1
Willingness to Pay
Willingness to pay is the maximum amount someone would be willing and able
to pay for a unit of a good, if it were available at that price.
We can break down willingness to pay into benefits and costs. We add
the benefits and subtract the costs. This value of benefits minus costs is called
individual surplus.
2
Opportunity Cost
Opportunity costs must be accounted for in decisions and refer to the value of
the next-best alternative. For example, by going to college one must account
for the foregone value of going directly into the workforce.
3
Sunk Costs
Sunk costs refer to costs have already been lost and cannot be recovered. Sunk
costs should not be accounted for in making decisions, because they have no
effect, as they are already lost.
However, people sometimes follow the sunk cost fallacy, and consider sunk
costs relevant to making decisions. For example, when a business bails on a
project that has caused losses, even if, after those losses, the project is now the
best option available because it can be quickly and easily finished.
4
The Production Possibility Frontier
The production possibility set describes all the possible combinations of goods
that can be produced. For example, below we can produce 15, 000 oranges and
zero apples, or zero oranges and 10, 000 apples. In between there is a trade-off
between the number of apples and oranges.
1
20,000
Oranges
15,000
10,000
5,000
0
0
5,000
10,000
15,000
20,000
Apples
The production possibility frontier is the subset of the production possibility set which is not wasteful, in the sense that maximal use is being made of
the available resources. To be in the PPF means that we cannot increase the
quantity of any one good without decreasing the quantity of another good. If
we could, it would be wasteful not to, as the gain in one quantity comes for free.
The PPF below is in red.
20,000
Oranges
15,000
10,000
5,000
0
0
5,000
10,000
15,000
20,000
Apples
5
Thinking on the Margin
We can break down decisions about how much of something to choose by thinking on the margin. Here, we look at the benefit of getting one more unit (the
2
marginal benefit) compared to the cost of getting one more unit (the marginal
cost). If the marginal benefit is greater than the marginal cost, we should get
that extra unit. If the marginal benefit is lower than the marginal cost, we
should not. For the purposes of this course, we always keep increasing our
quantity until the marginal benefit exceeds the marginal cost.
Marginal cost for suppliers is increasing because it’s harder to make an
extra unit when you’ve already used up the good resources. Marginal benefit
for consumers is decreasing: is a 125 ft yacht that much better than a 100 ft
yacht?
The marginal version of any quantity refers to the change in that quantity
from getting one more. So marginal surplus is the extra surplus gained or lost
from getting one more. It is equal to marginal benefit minus marginal cost.
6
Comparative Statics
Comparative statics refer to examining the effects of a change in certain variables, while holding others constant.
7
Demand
Individual demand, for a given individual, is the maximum quantity they would
be willing and able to consume at a given price, if the good were hypothetically
available in great enough numbers at that price. It is a function that takes in
a price, and spits out the individual’s quantity demanded. When we graph it,
we put price on the y-axis, and quantity on the x-axis. Demand is downwardsloping: when the price rises, we want less of a good. When it falls, we want
more. This is referred to as the law of demand.
3
Price
Individual demand
0
0
Qty. Demanded
Price
Market demand the maximum quantity the entire market would be willing
and able to consume at a given price. We can find it by adding up individual
demand for every consumer. For example, if in the market for cars, at $40, 000,
Ali has individual demand 1, Brenda has individual demand 0 and Chandra has
individual demand 2, and these three were the entire market, market demand
would be 1 + 0 + 2 = 3 at the price $40, 000. Market demand inherits the law
of demand from individual demand, and is downward-sloping as well. When we
simply say “demand” in these notes, unless there is context suggesting otherwise,
the statement applies to both individual and market demand. The same for
supply.
Market demand
Some individual’s demand
0
0
Qty. Demanded
4
Price
Both market demand and individual demand are relationships between
price and quantity demanded. If the price changes, it does not change the
demand curve. It causes a “movement” along the demand curve to another
point, at the new price. It does NOT move the demand curve. Below we see
the effect of an increase in price and then a decrease in price.
New price
Original price
Original qty.
New qty.
0
0
Price
Qty. Demanded
Original price
New price
New qty.
Original qty.
0
0
Qty. Demanded
There are many factors other than price that determine demand. Really,
demand functions just shows the relationship between price and quantity holding
many other factors constant. When we change these factors, we can change
the shape of the demand curve. This can have all kinds of effects, but we
look at simple changes which have simple effects, either increasing the quantity
5
demanded at all prices (a shift right), or decreasing the quantity demanded at
all prices (a shift left). Below are a shift right and then a shift left.
Price
New market demand
Original market demand
0
0
Qty. Demanded
Price
Original market demand
New market demand
0
0
Qty. Demanded
A change in income can shift demand. For most goods, quantity demanded
at each price will increase with an increase in income, and decrease with a decrease in income. These are called normal goods. However, some goods, inferior
goods, see quantity demanded decrease with income. This is because there are
better goods which become more affordable with the increase in income. For
example, with a rise in income, someone might switch from flying in economy
to flying in business.
The prices of other goods can shift demand. Usually, an increase in the
6
price of another good increases demand, and a decrease causes a decrease in
demand. When prices rise, consumers switch to buying other things. This
happens for goods called substitutes. Some substitutes are close, such as two
different kinds of car. We would expect to see a larger increase in demand for
one kind if the price of another increases than an increase in demand for, say, a
bicycle. There are also complements, which enhance each other, like a car and
fuel. If the price of fuel increases, a car is less desirable; it might be cheaper
to use a bike. So for complements, we see demand decrease with an increase
in price (of the complement good, NEVER the good for which we’re looking at
the demand curve), and increase with a decrease in price.
Expectations of future events effect demand. For example, if some expects
higher prices in the future, they may buy more durable goods like furniture in
the present, so they will not lose so much money by acquiring them later.
Preferences also affect demand. If a consumer likes a good more they will
demand more of it, and if they like it less they will demand less.
All of these are shifters of individual demand, and change market demand
through changing the individual demands that constitute it. Changes to market
demand aren’t as simple, and can take other forms. What is, say, an inferior
good or a normal good is in the eye of the beholder sometimes, so whether a
change in income across the economy will increase or decrease demand depends
on the composition of the market; the kinds of people in it. The size of the
market also matters: population growth can increase demand without changing
anyone’s individual demand.
8
Supply
Just as we can consider the amount an individual will buy at a given price, we
can also think about the amount an individual (or firm) will sell, if there were
enough buyers available, at a hypothetical price. This gives us our individual
supply curve. As always, price is on the y-axis and quantity demanded on the
x-axis. Supply is upward-sloping: when the price rises, we want to sell more of
a good. When it falls, we want to sell less. This is the law of supply.
7
Price
Individual Supply
0
0
Qty. Supplied
To find the maximum amount of a good that will be sold in an entire
market, we again simply add up. We take every market participant’s individual
demand at a given price, and we add them all together. For example, if in
the market for cars, at $40, 000, dealer A has individual supply 50, dealer B
has individual supply 0, because it’s a motorcycle dealership, and dealer C has
individual supply 60, and these three were the entire market, market supply
would be 50 + 0 + 60 = 110 at the price $40, 000. Market supply inherits the
law of supply from individual supply, and is upward-sloping.
Price
Some individual’s supply
Market Supply
0
0
Qty. Supplied
Again, a change in price does not change the individual or the market
supply curve. It merely gives a movement along the curve. Below is the result
8
of an increase in price, and then a decrease in price.
Price
New price
Original price
New qty.
Original qty.
0
0
Qty. Supplied
Price
Original price
New price
Original qty.
New qty.
0
0
Qty. Supplied
Again, supply is contingent on many factors other than demand which may
change the shape of the supply curve. Again, we’ll look at simple increases in
supply at all prices (shifts right), or decreases (shifts left). Below we see a shift
right and then a shift left.
9
Price
Original market supply
New market supply
0
0
Price
Qty. Supplied
New market supply
Original market supply
0
0
Qty. Supplied
The costs of the inputs for the production process of a supplier affect supply.
Increases in costs cause a shift left, as suppliers now need a higher price to make
the same profit, and decreases in costs cause a shift right.
Another shifter of supply is prices of related outputs (outputs that can
be made using the same production process). If a supplier can use the same
resources to make a more expensive good, they will. Such a good is called a
substitute-in-production. Therefore, if prices of substitutes-in-production increase, this shifts supply left, whereas if prices of substitutes-in-production decrease, this shifts supply right. Again being a substitute-in-production is a
scale: closer substitutes have more similar production methods. There are also
complements-in-production, where making one good makes it easier to make
10
another. If the price of a complement-in-production rises, it makes production
of complements more desirable, and so it makes production of the other good
(not the complement) more desirable because it’s easier. So an increase in the
price of complements-in-production increases supply, whereas a decrease in price
decreases supply.
Another shifter of supply is productivity. This refers to the ability to get
more out of the same resources. Improved technologies can achieve this, for
example, better machines in manufacturing. Better educated workers can also
be more productive. Productivity drives down the costs of producing more
units, so it shifts supply right. Productivity can also go backwards, such as if a
bad season hits a farm making it difficult to use the same land, plants, fertiliser,
etc. to produce more. A decrease in productivity shifts suppply left.
Like for demand, expectations of future events can affect supply. For example, if sellers expect higher prices in future, they might store units of a good
to sell later. And just as with demand, we need to consider how different sellers’
shifts in individual supply aggregate to shift market supply, so the composition
and size of supply can shift supply.
9
Fixed and Variable Costs
Some costs of sellers are born out before they produce a single unit, like buying
a factory. These are called fixed costs. These are sunk costs at the point of considering how much to produce, where the necessary facilities for production have
presumably already been purchased. Typically, fixed costs cannot be changed
in the short-run. Variable costs change with the number of units produced. For
example, if you want to make more windows, you need to buy more sand to
make the glass.
Supply and demand accurately predict how much sellers or buyers are respectively going to be willing and able to sell or buy, given a hypothetical price
and enough potential buyers or sellers. Not just the maximum amount.
10
Equilibrium
In a competitive market, there are many small buyers and sellers who do not
have a large impact on the market individually.
In a competitive market, prices will be set where market demand is equal to
market supply (WE CANNOT INFER EQUILIBRIUM FROM INDIVIDUAL
DEMANDS AND SUPPLIES), at market equilibrium. Equilibrium consists of
the quantity at which they are equalised, and the price achieving this quantity.
At equilibrium, the quantity traded is the same as the quantity demand and
the quantity supplied, as buyers and sellers can always find someone to sell to
11
them or buy from them respectively.
Price
Market Demand
Equilibrium Price
Market Supply
Market Equilibrium
Equilibrium Qty.
0
0
Quantity
The law of one price states that in a perfectly competitive market, a good
will only be sold at one price (or prices will tend toward a single value). This
is because if goods can be sold at two prices, sellers at the lower prices could
undercut the higher prices by just a little. Then, the low-prices sellers would
either retain their old customers, or be able to steal high-price sellers’ customers,
and make more money.
At a price lower than equilibrium (WHEN WE SAY A PRICE OR QUANTITY IS HIGHER OR LOWER THAN EQUILIBRIUM, THIS IS SHORTHAND FOR SAYING IT IS HIGHER OR LOWER THAN THE EQUILIBRIUM PRICE OR QUANTITY, RESPECTIVELY), demand will exceed supply, because demand increases with the lower price, but supply decreases, relative to being equal at equilibrium. This situation is called a shortage.
12
Market Supply
Price
Market Demand
Sub-equilibrium price
Shortage
0
0
Quantity
At this lower price, sellers would sell all of their units, and buyers would
be left wanting more, because demand exceeds supply. Sellers would be able to
set higher prices, and still sell all their units, since demand would still exceed
supply. Buyers can only accept the price hike, since the market is perfectly
competitive, and a buyer who refuses to accept the price will be priced out by
one of many other buyers who accepts the higher price. Buyers compete. This
pushes prices toward equilibrium.
At a price higher than equilibrium, supply will exceed demand, because
demand decreases with the higher price, but supply increases, relative to being
equal at equilibrium. This situation is called a surplus.
Market Demand
Market Supply
Above-equilibrium price
Price
Surplus
0
0
Quantity
13
At this higher price, buyers could buy everything they wanted, and sellers
would be left with more to sell, because supply exceeds demand. Buyers could
force lower prices, and still buy everything thing they want, since supply would
still exceed demand. Sellers can only accept the price decrease, since the market
is perfectly competitive, and a seller who refuses to accept the price will be
undercut by one of many other sellers who accepts the lower price. Sellers
compete. This again pushes prices toward equilibrium.
Comparative statics for equilibrium break down into looking at how demand
shifts, or supply shifts (or both), and then looking at the effect these shifts have
on equilibrium quantity.
An increase/shift right in demand causes a shortage, which drives prices
up (be sure to explain why). As prices rise, quantity supplied increases, while
quantity demanded decreases. At the original price, the (fixed) quantity supplied was the original equilibrium quantity. Therefore, as prices reach the new,
higher equilibrium level, quantity supplied rises to the new equilibrium level.
So equilibrium quantity increases.
Original demand
Price
New equilibrium
Original equilibrium
New demand
0
0
Quantity
A decrease in demand causes a surplus, which drives prices down. As
prices fall, quantity supplied decreases, while quantity demanded increases. At
the original price, the quantity supplied was the original equilibrium quantity,
therefore, as prices reach the new, lower equilibrium level, quantity supplied
falls to the new equilibrium level. So equilibrium quantity falls.
14
Original demand
Price
New demand
Original equilibrium
New equilibrium
0
0
Quantity
An increase in supply causes a surplus, which drives prices down. As prices
fall, quantity supplied decreases, while quantity demanded increases. At the
original price, the (fixed) quantity demanded was the original equilibrium quantity. Therefore, as prices reach the new, lower equilibrium level, quantity demanded rises to the new equilibrium level. So equilibrium quantity increases.
Original supply
Price
New supply
Original equilibrium
New equilibrium
0
0
Quantity
An decrease in supply causes a shortage, which drives prices up. As prices
rise, quantity supplied increases, while quantity demanded decreases. At the
original price, the quantity demanded was the original equilibrium quantity.
Therefore, as prices reach the new, higher equilibrium level, quantity demanded
falls to the new equilibrium level. So equilibrium quantity decreases.
15
Original supply
Price
New equilibrium
Original equilibrium
New supply
0
0
Quantity
A change, or multiple changes, may lead to a shift in both supply and
demand. As an example below, there is a shift right in both demand and supply.
The shift right in demand increases quantity, as does the shift right in supply.
So the cumulative effect of both is an increase in quantity. However, the supply
shift decreases price, while the demand shift increases prices. Either effect could
dominate, so if asked to examine the effect of an shift right in both supply and
demand, you would need to state this ambiguity. These two possibilities are
depicted below, first an increase in price, then a decrease. Be aware that you
may face other questions with ambiguities.
Price
New equilibrium
Original equilibrium
0
0
Quantity
16
Price
Original equilibrium
New equilibrium
0
0
Quantity
To calculate equilibrium from explicit an demand function QD (P ) of price P
and supply function QS (P ), we first solve for the equilibrium price P ∗ by setting
QS (P ∗ ) = QD (P ∗ ) (the definition condition of equilibrium is that quantity
demanded equals quantity supplied) and solving. For example, if QS (P ) =
2 + 2P and QD (P ) = 10 − 2P , then we set 2 + 2P ∗ = 10 − 2P ∗ , for 4P ∗ = 8, for
P ∗ = 2. To find the equilibrium quantity Q∗ , it is both quantity demanded and
quantity supplied at P ∗ , so we just sub P ∗ into either demand or supply. In
this case, subbing into supply, we have Q∗ = QS (P ∗ ) = 2 + 2P ∗ = 2 + 2 × 2 =
2 + 4 = 6.
11
Elasticity
The elasticity of some A with respect to B (where A is determined by B) is
built on the percentage change in A divided by the percentage change in B:
∆B
∆A
× 100 /
× 100 .
A
B
If A goes from A1 to A2 , then ∆A is A2 − A1 . We calculate elasticities using
2
, the average of A1 and A2 , halfway
the midpoint formula, where A is A1 +A
2
2
in-between them. If B goes from B1 to B2 , then ∆B is B2 −B1 , and B is B1 +B
2
This measures the sensitivity of A to a change in B.
We don’t just use
∆A
∆B
for elasticity, because we want it to be unit-invariant: if we changed the units
to measure A or B (for example, from kilos to pounds), we would want the same
value of elasticity. By looking at the percentage change instead of the absolute
17
change, we accomplish this, as a conversion rate representing a change of units
in the numerator, will be cancelled out by the same conversion rate from the
unit change in the denominator.
The expression two paragraphs above simplifies to a ratio of proportional
changes:
∆B
∆A
/
.
A
B
In terms of A1 , A2 , B1 and B2 , this is:
!
!
B2 − B1
A2 − A1
/
.
A1 +A2
B1 +B2
2
2
Cancelling out the factors of 12 in the denominators of the proportional changes
gives us
A2 − A1
B2 − B1
/
.
A1 + A2
B1 + B2
In this course we measure own-price elasticity, where B is the price of a
good and A is either its quantity demanded or supplied. We also look at crossprice elasticity, where B is the price of a good and A is the quantity demanded
or supplied of a different good. We also look at income elasticity, where B is
income. When we are looking at A as quantity demanded, we are looking at the
elasticity of demand (for example, the own-price elasticity of demand). When
we are looking at A as quantity supplied, we are looking at the elasticity of
supply.
We said above that elasticity is built on the formula given above, and not
actually equal to the formula
∆A
∆B
/
,
A
B
because, in the case of own-price elasticity of demand, a slight tweak is made
by putting a negative sign in front, so we have:
∆Q
∆P
−
/
,
Q
P
with Q for quantity demanded and P for price. All the other derived fromulae
are the same, except that they have the negative sign as well. We make this
alteration because the law of demand says that quantity demanded decreases
with price. So if price increases, that is, P2 − P1 is positive, then demand
decreases, so that Q2 − Q1 is negative. Similarly, if price decreases, P2 − P1 is
negative, but Q2 −Q1 is positive. Q and P will always be positive, so without the
tweak, we would always have negative own-price elasticity of demand otherwise.
18
Every other elasticity we look at does not have this slight tweak, because it
will usually, be positive. Own-price elasticity of supply is positive because of the
law of supply: ∆Q and ∆P will either both be positive or negative, cancelling
out.
Looking at the formula with A and B, we see that positive elasticity means
that A and B increase in tandem, and negative elasticity means that one increases while the other decreases, and vice versa. Therefore, income elasticity
of demand being positive means we are dealing with a normal good: increased
income leads to increased demand. Negative income elasticity of demand means
we are dealing with an inferior good. Positive cross-price elasticity of demand
means we are dealing with a substitute: price increases lead to quantity decreases of the other good. Negative cross-price elasticity of demand means we
are dealing with a complement.
Looking at elasticity graphically is a little tricky for two reasons. Firstly,
∆A
, but we’ll most often have B be the price P of a
it’s kind of like a “slope” ∆B
good, and A be the quantity demanded or supplied of that good. Then we can’t
think things the way we normally think of slopes, because then we talk about
slope as “rise over run”. The rise is on the y-axis, and the run is on the x-axis.
But here, price is on the y-axis, and quantity is on the x-axis. So we have a case
of run over rise. We are looking at the reciprocal of what we would normally
call a slope. This makes things go backwards. A steeper curve corresponds to
lower elasticity (think about it: in a steep curve, x does not change a lot when
we change y, so our ∆x
∆y will be low), and a flatter curve corresponds to higher
elasticity.
The second point, is that elasticity is not a slope. Our A and B formula
(which gets a negative sign put in front of it for own-price elasticity of demand
only), can be rewritten as:
∆A B
,
∆B A
so we have a slope times this term for unit-invariance B
A . So, at the same A
∆A
and B, then a change in the slope ∆B corresponds to a change in elasticity.
However, at we cannot visually compare slopes for different A and B.
If we have elasticity η, then we can ask how large it is by taking its absolute
value |η|. To get a sense of absolute value, it is the “magnitude” of a number:
|0| = 0, |1| = 1, | − 1| = 1, |2| = 2, | − 2| = 2, and so on. We care about absolute
value, because a large negative change in response to a change in something else,
still indicates high sensitivity, that is, high elasticity. If |η| = 0 (that is, η = 0,
then A does not change as B changes, and this is called perfect inelasticity.
If |η| < 1, then the proportional change in A is smaller than the proportional
change in B, and we call the situation inelastic. If |η| = 1, then the proportional
change in A is equal to the proportional change in B, and we call the situation
unit-elastic. If |η| > 1, then the proportional change in A is greater than the
19
proportional change in B, and we call the situation elastic.
Below are graphs of own-price elasticity of demand and then supply. We
see that perfectly inelasticity gives us a vertical curve, inelasticity gives us a
relatively steep curve, and elasticity gives us a relative flat curve. At the extreme
end we have perfect elastictiy, with a sudden jump in quantity from a horizontal
curve. The difference for supply and demand is that supply goes up and demand
goes down. There is a bit of hand-waving here, because it’s as if we’re talking
about elasticity at a single point, but in this course, elasticity is always between
two distinct points. This hand-waving is acceptable in an answer to a question
where you are asked to refer to a graph. NOT in a question where you are asked
to actually calculate elasticity. And, IMPORTANTLY, it is only because we set
the point on the line x = y, that unit-elasticity corresponds to a slope of 1 or
−1. With different ratios of Q and P , unit-elasticity might look different.
Price
P =Q
Perf. elastic
Elastic
Unit elastic
Inelastic
Perf. inelastic
0
0
Quantity
20
Perf. inelastic
Inelastic
Unit elastic
Price
Elastic
Perf. elastic
P =Q
0
0
Quantity
12
Taxes and Subsidies
There are many kinds of taxes and subsidies, but in this course we are concerned
with per-unit taxes and subsidies. Taxes, as you presumably know, are charges
by the government. Subsidies are grants of money from the government to
encourage particular activities. A per-unit tax or subsidy means that for each
unit you buy (if the tax or subsidy is on buyers) or sell (if the tax or subsidy
is on sellers) you pay (for a tax) or receive (for a subsidy) a fixed amount of
money. Subsidies are just the negative version of taxes. Instead of giving money
to the government, you are getting it from the government.
In a supply or demand graph, the y-axis will always denote price not including any taxes or subsidies. A per-unit tax of t on demand will move the
demand curve down by t on the y-axis. This is because, at a given price, the
buyer cares about the amount they actually spend per unit, which is not just
the pre-tax price, but also the tax t. Therefore at a price p, they will demand
the same quantity that their demand curve without any tax specifies at a price
of p + t. A per-unit subsidy of s is just a negative tax, so it shifts demand up
by s. Below are depicted the effects of a tax and subsidy of the same size c on
demand.
21
Demand w/ subsidy
Price
p+c
c
c
p
Demand w/ tax
0
0
Qty. Demanded
On the supply side, sellers receive the price p, so a tax of t has them
receiveing p − t per unit, so supply shifts up by t, to the level as if the price were
lowered by t. Similarly, if sellers receive a per-unit subsidy s, then this shifts
supply down by s. Below are depicted the effects of a tax and subsidy of the
same size c on supply.
Supply w/ tax
Price
p+c
c
c
p
Supply w/ subsidy
0
0
Qty. Supplied
In a particular market, after the introduction of a per-unit tax of t on demand, demand falls by t. So the new equilibrium will be at the quantity where
market demand falls onto market supply (REMEMBER, EQUILIBRIUM IS
DETERMINED BY MARKET DEMAND AND MARKET SUPPLY ONLY,
NOT INDIVIDUAL DEMANDS AND SUPPLIES), the point at which the orig-
22
inal demand, before the tax, was t above supply. Similarly, if a subsidy of s is
introduced on demand, the new equilibrium quantity will be where demand rises
by s to meet supply, so that original demand must have been s below supply.
Demand w/ subsidy
Price
Equilibrium w/ subsidy
s
t
Equilibrium w/ tax
Demand w/ tax
0
0
Qty. Demanded
If a tax of t is introduced on supply, supply rises by t, at the new equilibrium
quantity, demand must have been t above supply. If a subsidy of s is introduced
on supply, supply falls by s, so at the new equilibrium quantity, demand must
have been t below the original supply.
Supply w/ tax
Price
Equilibrium w/ tax
s
t
Equilibrium w/ subsidy
Supply w/ subsidy
0
0
Qty. Supplied
23
13
The Statutory Incidence of Taxes and Subsidies
The statutory incidence of a tax or subsidy refers to who (supply or demand)
the tax or subsidy is levied on by the government. So the statutory incidence
is on sellers if sellers are taxed or subsidised and on buyers if buyers are taxed
or subsidised.
Price
We now consider the effects of swapping the statutory incidence of a perunit tax or subsidy of the same size. By super-imposing the last two graphs, we
see that the equilibrium quantity for a tax of t on sellers is the same as that of
a tax of t on buyers, and the same for a subsidy of size s. This is because the
equilibrium for either tax occurs where supply is t above demand, and there is
only one such point. Similarly for supply. For the tax, the equilibrium quantity
is lower, because we have a shift left in one factor (be able to explain why). For
the subsidy, the equilibrium quantity is higher because we have a shift right in
one factor.
s
t
0
0
Qty. Demanded
We can also see that the difference in equilibrium price between the buyer
tax and the seller tax is t. We’ll call the buyer tax price p and the seller tax
price p′ , so that p′ = p + t. We’ll call the equilibrium quantity under the taxes
(which is the same) q. Then, under the buyer tax, buyers pay p (the buyer tax
equilibrium price) per unit, but also tax t, so that they wind up spending p + t
per unit. Under the seller tax, they just pay the seller tax equilibrium price
p′ . But p′ = p + t, so they’re paying the same thing per-unit. Under the buyer
tax, sellers receive p per-unit, since they aren’t being taxed. Under the seller
tax, they receive p′ − t per unit. But these are again equal. The government
receives t per-unit in either case. The amount of money everyone loses or gains
24
per-unit is the same whether the tax is on sellers or buyers, and the number of
units q is the same, so every one is getting or giving up the same amount of
the good, while getting or giving up the same total amount of money, which is
just q times the per-unit amount of money (the latter being independent of the
statutory incidence of the tax).
For a subsidy of size s, we’ll reuse the name q for the quantity. Now, the
price p for the buyer subsidy is s above the price p′ for the seller subsidy. So
p = p′ + s. With the buyer subsidy, buyers pay p − s per-unit, since they’re
getting the per-unit subsidy back. Under the seller subsidy, buyers pay p′ per
unit. But these are equal. Under the buyer subsidy, sellers receive no subsidy,
and receive the price p per unit. Under the seller subsidy, they receive p′ + s.
Again these are equal. The government spends s per-unit in either case. Again,
everyone spends the same amount per-unit, and the same number of units are
traded. So everyone loses, and gets the same stuff.
When we say everyone there, we mean supply as a whole, demand as a
whole, and the government. But what about individual buyers and sellers?
Well, we know that for a tax of t, buyers’ individual demand shifts down by t.
But we’ve also seen that if the tax is on buyers instead of sellers, the equilibrium
price that buyers are paying also comes down by t. This corresponds to just
shifting the whole graph down by t, which doesn’t do anything on the x-axis,
quantity demanded, so the amount the individual demands, (which is just what
they consume in equilibrium, where buyers can always find sellers), does not
change depending on whether the tax is on buyers or sellers. Similarly, for a
subsidy of s for buyers as opposed to sellers, demand shifts up by s, but so does
price, so quantity consumed is unchanged. In the diagram below, the two are
merged and the size of the tax and the size of the subsidy are both c.
Price
Seller tax/buyer subsidy price
c
c
Buyer tax/seller subsidy price
Tax qty.
0
Subsidy qty.
0
Qty. Demanded
25
For sellers, under the seller tax supply shifts up by t, but so does price.
Under the buyer tax, supply shifts down by s, but so does price. Again, the
quantity sold is independent of the statutory incidence of the tax.
Price
Seller tax/buyer subsidy price
c
c
Buyer tax/seller subsidy price
Tax qty.
0
Subsidy qty.
0
Qty. Demanded
So even at the level of individual buyers or sellers, again, the amount of
money gained or loss and the amount of goods gained or lost is exactly the
same. So, for a per-unit tax or subsidy of the same size, the statutory incidence
has no meaningful effects within a given market.
14
The Economic Incidence of Taxation
While the statutory incidence of a tax is meaningless in a market as to who
pays more or less, the economic incidence of a tax does have meaningful effects.
This refers to the relative difference in what buyers and sellers are respectively
paying or receiving per-unit, relative to if there were no taxes. The amount
buyers are paying per-unit when taxed is just the price given by their demand
curve at the equilibrium quantity with a tax. Their demand curve with a buyer
tax is just their no-tax demand curve shifted down by the tax t (as above). So,
adding the tax t to what they pay per-unit, it shifts the curve back up to their
no-tax demand curve. With no tax on buyers, buyers just pay the price, given
by their no-tax demand curve. Either way, what buyers pay per-unit is given
by their no-tax demand curve.
If sellers are taxed, the amount they receive per-unit is given by their taxed
supply curve at the equilibrium quantity. This is just supply shifted up by t.
But they also lose t in taxes. So the amount sellers receive with a tax on sellers
just shifts back down by t to the no-tax supply curve. If there is no tax on
sellers, what they pay is just given by their no-tax supply curve, as they pay
26
no tax on top of this market price. Either way, what sellers receive per-unit is
given by their no-tax supply curve.
Now we can find the economic incidence. We just look at the equilibrium
quantity with the tax: the point where demand is t above supply, and see if
the difference between the no-tax demand curve and no-tax equilibrium price
is greater or smaller than the difference between the no-tax supply curve and
the no-tax equilibrium price, at that quantity. If the gap is bigger for buyers, it
means that buyers, per-unit, have a worse deal than sellers, relative to no tax,
because the amount that they pay has increased more than the decrease in the
amount sellers receive. If the gap is bigger for sellers, then per-unit, sellers have
a worse deal, relative to no tax.
The economic incidence of a tax is determined by the relative elasticities
of supply and demand. We can see this by noting that elasticity is roughly
like slope. A steep curve has low elasticity, whereas a flatter curve has high
elasticity. To find the equilibrium quantity with tax, we go back to find where
supply exceeds demand by the per-unit tax t. A steep curve, with low elasticity,
has a larger change in price as we move back. A flat curve, with high elasticity,
has a smaller change in price. Therefore, when we get to the place when price
for demand is above supply by t, the steep curve will have contributed more
to that distance, and be further away from the no-tax price. That is to say,
whichever factor, supply or demand, has lower elasticity, bears the economic
incidence of the tax. We can see this in the graphs below. In the first, supply
is more elastic (flatter) than demand, and the difference between demand and
the no-tax equilibrium price, is greater than the distance between supply and
the no-tax price. In the second, demand is more elastic than supply, and the
difference between demand and the no-tax equilibrium price, is lesser than the
distance between supply and the no-tax price.
Price
Buyer’s price
Per-unit tax t
No-tax price
Seller’s price
0
0
Quantity
27
Price
Buyer’s price
No-tax price
Per-unit tax t
Seller’s price
0
0
Quantity
15
Price Controls
Price controls refer to when the government regulates the price at which a
particular good can be sold. Price floors forbid the good from being sold below
a minimum price (like the minimum wage). Price ceilings forbid the good from
being sold above a maximum price.
The arguments presented in the section on equilibrium for the law of one
price, and that prices will adjust to approach equilibrium still apply in a perfectly competitive market with price controls (try to get a handle on this). In
fact, if a price floor below equilibrium price, then goods can legally be sold at
equilibrium prices, and price can adjust closer to equilibrium from below or
above, so such a price floor has no effect, and the good is sold at the equilibrium
quantity and equilibrium price. Similarly, if a price ceiling is above equilibrium
price, goods can legally be sold at the equilibrium price, and price can adjust
closer to it from above and below, so such a price ceiling has no effect, and the
good is sold at the equilibrium quantity and equilibrium price. We can see this
in the graphs below.
28
Price
Price w/ Floor
Ineffective Floor
Quantity w/ Floor
0
0
Quantity
Price
Ineffective Ceiling
Price w/ Ceiling
Quantity w/ Ceiling
0
0
Quantity
When a price floor is set above equilibrium, prices still adjust down toward
equilibrium from above, it’s just that, once they hit the floor, they can no longer
go down any further, and that will be the price in the market. The floor binds.
At this point, because we have a price higher than equilibrium, supply exceeds
demand. Buyers can find sellers easily, but eventually they will get all the goods
they want. Then, sellers will have no one left to sell to, even though they’d like
to sell more, so the quantity traded with the binding floor will be supply at the
floor, as on the graph below.
29
Binding Floor
Price
Quantity,
Demand
Supply
0
0
Quantity
Price
When a price ceiling is set above equilibrium, prices still adjust up toward
equilibrium from below, it’s just that, once they hit the ceiling, they can no
longer go up any further, and that will be the price in the market. The ceiling
binds. At this point, because we have a price lower than equilibrium, demand
exceeds supply. Sellers can find buyers easily, but eventually they will sell all
the goods that they are willing to sell. Then, buyers will have no one left to
buy from, even though they’d like to buy more, so the quantity traded with the
binding ceiling will be supply at the ceiling, as on the graph below.
Quantity,
Supply
Demand
Binding Ceiling
0
0
Quantity
In general, a binding price control will result in the quantity traded being
the lesser of supply and demand at the limit on price set by the price control,
30
which will also be the price.
Sometimes, agents in markets can legally get around price controls by
changing other prices. For example, if a landlord has to sell with low rent,
they might still be able increase the maintenance fees for an apartment.
16
Quotas
When the government limits the quantity of a good that can be sold to some
maximum level, this is called a quota. The arguments in the section on equilibrium justifying the law of one price, and prices and quantities moving toward
equilibrium still hold, until the quantity hits the quota, similar to a how prices
can adjust toward equilibrium until they hit a limit imposed by a price control
(try to get a handle on this).
So, when a quota is set above equilibrium quantity, it does not change the
price or quantity sold in the market, relative to equilibrium.
Price
Ineffective Quota
Price w/ Quota
Quantity w/ Quota
0
0
Quantity
When a quota is set below equilibrium quantity, it has meaningful effects.
At a quantity lower than equilibrium (and therefore every quantity lower than
the quota), the maximum price that buyers are willing to pay will exceed the
minimum price at which sellers are willing to sell. This is because we can read
their willingness to pay off the demand and supply curves. At a given quantity,
buyers are willing to pay the price given by their demand curve for that quantity,
by definition. But at any higher a price, they would decrease demand, so they
would not be willing to buy the quantity. So at any quantity, we can look up
to the demand curve and read off the maximum price buyers are willing to pay
for the quantity, as below. This is not the maximum total amount they would
31
Price
spend on the quantity, but the maximum per-unit price.
Maximum price buyers will pay for it
Some quantity
0
0
Quantity
Price
For sellers, by definition, sellers are willing to sell a given quantity at the
price corresponding to that quantity on their supply curve. But, if the price
were any lower, sellers would only be willing to sell a lower quantity, because of
the law of supply. So at any quantity, we can look up to the supply curve and
read off the minimum price sellers are willing to sell the quantity for, as below.
This is not the minimum total amount they would sell the quantity for, but the
minimum per-unit price.
Minimum price sellers will sell it for
Some quantity
0
0
Quantity
So, below a quota which is itself below equilibrium, buyers are willing to pay
32
more than sellers need. Because buyers will compete with each other, sellers can
sell at the maximum price buyers are willing to pay, as any buyer who refuses
to accept that price will be priced out by another buyer. This maximum price
is given by the demand curve, as above. This higher price incentivises sellers
to increase production. They will do so, until they no longer can, because the
quantity produced has hit the quota. Then the quantity produced will be stuck
at the quota, and be sold at the maximum price buyers are willing to pay for
it, given by the demand curve, as below.
Binding Quota
Price
Price w/ Quota
0
0
Quantity
17
Pareto Efficiency
A Pareto improvement is a change that can be made which makes some people
better off, without making anyone else worse off. This is a very basic standard for when a change should be considered socially desirable. For example,
vaccination against smallpox made everyone better off, at the cost of no one.
As a counterexample, if the industrial revolution radically increased the world’s
productive capacity, but it lead to a temporary increase in unemployment as
jobs were automated. Those who lost jobs and did not later feel the benefits of
the industrial revolution were made worse off. So even though the change had
huge long-term benefits for humanity, it was not a Pareto improvement.
Pareto efficiency refers to a situation in which no Pareto improvements can
be made: if we try to make any one individual better off, it would force us
to make another individual worse off. We would always want to make Pareto
improvements if we could, so a necessary condition for a situation being socially
optimal is that it is Pareto efficient.
That doesn’t mean it is a sufficient condition. Pareto efficiency does not
33
necessarily care about equity. North Korea is a Pareto efficient country: no one
can be made better off without making the supreme leader worse off.
18
Consumer Surplus
To find individual surplus, we just add up marginal benefits, and subtract
marginal costs. For buyers, marginal cost is just price. Their marginal benefit
(there’s some background stuff you don’t have to know going on here) is specified by their individual demand curve. That is because their marginal benefit
is defined as their willingness to pay for the next unit of a good. By definition,
they are willing to pay the price corresponding to a quantity on their demand
curve. But at any higher a price, because of the law of demand, they would
demand less, and so not be willing to pay for that last unit. Therefore, buyers’
marginal benefit at a quantity is the price corresponding to that quantity on
their individual demand graph.
Price
Individual demand
Individual buyer’s marginal benefit for it
Some quantity
0
0
Quantity
It is just the same for the whole market, adding all consumers’ individual
surpluses together. THIS IS CALLED CONSUMER SURPLUS. Given a certain price, and the corresponding market quantity demanded (we’re assuming
everything demanded is consumed here), the last individual to buy the last unit
up to that quantity (so that the willingness to pay for that last unit is lower
than all previous units) must have that price below their willingness to pay, otherwise they wouldn’t buy that last unit. But at any higher a price, the quantity
demanded would be lower, so that last individual wouldn’t buy that last unit, so
the price must exceed their willingness to pay. Therefore, the marginal benefit
to all buyers is given by market demand.
34
Price
Market demand
All buyers’ marginal benefit for it
Some quantity
0
0
Quantity
Maybe it’s a little strange to think of adding this up over all units when
dealing with a continuous quantity, but for any unit demanded, given by some
quantity below the total quantity demanded, we can see the marginal consumer
surplus at that quantity as the line segment between demand (marginal benefit),
and price (marginal cost), as below.
Price
Marginal consumer surplus
Price for the market
Some quantity
0
0
Quantity
The consumer surplus is all of the marginal surpluses added up, up to the
quantity consumed (quantity demanded). At a gut feeling level, it makes sense
to think of adding up all these lines as giving the area, up to the quantity
consumed, between demand and the price.
35
Price
Consumer surplus
Price for the market
0
Quantity consumed
0
Quantity
In the depiction, with linear supply, consumer surplus is a triangle. So
know how to calculate the area of a triangle.
19
Producer Surplus
As we said in the last section, to find individual surplus, we just add up marginal
benefits, and subtract marginal costs. For sellers, marginal benefit is just price.
Their marginal cost (there’s some background stuff you don’t have to know
going on here) is specified by their individual supply curve. That is because
their marginal cost is defined as the minimum amount they are willing to accept
to sell another unit of a good. By definition, they are willing to accept the price
corresponding to a quantity on their supply curve. But at any lower a price,
because of the law of supply, they would supply less, and so not be willing to
sell that last unit. Therefore, sellers’ marginal cost at a quantity is the price
corresponding to that quantity on their individual supply graph.
36
Price
Market supply
All sellers’ marginal cost for it
Some quantity
0
0
Quantity
It is just the same for the whole market, adding all sellers’ individual surpluses together. THIS IS CALLED PRODUCER SURPLUS. Given a certain
price, and the corresponding market quantity supplied (we’re assuming everything supplied is sold here), the last individual to sell the last unit up to that
quantity (so that the willingness to sell that last unit is lower than all previous
units) must have that price above their marginal cost, otherwise they wouldn’t
sell that last unit. But at any lower a price, the quantity supplied would be
lower, so that last individual wouldn’t sell that last unit, so the price must be
lower than their marginal cost. Therefore, the marginal cost to all buyers is
given by market supply.
Price
Market supply
Individual sellers’ marginal cost for it
Some quantity
0
0
Quantity
37
Price
Maybe it’s a little strange to think of adding this up over all units when
dealing with a continuous quantity, but for any unit supplied, given by some
quantity below the total quantity supplied, we can see the marginal producer
surplus at that quantity as the line segment between price (marginal benefit),
and market supply (marginal cost), as below.
Price for the market
Marginal producer surplus
Some quantity
0
0
Quantity
Price
The producer surplus is all of the marginal surpluses added up, up to the
quantity sold (quantity supplied). At a gut feeling level, it makes sense to think
of adding up all these lines as giving the area, up to the quantity consumed,
between price and the supply.
Price for the market
Producer surplus
Quantity sold
0
0
Quantity
38
In the depiction, with linear supply, producer surplus is a triangle. So know
how to calculate the area of a triangle.
20
Markets Maximise Surplus
Total surplus is the surplus for everyone in the market added up, or just consumer surplus (for all the buyers) added to producer surplus (for all the sellers).
If the government steps in, we need to add government revenue (if the government makes money) or subtract government spending (if the government loses
money).
Price
So, in equilibrium, without government intervention, we just join up the
two areas of producer and consumer surplus.
Price for the market
Total surplus
Market quantity
0
0
Quantity
Again, in our examples, with linear supply and demand, this is a triangle.
So know how to calculate the area of a triangle.
Our goal is now to show that markets maximise surplus. To do this, we’ll
need to consider what would happen if the price and quantity for producer
surplus or consumer surplus were not given, respectively, by the demand or
supply curve (so, not by any possible equilibrium).
We assume (which we will justify shortly), that the same individuals consume or produce up at a given quantity, as would consume or produce, respectively, were that quantity given by the market price. This means that we can
still use demand for marginal benefit for consumers, and supply for marginal
cost for producers.
For consumer surplus, the first graph below depicts a quantity less than
39
Price
the quantity demanded at the given price. Here we still add up all those line
segments between price (marginal cost), and demand (marginal benefit), to give
an area. But now the area consists of a triangle and a rectangle. So be able to
calculate the areas of triangles and rectangles. For the quantity above that given
by market demand for the price, we see that the price has exceeded willingness
to pay. That is, marginal cost is greater than marginal benefit. So the lines past
this point, up to the market quantity, must be subtracted, giving us an area to
subtract in red.
Market Price
Market quantity
0
0
Price
Quantity
Subtract
Price
Add
Quantity
0
0
Quantity
For producer surplus, the first graph below depicts a quantity less than
the quantity supplied at the given price. Here we still add up all those line
segments between supply (marginal cost), and price (marginal benefit), to give
40
Price
an area. But now the area consists of a triangle and a rectangle. So be able
to calculate the areas of triangles and rectangles. For the quantity above that
given by market supply for the price, we see that the price is below what we
need to accept. That is, marginal cost is greater than marginal benefit. So the
lines past this point, up to the market quantity, must be subtracted, giving us
an area to subtract in red.
Market Price
Market quantity
0
0
Price
Quantity
Add
Price
Subtract
Quantity
0
0
Quantity
We don’t actually need to worry about the price when looking at total
surplus. The price of each unit is added for suppliers, and subtracted for consumers. So, it won’t make a difference when looking at total surplus. Below we
show total surplus by joining demand and supply (market demand and supply,
total surplus is about the WHOLE EQUILIBRIUM), from a below equilibrium
41
Price
quantity, and an above equilibrium quantity. Again, we use blue for the area
we add, and red for what we subtract. Again, know how to add the areas of
rectangles and triangles.
Quantity
0
0
Price
Quantity
Quantity
0
0
Quantity
Now let’s put all this to use. Markets maximising efficiency means that equilibrium maximises efficiency. Markets maximise efficiency because they achieve
three things. Production efficiency: minimising the costs of the quantity produced. Allocative efficiency: maximising the benefits of the quantity consumed.
Product-mix efficiency: choosing the best quantity, conditional on having production and allocative efficiency.
For production efficiency, observe that in a free market, the people who
42
produce and sell the good are precisely those with their marginal cost lower
than their marginal benefit; the price. If we fixed the quantity produced, then
any change-up in who produces what would leave some people producing more,
and others less. But because marginal cost is increasing in quantity, those who
produce more have a higher marginal cost, and those who produce less have
a lower marginal cost than the price that gave that quantity supplied. This
means swapping units from a high-cost seller to a low-cost seller gives us the
same quantity, at a lower cost. If we keep doing this, we will get back to the
way the market did things, so markets must minimise costs for a given quantity:
they are productively efficient.
We depict this by looking at two different sellers’ individual supply curves.
We suppose seller 1 decreases quantity from their individual quantity supplied at
a given price (which they would sell in an equilibrium with that price), and seller
2 increases from their individual quantity supplied at the price to compensate.
The blue quantities are given by the market price. The red quantities show the
non-market deviation.
Seller 1
Seller 2
Price
Higher marginal cost
Price
Lower marginal cost
0
0
Quantity
For allocative efficiency, observe that in a free market, the people who
buy the good are precisely those with their marginal benefit higher than their
marginal cost; the price. If we fixed the quantity produced, then any change-up
in who produces what would leave some people consuming more, and others
less. But because marginal benefit is decreasing in quantity, those who produce
more have a lower marginal benefit, and those who produce less have a higher
marginal benefit than the price that gave that quantity supplied. This means
swapping units from a low-benefit buyer to a high-cost seller gives us the same
quantity, at a higher total benefit. If we keep doing this, we will get back to the
way the market did things, so markets must maximise total benefit for a given
quantity: they are allocatively efficient.
43
We depict this by looking at two different buyers’ individual demand curves.
We suppose buyer 1 decreases quantity from their individual quantity demanded
at a given price (which they would consume in an equilibrium with that price),
and buyer 2 increases from their individual quantity demanded at the price
to compensate. The blue quantities are given by the market price. The red
quantities show the non-market deviation.
Price
Higher marginal benefit
Price
Lower marginal benefit
Buyer 1
0
Buyer 2
0
Quantity
We’ve basically already shown product-mix efficiency. We considered what
would happen if the same buyers as the market chose got the same amounts of
a good, and the same sellers gave it up, but at the wrong price. But the market
chooses the efficient levels of consumption of buyers and sellers for any quantity,
as we have just shown. We then combined the two and found that the price
didn’t make a difference. What mattered was the quantity. But let us return
to the graphs above with total surplus at non-equilibrium quantities. A belowequilibrium quantity results in wasted surplus, when there are still buyers with
their marginal benefits higher than sellers marginal costs. An above-equilibrium
quantity results in sellers marginal costs getting higher than buyers marginal
benefits, so we have to subtract marginal surplus past equilibrium, for a lower
total surplus. Therefore, markets satisfy product-mix efficiency.
21
Example of Deadweight Loss with Taxation
Deadweight loss refers to the difference in total surplus between on situation,
and the optimal situation (given by the market in our analysis above, although
under other circumstances, markets can fail). If the deadweight loss is positive,
it means we are doing worse than optimal.
Let’s consider the effects of a per-unit tax on buyers. Buyers pay price plus
44
tax now, shifting their demand (marginal benefit) down by the level of the tax
(as in the section on taxes and subsidies). But they still consume until price is
greater than marginal benefit, as they would without the tax. So the highest
marginal benefits still are the ones that consume the equilibrium quantity, with
tax. Allocative efficiency is still satisfied. We can think of buyers as getting
their marginal benefit from the no-tax demand curve, but losing price plus tax.
This just shifts both the curve and the price up by the tax, but it puts consumer
surplus in a more convenient location on the graph we will show.
Sellers have no tax, and just make exactly the same decisions as they would
without one, given the market quantity. So we still have production efficiency,
and we can depict as we would normally.
The government is also making money, which needs to be counted to total
surplus too, this is just the quantity times the tax. This add up to give us the
right value for the quantity assuming production and allocative efficiency, but
the quantity is lower than the, surplus-maximising, no-tax equilibrium, so we
must have a deadweight loss. All this is depicted in the graph below. Consumer surplus is in red stripes, producer surplus blue, and government revenue
in purple. Market surplus is all three added together. (DEMAND AND SUPPLY HERE ARE MARKET DEMAND AND MARKET SUPPLY, WE’RE
TALKING ABOUT EQUILIBRIUM AND TOTAL SURPLUS, WHICH ARE
ABOUT THE WHOLE MARKET.)
Market surplus
Price
Deadweight loss
Tax
Equilibrium qty.
Quantity
0
0
Quantity
If the tax were on sellers, the only difference is that supply (marginal cost)
would shift up by the tax, buyers would make the same choices as usual, since
they weren’t being taxed, and we could depict consumer surplus as normal.
But consumer surplus. Sellers still consume until marginal cost is greater than
marginal benefit, so we still have production efficiency. We can think of sellers
45
having the marginal cost given by their no-tax supply curve, and losing price
minus tax. This just shifts everything down by the tax, but puts producers
surplus in a more convenient location for the graph. Deadweight loss is the
same if the buyer and seller taxes are of the same size. We don’t need any
special tools to show this, we’ve already seen that within a market, under a
buyer or seller tax, everyone gives and gets the same things. So, they must all
have the same marginal benefits and costs.
Price
Deadweight loss
Tax
Equilibrium qty.
Quantity
Market surplus
0
0
Quantity
46