 160 (which is what we calculated above by
subtracting the TC to the TR)
Week 8 - Externalities and Public Goods (and continuation
Monopoly)
Shutdown Condition for Monopolist
The Profit-Maximizing Monopolist
Shutdown condition for a monopolist tells us that production should cease
whenever average revenue is less than average variable cost at every level of output
- TR = AR*Q, VC = AVC*Q. This tells us that the monopolist should shut down
when the VC is higher than TR at every level of output the monopolist should
not produce
That is essentially equal to when there is no point where the demand curve lies
above the average variable costs.
- The demand curve is essentially giving us the price of the monopolist.
- Contingent on how much the monopolist chooses to produce, we can read the
subsequent price on the demand curve
- For the perfectly competitive company firms are simply price takes
● MC = MR, is a necessary but not sufficient condition for profit maximization
● Below we see a graph of a monopolist who should shut down in the short run
● We have the demand curve, the Marginal Revenue Curve and the Short-run
Marginal Cost Curve and the Average Variable Cost Curve
● The Demand Curve (price) is always lower than the average variable costs.
The monopolist should shut down
- The demand is not high enough to justify production in this market.
● Regarding the necessary condition MR = MC, we see this in the graph where
these curves intersect at the first point.
- MR curve intersects the MC curve from below, meaning the monopolist
is better off at points close by on the demand curve
- If the monopolist chose to increase production from this point of
intersection, the monopolist would move to a point where MR is
exceeding SMC, meaning the monopolist would be better of to
increase production.
- But the monopolist would be even better of decreasing production at
this point because he would reduce the costs more than the revenue
that is being lost.
- We therefore know that this intersection cannot be the optimal point of
production
●
MR is also equal to MC at the Q1. Here MR intersects MC from above, which
is necessary but not sufficient condition for profit maximization
- This is because we have seen that the Demand Curve (the price) is
always lower than Average Variable Cost in this case, meaning the
monopolist should shut down.
- Importantly, the second intersection, where MR intersects SMC from
above, is what we are looking for when profit maximizing for a
monopolist. But it is not sufficient as the Demand curve (price) is
always lower than AVC so it doesn’t make sense for the monopolist to
produce
A Monopolist has no supply Curve
-
The Monopolist is a price maker.
- In contrast to firms in perfect competition who are price takers
-
When demand shifts rightward, elasticity at a given price may either increase
or decrease.
- So there can be no unique correspondence between the price a
monopolist charges and the amount the monopolist chooses to
produce
- Instead of having a supply curve, the monopolist has a supply rule
Monopolist has a supply rule, which is to produce where marginal revenue
equals marginal cost
Perfect Competition vs Monopoly
Perfect Competition
Suppliers maximize profit by:
- Necessary Condition
MC = P
with
P > min AVC
-
Demand Curve is perfectly elastic
Suppliers are price takers
Efficient allocation of resources
- No possibilities for additional gains from exchange
Monopoly
Monopolist maximizes profit by:
- Necessary Condition:
MC = MR
with
AR > min AVC
AR = Demand Curve, which means the demand curve needs to be above the min
AVC
-
Monopolist is a price maker - he determines the price based on the quantity
he produces
Inefficient allocation of resources as prices charged are higher than marginal
cost
Answer:
Deman Curve:
P = 100 - 1/10Q
Marginal Cost of Production:
MC = 1/15Q
a) Perfect Competition - Suppliers are price takers
Set Demand equal to marginal cost (that represents the supply curve)
b) Monopoly - monopolist is a price maker
Find the marginal revenue curve:
- can be derived by simply multiplying the slope with 2 or multiplying the
demand curve with Q, resulting in the total revenue curve and taking the first
derivative of TR resulting in MR which is the same as the demand curve with
2x the slope
Find the marginal revenue curve:
MR = 100 – 1/5Q
set the marginal revenue curve equal to the marginal cost curve:
For perfect competition:
- As the minimum of the AVC is 0 the supply curve in a market of perfect
competition is the Marginal Cost Curve, which intersects at Q = 600 and P=40
For the Monopolist
- We look at where the Marginal Revenue Curve intersects with the Marginal
Cost Curve and plugg that quantity into the demand curve leading to Q=375
and P=62.5
C) Surplus and Total Welfare
Perfect Competition
- the area above the price and below the demand curve is the consumer
surplus
- The Producer surplus is the area below the price and above the industry
supply curve (marginal cost curve above AVC)
Monopolist
-
-
The consumer surplus is derived the same way, it is the triangle below the
demand curve and above the price.
The Producer Surplus is derived differently as it is the purple area
The triangle called dead weight loss is the welfare that is lost when the
monopolist produces instead of a perfectly competitive market
c) Welfare Calculations
Welfare Calculations Perfect Competition
Welfare Calculations Monopoly
-
-
To Calculate the Producer Surplus for the Monopolist we divide up the are into
2 areas a triangle and a square
First we calculate the triangle, which is the are above the MC curve and
Below the price where MC and MR interset, in this case 25.
- Triangle (25*375) / 2
Then we calculated the remaining rectangle which is equal to the area above
the Price where MC = MR and below the Price equilibrium, as well as
between the y-axis and the quantity supplied by the monopolist (375)
-
-
-
Rectangle = (62.5 – 25) * 375
In the case of a monopoly (compared to perfect competition) surplus is shifted
from the consumer to the monopolist. (we can see this as the PS increases
and the CS decreases.
Nevertheless, when comparing the total welfare, we see that monopoly is
decreasing total welfare by 4 218.75
We call this loss in welfare Deadweight loss from Monopoly
The Efficiency Loss from Monopoly
Deadweight loss from monopoly: the loss of efficiency due to the presence of a
monopoly
A competitive market is efficient when it maximizes the net benefits to its participants
(total welfare)
The deadweight loss from the monopoly is the result of a failure of the monopolist to
price discriminate perfectly. If the monopolist could price discriminate perfectly
essentially there would only be producer surplus and no consumer surplus and the
total welfare would be equal to producer surplus which would be equal to the total
welfare in the situation of a perfectly competitive market
Public Policy & Monopolies
Public Policy Towards Natural Monopoly
-
Public policies towards natural monopolies can differ quite a bit and there is
different approaches in terms of how to deal with natural monopolies
●
●
●
●
●
State Ownership and Management
State Regulation of Private Monopolies
Exclusive Contracting for Natural Monopoly
Vigorous Enforcement of Antitrust Laws
A Laissez-faire Policy towards Natural Monopoly
None of these approaches completely eliminates the difficulties that aries
when a single seller serves the market.
[book p.393]
Dynamic Efficiency of Monopoly
What is the alternative (counterfactual) to the current situation, the monopoly?
- Not clear that a society which exploits all current gains from exchange, but
fails to invest in future product development, is efficient.
- For perfect competition all economic profits are exhausted meaning
there is less money for R&D
- The ability to have a monopoly creates possibility to reap the benefits
of investing in R&D and innovation which serves as an incentive to
invest in innovation
- ‘Rich’ Firms (possibly monopolys) also have more money to invest in
innovation which may lead to faster innovation
- Summary: Less Incentive & less funds
-
Short-term gain may result in a long-term welfare loss due to the lack of new
products or cost-saving production techniques
Externalities and Public Goods
Externality
An externality is an economic term referring to a cost or benefit incurred or received
by a third party who has no control over how that cost or benefit was created
Externalities
-
Negative externality: an activity that imposes external costs on others
- A smoker disturbs other individuals around and negatively affects their
health.
- Driving a car causes noise and air pollution which is imposed on third
parties
- A coal power plant emits CO2 which affects the climate
-
Positive externality: an activity that creates external benefits for others.
- NASA invented Teflon for space travel which is now being used as
coating for pans
- The construction of the new metro stations in Copenhagen raises the
prices for real estate close by - which is ofcourse positive for thos who
own the apartments, negative for those who want to purchase though
- When fixed line telephony was rolled out in the US in the early 20th
century another adopter meant that you could call more people (direct
network externality)
- If another person purchased an adopter it meant you could call
one more person
- Another PlayStation 4 user means that a PS4 game producer can
potentially sell games to more consumers (indirect network
externality)
Externalities and Market Efficiency
-
Cost benefit analysis says do activity x if
B(x) > C(x)
here B(x) and C(x) measure private benefit and cost
-
Efficiency requires to do activity x if
SB(x) Z SC(x)
Where SB(x) and SC(x) measure Social benefit and cost.
-
In the absence of externalities, private and social benefit are identical
- In the absence of externalities, the 2 equations above are identical.
-
In this case suppliers internalize all social costs and benefits and make
efficient decision regarding their output
In the presence of externalities this is not the case anymore as the externalities
occur with somebody else and are not taken into consideration when making a
decision
Example: Environmental Protection
When a firm decides how much to invest in environment protection, the managers
compare the cost of reducing emissions with the (private) benefits of emissions
reduction.
- But there are also other firms/consumers that benefit from such an investment
- This additional benefit is not internalized by the profit maximizing firm
- Therefore a free competitive market leada here to an underinvestment in
environmental protection
- The firm should have invested more in environmental protection than it
did because it is only looking at private benefit and cost and not
internalizing social benefits and costs
This leads to an inefficient allocation of resources
Social Optimal Level
It is efficient to increase the level of activity as long as
MSB (Marginal Social Benefit) >
MSC (Marginal Social Cost)
Where demand equals supply in perfect competition, we have marginal private cost
equal marginal private benefit
- If there are externalities in the market, this is not an efficient way to set
quantities and prices
Example:
-
Below are market demand and supply curves for the market of electricity
given.
-
The equilibrium, decided as usual, is at Q = 1000 units of electricity at P=50
-
Scientist estimate that production Q causes marginal environmental damage
equivalent to €Q/40 = 1/40Q €
If we take that into account we would have to recalculate Marginal Cost to get
to the Marginal Social Cost which equals the supply curve.
Calculate the MSC/supply curve taking into account the social costs:
-
-
Taking social costs into account results in an upward rotation of our supply
curve which is denoted MSC
This new supply curve intersects with price at a lower level of Q and higher
level of P. Leading to less quantity produced at a higher price, as the social
costs are taken into account
Internalizing Externalities
-
-
Extremely important problem in today's society, an example is pollution, where
the private costs and social costs differ quite substantially leading to inefficient
outcomes if social costs are taken into account.
We see how important it is to figure out economic mechanisms to make sure
social costs are internalized
How to internalize Costs and Benefits from externalities
1.
2.
3.
4.
5.
-
Contracts (Coase Theorem)
Taxes
Mergers and Acquisitions
Creating Markets for Externalities
Government Intervention and Regulation
All the above are mechanisms to internalize externalities (social costs
and benefits)
Internalizing Externalities with Contracts
-
Closely related to the Coase Theorem
1. Contracts - The Coase Theorem
The Coase Theorem:
When the parties affected by externalities can negotiate costlessly with one
another and property rights are well defined, an efficient outcome results no
matter how the law assigns responsibility for damages
- Efficient in that the outcome is efficient no matter how the law assigns
responsibility and in that no government intervention is needed
● Efficient laws and social institutions are the ones that place the burden of
adjustment to externalities on those who can accomplish the adjustment at
least cost
Coase Theorem and Positive Externalities
-
The coase theorem applies not only to negative externalities but also to
positive ones.
For example, a beekeeper and an apple grower operating on adjacent
properties that confer positive externalities on each other
These positive externalities if ignored will result in sub-optimally small levels
of both apple and honey production
Inefficiencies result only if it is costly or impractical to negotiate agreements to
correct them
If it is not costly to negotiate the apple grower and beekeeper will find a way to
maximize profits of both involved parties, leading to the most efficient
outcome.
Coase Theorem and Property Rights
● The Coase Theorem shows that market efficiency will result if there are
clearly defined property rights and negotiation is costless
● No free-market economy can function successfully without laws that govern
the use of private property.
-
We do need property rights to qualify who is responsible in the case of
twists, and these rights need to be enforced.
Transaction Costs Limiting the Coase Theorem
-
Transaction costs can limit the coase theorem quite drastically and so the
mechanism of contracts is used to internalize these externalities
-
The larger the number of affected parties the more difficult and costly are
negotiations
- Takes a lot of time and effort
-
Private negotiations might be impossible as the affected do not know each
other
- An example is people who like to drive very fast on highways and so
impose negative externalities on others, as the different drivers do not
know each other it is very hard for them to negotiate a price that the
safe drivers should be compensated for the negative externalities
imposed by the reckless driver. The negotiation would as well have to
take place among a large number of parties making it to costly
Asymmetric information regarding the benefit and/or costs can lead to
inefficient allocations
- Often it is not know what the social benefits and costs are
- Example the fast driver, he would have an incentive to say that his
benefit from driving fast is not very high so that he is not required to
pay that much for the right to drive fast. While the other people would
have an incentive to say that the negative social costs imposed on
them are very high as the risk is very high so that they can be
rewarded high compensation
- If we are not able to find an objective measure for the social costs and
benefits then we might also end up with an inefficient allocation
-
-
Contracts might be incomplete – it is too costly to codify all possible external
effects that can occur
Exercise: Internalizing Externalities with Contracts
-
-
Commonly there are too many parties (other guests) involved in a cafe for
which individual negotiations would need to be held
- Alot of negotiations and transaction costs
The affected could be identified but there is a lot of fluctuation of guests in a
cafe
Smokers would have an interest to overstate their benefits of smoking and
other guests to overstate the costs of the negative externality
- It is hard to objectively decide the social benefits and costs.
Internalizing Externalities with Taxes
2. Taxing Externalities
If A carries out an activity that imposes a cost on B, then taxing A by the amount of
that cost will provide him with the proper incentive to consider the externality in his
production decisions.
● Efficiency here depends on details of respective externality [see example with
doctor and confectioner p.566]
● If negotiation is costless, taxing will always lead to an efficient outcome
Internalizing Externalities through Mergers & Acquisitions
3. Mergers & Acquisitions (M&As)
If firm A causes negative externalities that affect firm B, then the externalities can be
internalized by the two firms merging or firm B acquiring firm A
● Externalities are a main motivation for M&As. Additional profit that is
generated by internalizing externalities is also called synergy.
- Unlock positive externalities or deal with negative externalities
● M&As also work when contracts cannot be used as a measure to internalize
externalities
● But M&As might be problematic as they limit competition and might be
regulated by policy makers
○ This relates to efficiency of markets, if regulators believe that a merger
will result in a monopoly market they might see the necessity to
intervene. In that case M&A would not be a possible solution to
internalize externalities
Internalizing Externalities through Creation of Markets
-
Another means to internalize externalities is through the creation of markets
4. Creating Markets for Externalities
We can interpret the issue of externalities as an issue of a missing market for
externalities.
One solution could be to create a market for externalities, e.g the right to emit CO2
Example:
- X* is the efficient amount of CO2 emissions
- The policy maker creates X* certificates that provide the right to emit CO2
(well-defined property rights, who is allowed to emit CO2 in the market)
- With the help of an auction these emission rights are sold off. The auctioneer
calls out a price. All firms submit simultaneously how many certificates they
want to buy for the price the auctioneer is calling out
- At the price where all emission rights are auctioned off, the certificates are
being traded
This process represents an efficient allocation:
● There will be exactly the optimal amount of emission, X*
● The firms that can avoid emissions more easily, i.e in a cheaper manner, will
reduce their emission more as it is cheaper than to buy emission rights
● In contrast the firms that have the highest costs to avoid emissions will buy
emission certificates
● This means the emission reduction is implemented at the lowest possible cost
● Importantly in this case, the firms self-select into which means is the best way
for them to reduce CO2, is it cheaper for them to avoid emission or is it better
to purchase the emission rights because it is too costly to reduce the
emission. This is why we reach an efficient solution where the emission
reduction is implemented at the lowest possible cost.
See EU Emissions Trading System ( EU ETS)
Internalizing Externalities through Government Regulation
5. Government Regulation
-
Probably the most common method to regulate externalities are laws and
regulations.
This Method has some disadvantages:
- The regulator needs to have a good idea about the costs and benefits of the
involved parties to be able to come up with proper regulation
- The regulation forces everyone to behave in the same way despite their very
different cost structures, other methods may lead to more efficient allocation,
here all parties are forced to behave in the same manner. If another method
were to be used, a more efficient allocation could possibly be achieved
- Taxes and Markets for Externalities are often more efficient as they allow for
room of making efficient decisions for the involved parties, in contrast to the
one size fits all solution of regulations and laws
Teacher: ‘we haven’t gone into much depth of the solutions for dealing with
externalities but it is important to know what possible solutions exist, to deal
with externalities that present a challenge for today's societies’
Public Goods
-
Can be interpreted as a special case of externalities
Public Goods
Public Goods are goods for which no rivalry in consumption exists.
- In extreme cases this means if a consumer A in a group of individuals
consumes the good it is also available for consumption to all other individuals
without decreasing the benefits or causing additional costs of consumption for
A.
Examples:
- National Defense
- Benefits all consumers at the same time
- Infrastructure
- TV and radio programs
- Software, Movies, Streaming Services
● Most public goods are not ‘pure’ public good as there are additional costs to
consumption with an increasing number of consumers:
○ Traffic jams on roads
○ Longer loading times on websites
○ Not pure public goods in the sense that there is some rivalry at some
point of mass consumption
● It is not important for public goods that other consumers cannot be excluded
from consumption, this is technically often possible (highway tolls, patents,
encryption of TV signal)
○ Exclusion is not what determines if a good is a public good
● The important aspect is that there is no rivalry in consumption
● Public goods can be interpreted as a special type of external effect: if one
consumer consumes an additional unit of the public good then all other
consumers can consume this unit as well
○ This could be thought of as, if a consumer makes the decision to
consume the public good, he at the same time provides this opportunity
of consumption for everyone else for free, This is Where the problem
of public goods come from
Market Failure due to Public Good Provision
we can have market failure due to public good provision
In the provision of public goods we often face an inefficient allocation:
● Every consumer hopes that another consumer provides the public good to
use it for free.
○ All of us are hoping that one consumer makes the decision to provide a
specific public good so that we all can use it for free. Why should we be
the one to pay for the public good and provide it to everyone
● Often this leads to no provision of the public good
-
That is what we call a Free-rider problem
Which is more severe when:
- Involved parties do not know each others willingness to pay for the public
good
- More parties are involved
- The parties do not interact regularly
-
-
If parties would know each others willingness to pay, and were able to interact
and negotiate they could potentially come up with a way to jointly provide the
public good and all benefit from it while all contribute to it.
But again if there are many parties involved then this type of negotiation
becomes very difficult
How to overcome the Free-Rider Problem
1. Private Negotiations
- With few involved parties
- Well known willingness to pay
2. Private Provision
- A private provider can provide the good given the provider can charge
the consumers for using the good (i.e highway tolls when private
provider build and maintain the road)
3. Public Provision
- The government provides the public good (e.g infrastructure) paid with
taxes that are being redistributed
- That is related to the question we have discussed earlier. When should
the public good then be provided? should be contingent on the
consumer surplus, that the regulators estimate. What is the aggregate
willingness to pay of the consumers that would make use of the public
good and only if the cost of provision is lower than this aggregated
benefit then this public good should be provided
Network Externalities & Exercise: External Reading
Reading: 6 Reasons Platforms Fail
Platform managers fail to manage the growth and evolution of digital platforms
inadequately because of:
1. Failure to optimize ‘openness’
- To what extent do you give different types of stakeholders access to
the platform.
- Example IOS: to what extent do developers get access to the platform
and are able to make use of the platform
2. Failure to engage developers
- You need to find a way to make it attractive for third parties to develop
apps or other services and complementary products on your platform.
3. Failure to share the surplus
- The platform need to share the surplus in a way that makes it attractive
for all parties, example an auction site which only benefits customers
will not engage any producers
4. Failure to launch the right side
- Commonly we have 2 sided platforms like ebay with sellers and
buyers. Contingent on how a platform is growing we need to
understand which side needs support and attraction.
5. Failure to put critical mass ahead of money
- It is important to first focus on attracting a critical mass before focusing
on extracting money as the platform otherwise will stall.
6. Failure of Imagination
- Establish players which fail to see the value of platforms and run their
company more traditionally leading to them losing out on value and
being outcompeted
Positive Network Externalities
Direct Network Externalities:
- An increase in the number of users leads to an increase in the consumer’s
utility for the good. E. g:
- Fax and telephone connections
- Social Networks, the larger number of people on social networks the
larger number of people to communicate with, the larger value
Indirect Network Externalities:
- An increase in the number of users causes an increase in the utility for
providers of complementary goods which in turn cause an increase in the
utility for the focal good. E.g:
- Video Consoles and games
- becomes more attractive to provide games for a console if there
are more consumers using the console and then then console
comes become more attractive
- Smartphone operating systems and apps
- Positive feedback loop
Negative Network Externalities
Network Externalities can also be negative.
Negative Direct Network Externalities:
- More console game produces compete against each other, from a game
producer standpoint
-
More users of a telephone service causes waiting time to reach the customer
support
Negative Indirect Network:
When a network becomes more popular, unwanted complementary products can
enter the market:
- Computer viruses: the more people using an operating system the more
attractive it becomes more attractive to produce viruses on the platform
- More advertising on social media platform
Exercise - 6 Reasons Platforms Fail
Answer
a) The marginal cost of adding another user is zero. Instagram is also not
directly charging consumers to use the platform but indirectly by selling the
opportunity to show ads to users.
- The supply curve would be horizontal at a price equal to 0. As
Instagram is willing to add another user for free. The marginal cost is 0
in the short run
b) The network effects have no influence on the supply curve but does have an
influence on the demand. As the utility of the platform increases with the
number of users the demand curve shifts outwards. Leading to an increase in
the quantity demanded – the number of users that want to use the platform
- Here we have demand side network externalities that increase the
utility of the consumers meaning it will increase the willingness to pay
by the consumers and it will shift the demand curve outwards, leading
to an increase in quantity demanded.
c) Indirect Network Externalities: The more users are present on the platform the
more interesting it becomes for advertisers to serve ass on the platform. The
more advertises are on the platform:
- The more interesting ads consumers might see
- The more ads that annoy users will be displayed
Both Positive and negative indirect network effects are present in this example