MGEA02H3 F All Sections 20249:Introduction to Microeconomics: A Mathematical Approach
Notes
Topic 1:
Opportunity cost is something you give up to achieve something.
OC = explicit cost (monetary) + implicit cost (non-monetary)
Cost-benefit decisions:
- Calculate total benefit and total cost properly
- Total benefit > Total cost
- The difference between total benefit and total cost should be the largest
The production possibilities frontier (PPF) shows a set of feasible output possibilities with a fixed
amount of resources.
- Points above the PPF are unattainable with current resources and tech
- Points on or below the PPF are attainable
- Points on the PPF are efficient
- Points below the PPF are inefficient
- PPF is described by an equation similar to 𝑦 = . . . . . ..
Constant opportunity cost:
𝑦𝑦
𝑦𝑦
1
𝑦𝑦𝑦 =
𝑦𝑦𝑦
𝑦𝑦𝑦 = −
𝑦2 𝑦
𝑦𝑦𝑦 is increasing if 𝑦𝑦2 < 0
Shifts of the PPF:
- Price will never shift the PPF curve, except for substitute products (eg: coke and Pepsi) or
complement products (eg: cereal and milk)
- Shift to the right is an improvement
- Shift to the left is a negative development
Value/Utility functions are mathematical representations that assign numerical values to satisfaction
levels derived from consuming different combinations of goods.
Optimal production bundle:
1. Sub ‘y’ (PPF curve equation) into ‘V’ (Value/Utility function)
2. Simplify
𝑦𝑦
3. Find 𝑦𝑦
4. Equate to 0
5. Solve for ‘x’
6. If required to solve for ‘y’, do so by inserting the ‘x’ value in PPF equation
Topic 2:
A market is a set of institutional arrangements that bring buyers and sellers together to negotiate the
terms of exchange of a good (tangible) or service (intangible).
The demand curve displays the behavior of the buyers and it has a negative slope due to diminishing
marginal utility. We usually assume that our marginal utility (satisfaction) decreases as we add
incremental consumption units. The curve shows the maximum price a consumer will be willing to pay
for a certain quantity.
The supply curve displays the behavior of sellers as it shows the minimum price suppliers are willing to
charge for any particular quantity. The minimum price is the marginal cost (cost of production) and an
increase in the marginal cost leads to an increase in price hence the curve has a positive slope. In the
long run, supply is less steeply sloped and often it is horizontal.
Equilibrium occurs when the behavior of the buyers and sellers is consistent (the supply and demand
curve intersect). Price brings these behaviors into equilibrium.
Perfectly competitive market:
1.
2.
3.
4.
Information is transparent
Products are homogenous (little brand loyalty)
Price takers - same price
No barriers to entry or exit
Income effect: the resultant change in demand for a good or service caused by an increase or decrease in
a consumer's purchasing power or real income
Normal good: An increase in income leads to a rise in demand so the demand curve shifts to the right
Inferior good: An increase in income leads to a decrease in demand so the demand curve shifts to the left
Government interferences:
Price ceiling: max price set by the government for a good or service (below equilibrium)
Price floor: the price set by the government for a good or service (above equilibrium)
If the market cannot reach equilibrium, the lowest quantity demanded and supplied will prevail and there
will either be excess demand or supply.
Topic 3
Marginal utility =
𝑦𝑦
𝑦𝑦
MU is positive but as Q increases this gets smaller, meaning it diminishes.
Consumer surplus is the difference between the satisfaction and the cost
𝑦𝑦 = 𝑦(𝑦) − (𝑦 ∗ 𝑦)
Maximize CS:
𝑦𝑦
−𝑦=0
𝑦𝑦
Optimal purchase rule: The demand curve and the marginal utility curve are the same.
Consumers use until → MU=P
Market Demand Curve :
1. Express each person's demand curve as a Q(P).
2. Sum up all the individual quantity curves.
3. Make P the subject again
MOS questions have multiple ways of buying :
1. Find CS when there is a fixed price/ total expenditure to pay.
Utility is found by subn Q in U(Q) for Q where the MU =0.
2. Find CS for the other case (Find Quantity by the price given) usse U(Q) bhi aa jayega since Q
pata hai �.
3. Jismai zyada CS hai thats the best option.
Topic 5: Production, Productivity and Costs
Productivity:
We assume that firms' objective is to maximize profits. To do so, they hire labor and purchase capital
equipment. Furthermore, they use technology, and as an output, goods, and services are sold for profits
(profits could also be negative and zero).
Economic profit includes (implicit) opportunity costs as well.
𝛱 = 𝑦𝑦𝑦𝑦𝑦 𝑦𝑦𝑦𝑦𝑦𝑦𝑦 − 𝑦𝑦𝑦𝑦𝑦 𝑦𝑦𝑦𝑦(𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦 𝑦𝑦𝑦𝑦)
𝛱 = 𝑦𝑦𝑦𝑦𝑦 × 𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦 − (𝑦𝑦𝑦𝑦𝑦𝑦 ∗ 𝑦 − 𝑦𝑦𝑦𝑦𝑦𝑦 ∗ 𝑦)
L = inputs of labor
K = inputs of capital
Marginal and Average product of labor:
𝑦𝑦
𝑦𝑦𝑦 = 𝑦𝑦 → {a measurement of a change in output when additional labor is added}
𝑦𝑦𝑦 =
𝑦
→ {average amount of output per worker}
𝑦
Costs:
𝑦𝑦𝑦𝑦𝑦 𝑦𝑦𝑦𝑦 = (𝑦𝑦 ∗ 𝑦) + (𝑦𝑦 ∗ 𝑦)
Marginal and average cost:
𝑦𝑦𝑦
𝑦𝑦 = 𝑦𝑦 → {change in costs as output changes}
𝑦𝑦 =
𝑦𝑦
𝑦
As long as there are fixed inputs (eg: capital equipment) in the short run, the average cost and marginal
cost curves will have the following shape.
MC and AC intersect at the minima of AC.
Most firms, most of the time, have no control over the production technology available. Hence they adopt
existing technology.
𝑦 = 𝑦(𝑦, 𝑦)
Cobb-Douglas function:
𝑦 = 𝑦𝑦 𝑦 𝑦
Time periods:
1. Short run: period too short for firms to change production capacity of existing technology and
capital (‘K’)
(𝑦 = 𝑦(𝑦)) → K is constant here
2. Long run: period long enough for firms to change the production capacity of existing technology
(‘K’) and for new firms to enter or exit the industry. (𝑦 = 𝑦(𝑦, 𝑦))
3. Very long run: period long enough for technology to change (potentially)
Technology
Capital
Labor
Short run
Fixed
Fixed
Variable
Long run
Fixed
Variable
Variable
Very long run
Might change
Variable
Variable
Law of diminishing returns:
MPL and APL intersect at APL ka max
Topic 6: Cost of production
Cost curves in the short run:
-
Fixed costs need to be paid regardless of the number of output units
Variable costs usually refer to the cost of labor, which is dependent on the number of output
goods
Total cost is the sum of fixed and variable cost
Marginal and average cost curves in the short run:
-
When the marginal cost is below average, average cost is decreasing
When the marginal cost is above average, average cost is increasing
When the marginal cost is equal to the average, average cost is at its minimum
In general terms:
𝑦𝑦 = 𝑦𝑦2 + 𝑦𝑦 + 𝑦
𝑦𝑦 = 𝑦
2
𝑦𝑦 = 𝑦𝑦 + 𝑦𝑦 + (𝑦 + 𝑦) ← AC+FC
𝑦
𝑦𝑦 = 𝑦𝑦 + 𝑦 + 𝑦 ← VC/q
𝑦𝑦 = 2𝑦𝑦 + 𝑦
-
A change in A or C moves the location of the minimum of the AVC curve along the x axis
A change in A,C, or D moves the location of the AC curve along the x axis
Topic 7: Perfect competition (Short run)
Assumptions: (main ones)
1. Many buyers, many sellers (price takers; no market power)
2. Homogeneous goods/standardized (no brand loyalty)
3. Free entry and exit in the long run (no long-run barriers to competition)
4. Perfect information (consumers do not make mistakes and always find the lowest price)
These markets do not exist but matter because this model is a good estimate of some markets.
Firms in perfectly competitive environments will try to maximize profits.
In the short run:
- It can't change its cost curves (based on tech and prices of inputs)
- It can't push up the price (perfectly competitive curve = price taker)
- It can't distinguish its product from others by the advertising of product innovation
- All it can do is choose the profit-maximizing level of output (choose q to maximize profit)
𝑦𝑦 𝑦𝑦𝑦 𝑦𝑦𝑦
=
−
=0
𝑦𝑦
𝑦𝑦
𝑦𝑦
*Choose to produce at the level of output at which MR=MC=P (price is at least as much as average
variable cost)
Since firms in perfect competition are price takers, the demand curves the firms face are horizontal
(perfectly elastic).
𝑦𝑦 = 𝑦 ∗ 𝑦
𝑦𝑦 = 𝑦 → the change in total revenue, if this firm produces one more output unit, is just the
current market price.
The industry supply curve is flatter than the supply curves of each curve. (more elastic)
An increase in the market demand would result in an increase in the price set for a firm. This would be
more profitable for firms in perfect competition.
Topic 8: Perfect competition (Long run)
-
All inputs are variable for the firms
There is free entry and exit to the industry
Only technology is fixed
Supply is more responsive in the long run to price changes (more elastic → flatter)
Supply curve in the long run is:
𝑦 = 𝑦𝑦 = 𝑦𝑦𝑦
The number of firms will vary in the long run until:
𝑦 = 𝑦𝑦𝑦 ⇔ 𝑦𝑦𝑦 = 0
There are 3 ways that the supply curve of the industry can look in the long run:
1. Constant costs: horizontal curve (only this is considered for this course)
2. Increasing costs: upward-sloping curve
3. Decreasing costs downward sloping curve
Long run market equilibrium occurs when:
𝑦𝑦𝑦 = 𝑦𝑦𝑦 = 𝑦
In the long run we are determining how many firms we have in the market.
In the long run, the firm will operate at the bottom of the long run average cost curve and will make this
quantity using the right amount of K.
Firms enter and exit until profits are zero.
How many firms enter or exit in the long run?
1. Take D = Supply in the long run (i.e @ min LRAC)
2. Solve for Q
3. N = Q/q
Efficiency is achieved when resources are allocated to deliver the most benefit to society.
𝑦𝑦𝑦 = 𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦 𝑦𝑦𝑦𝑦𝑦𝑦𝑦 + 𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦 𝑦𝑦𝑦𝑦𝑦𝑦𝑦 + Govt. surplus
In a simple situation (no taxes or tariffs, external benefits, external costs, public goods) the benefits to
society are the benefits to the individuals that are participating in consuming and producing.
In the short run:
𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦 𝑦𝑦𝑦𝑦𝑦𝑦𝑦 = 𝑦 + 𝑦𝑦𝑦
Topic 9: Monopoly
In the monopoly model there is only a single supplier.
*Being the only supplier gives you market power but does not assure that you will have profits.
Types of efficiency:
1. Allocative: who gets what benefits? What is the GTS?
2. Productive: are we operating at the bottom of the AC curve.
3. Dynamic: over time how does technology change (short term vs long term trade off )
pc
monopoly
-
lots of firms
no market power (price takers)
max degree of competition
free entry and exit
max amount of social welfare in the
simple case
-
1 supplier only
lots of market power (price maker)
min amount of competition
barriers to entry
deadweight loss
The monopolist picks a quantity and a price at which production will take place. There is no supply curve
in this case.
-
necessary condition: MR = MC (determines q) ← supply rule only to max. profits
demand curve with the determined quantity determines the price
shutdown condition: P >= AVC
*marginal revenue (mr) is not equal to price (p)
1
)
𝑦𝑦
MR has the same intercept but twice as much of the slope of the linear demand curve.
𝑦𝑦 = 𝑦(1 −
Efficiency:
- Yes, once the quantity is picked, they make this output at the lowest cost
- The firm might not operate at the minimum long run average cost
*there is no price discrimination
Gain to society: net total economic surplus = CS+PS+GS (unexploited beneficial trades exist)
*operate on the elastic portion of the demand curve
*monopolies are allocatively inefficient
Gain to society:
Marginal social benefit = marginal private benefit = marginal utility =price
marginal social cost = marginal private = marginal cost
Allocative efficiency is achieved when resources are a;;located in a way that delivers the most gain to
society. (Msb = msc)
Deadweight loss = gts in pc - gts in monopoly (this is completely lost to society rather than transferred to
someone else)
How does a monopoly persist:
1. Government license / patent
2. ownership of scarce but essential resources
3. Some other barriers to entry
4. cost advantage (economies of scale)
In the case of a natural monopoly, governments may regulate the monopolist.
Rate of return regulation: control monopolists by forcing it to charge a certain price that will affect the
profits and production of the monopolist.
- do nothing
- marginal cost pricing
- average cost pricing
Topic 10: Oligopoly
Oligopoly is a market in which there are only a few sellers. (for this course we assume there are 2 firms)
There are competitors but the firms have some market power. This market structure is somewhere
between perfectly competitive markets and monopolies.
Firm 1 decides q1 given q2
Firm 2 decides q2 given q1
Each firm has MC = AC no matter how much they produce
-
Same technology
There are no fixed costs
Each firm chooses its own production output, however price is determined by both firms
(strategic interaction)
The goal is profit maximization not to destroy the other firm (nash equilibrium)
Cartel: the firms act as one (monopoly)
Payoff matrix:
Firm 2
Cooperate
Firm 1
Cooperate
Cheat
Cheat
Cooperative (cartel)
illegal*
Competitive (nash)
The reaction function, also known as the best response function, is a way to solve for each firm’s
optimal decision.
What would firm #1 do given that firm #2 produces q2?
𝑦1 = 𝑦(𝑦2 )
- Find profit function
- Derive and set to 0
- This gives the reaction function for firm one
- The intercept of the reaction functions for both firms shows the point of nash equilibrium
Joint profit maximization requires collusion, which is illegal. Real oligopolists use secret deals and/or
threats.
Society tries to:
1. Encourage competition
2. Preserve possibility of entry
Topic 11: Externalities and public goods
An externality is created when the action of producing or selling a good affects bystanders as well as
market participants and there is no payment of compensation that offsets the effects on
bystanders.(markets make wrong decisions)
Externalities can be both positive or negative:
1. Positive = external benefit (market under performs) → affects demand curve
- Education
- Developing new technology
- Providing public art, open space in the city
2. Negative = external cost (market over performs) → affects supply curve
- Burning fossil fuels
- Second-hand smoke
- Noisy activities
A public good is one that is consumed collectively and a good that is difficult to exclude people from
using. (marginal external benefit > 0 and marginal private cost = 0)
Markets work
1. Perfect competition
Markets fail
1.
2.
3.
4.
5.
Monopoly
Oligopoly
External costs
External benefits
Public goods
The Coase theorem: when a small number of people are affected, private negotiations can solve the
problem.
When a large number of people are affected, market failure occurs.
𝑦𝑦𝑦𝑦𝑦 𝑦𝑦𝑦𝑦𝑦𝑦 𝑦𝑦𝑦𝑦𝑦𝑦𝑦
= 𝑦𝑦𝑦𝑦𝑦 𝑦𝑦𝑦𝑦𝑦𝑦𝑦 𝑦𝑦𝑦𝑦𝑦𝑦𝑦 + 𝑦𝑦𝑦𝑦𝑦 𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦 𝑦𝑦𝑦𝑦𝑦𝑦𝑦
𝑦𝑦𝑦𝑦𝑦 𝑦𝑦𝑦𝑦𝑦𝑦 𝑦𝑦𝑦𝑦 = 𝑦𝑦𝑦𝑦𝑦 𝑦𝑦𝑦𝑦𝑦𝑦𝑦 𝑦𝑦𝑦𝑦 + 𝑦𝑦𝑦𝑦𝑦 𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦 𝑦𝑦𝑦𝑦
𝑦𝑦𝑦 = 𝑦𝑦𝑦 = 𝑦𝑦𝑦
At max GTS: MSB=MSC
Optimally:
𝑦 = 𝑦𝑦𝑦 at the optimum quantity
Tradable emissions permits: Each firm is allocated a certain number of emission permits per year. These
permits may be used or traded. Firms that have the highest costs of abatement will seek to buy extra
permits and those who have low costs of abatements will seek to sell. Demand and supply for permits will
establish the equilibrium price of a fixed amount of pollution permits. Public authority will determine the
amount of emissions that will be allowed. This creates a market for externalities and internalizes external
costs.
No one likes to pay for public goods but everyone likes to consume them. Therefore, private markets
cannot generally sell such goods to individual consumers. (governments should pay)
→ 𝑦𝑦 = 𝑦
𝛴𝑦𝑦 = 𝑦𝑦
Topic 12: International trade
Exports: goods and services sold to other countries
Imports: goods and services purchased from other countries
Barriers to trade:
- Tarrif: a tax on imported/exported products
- Quota: a limit imposed on the total value that can be imported each year
- Preferential government purchasing arrangements
The theory of comparative advantage: David
Absolute advantage: if a country uses fewer resources to produce that commodity
Comparative advantage: if it can produce that commodity at lower opportunity cost (trade is based on
this)
Autarchy: situation of self sufficiency
Terms of trade: the rate at which a country’s export trades for its imports