IMpact of Floor

Policy & the Perfectly Competitive Model: Consumer & Producer Surplus

Recall: Consumer surplus is the difference between what the consumer has to pay for a good and the amount he/she is willing to pay. It is the area under the demand curve & above the price.

P

S P*

D Q* Q

Producer surplus is the difference between what the producer receives for the good and the amount he/she must receive to be willing to provide the good. It is the area above the supply curve & below the price.

P

S P*

D Q* Q

Social WelfareSocial welfare = consumer surplus + producer surplus. In cases where there is tax revenue involved, that is added as well in the computation of social welfare.

Lets look at the sizes of the consumer & producer surpluses at various output levels.

At quantity Q1 & price P1, consumer surplus is the purple area & producer surplus is the green area.

P P1

S

D Q1 Q

As we increase the quantity & reduce the price, the total area of the consumer & producer surpluses increases,

P

SP2

D Q2 Q

and increases,

P

SP3

D Q3 Q

until we reach the perfectly competitive equilibrium.

P

S P*

D Q* Q

We can not continue this process beyond that equilibrium however. Output levels greater than the equilibrium will only be purchased at prices below the equilibrium price, but they will only be produced at prices above the equilibrium price. So there is no price at which those output levels will be produced & sold.

PPS PD

S

DQ4

Q

We have found that social welfare, which equals total consumer & producer surplus, is maximized at the perfectly competitive equilibrium.

How do we compare the social welfare of two different situations?1. Calculate the welfare from situation 1 by summing its consumer surplus and producer surplus: W1 = CS1 + PS1. 2. Calculate the welfare from situation 2 by summing its consumer surplus and producer surplus: W2 = CS2 + PS2. 3. Calculate the difference, W2 W1 = (CS2 + PS2) (CS1 + PS1). This tells us the gain or loss of welfare of one situation relative to the other. When a policy results in a loss of welfare to society, that loss is often referred to as the deadweight loss.

Notice that we just calculated the social welfare gain or loss as the difference in combined consumer and producer surplus, W2 W1 = (CS2 + PS2) (CS1 + PS1).An alternative equivalent way is the following. 1. Calculate the change in consumer surplus: CS = CS2 CS1 . 2. Calculate the change in producer surplus: PS = PS2 PS1 . 3. Add to get the total gain or loss in social welfare: CS + PS = (CS2 CS1) + (PS2 PS1)

Lets explore the welfare effects of some government policies.

Price CeilingsWithout the ceiling our consumer & producer surpluses are as shown by the purple & green areas.

P

S P*

D Q* Q

With price ceiling, Pc , the consumer & producer surpluses are as shown.

P

S

Pc D Qc Q

Consumers have lost area V but gained area U.

P

SV

Pc

U

D Qc Q

The consumers who gain are those who get the product at a lower price. The consumers who lose are those who are no longer able to buy the product because there is less supplied.

PSV

Pc

U

D

Qc

Q

In the graph shown, area U is larger than area V, so consumers as a whole gain. However, if area U is smaller than area V, consumers lose.

P

SV

Pc

U

D Qc Q

Producers have lost areas U and W.

P

S

Pc

U

W

D Qc Q

So area U just moved from producers to consumers, but areas V and W were lost to everyone.

P

SV W

Pc

U

D Qc Q

Area V+W is the difference in the total consumer and producer surplus with and without the policy (CS2 + PS2) (CS1 + PS1).

P

SV W

Pc

It is the deadweight loss to society that results from the policy.

D Qc Q

Price Ceiling Example: Rent Controls Suppose in the absence of controls, equilibrium rent would be 8 thousand dollars per year & equilibrium quantity would be 2 million apartments.Rent (thousands of dollars per year)

S

8

D0 2.0 Quantity of apartments (millions)

Next suppose that a price ceiling of 7 thousand dollars is imposed. As a result the quantity supplied drops to 1.8 million.Rent (thousands of dollars per year)

S

8 7

D0 1.8 2.0 Quantity of apartments (millions)

Based on the graph, determine the effects on consumers, producers, & society as a whole.Rent (thousands of dollars per year)

S

9 8 7

D0 1.8 2.0 Quantity of apartments (millions)

Recall that consumers gain area U and lose area V. Producers lose areas U and W.Rent (thousands of dollars per year)

SV W

9 8 7U

D0 1.8 2.0 Quantity of apartments (millions)

U = (1.8 million) (8,000 7,000) = $1,800 million V = (1/2)(0.2 million)(1,000) = $100 million W = (1/2)(0.2 million)(1,000) = $100 millionRent (thousands of dollars per year)

SV W

9 8 7U

D0 1.8 2.0 Quantity of apartments (millions)

Consumers gain U V = $1,800 million - $100 million = $1,700 million. Producers lose U + W = $1,800 million + $100 million = $1,900 millionRent (thousands of dollars per year)

SV W

9 8 7U

D0 1.8 2.0 Quantity of apartments (millions)

Producers lose $200 million dollars more than consumers gain. So there is a deadweight loss of $200 million per year.Rent (thousands of dollars per year)

SV W

9 8 7U

D0 1.8 2.0 Quantity of apartments (millions)

Are the effects of price floors similar to those of price ceilings?

Once again without the floor, consumer & producer surpluses are as shown by the purple & green areas.

P

S P*

D Q* Q

If a price floor of Pf is imposed, consumer & producer surpluses are these purple & green areas.

P

SPf

D Qf Q

Consumers lose areas U & V.P

SPfU

V

D Qf Q

Producers gain area U & lose area W.P

SPfU W

D Qf Q

Again the deadweight loss is area V+W .P

SPfV W

D Qf Q

In the analysis that we just did, we assumed that producers cut their output so that it was just equal to Qf, the quantity demanded.

P

SPf

D Qf Q

However, it doesnt always work that way. In the case of agricultural price supports, producers grow as much as they want and the government buys the surplus.

At a price of Pf, producers will supply Qs. The resulting surplus is Qs Qd, which is purchased by the government with taxpayer money at price Pf. This represents a cost to consumers of the gray rectangle T.

P

SPf

P*T

D Qd Qs Q

Consumer surplus also falls by area U + V. So consumers lose a total of T + U + V .

P

SPfU

P*

VT

D Qd Qs Q

Remember that producer surplus is the area under the price and above the supply curve. So producer surplus increases from the orange area to the yellow area.

P

SPf

P*D Qf Q

The increase in producer surplus is the pink area.

P

SPf

P*D Qf Q

That gain to producers is much smaller than the loss to consumers (T + U + V).

P

SPfU

P*

VT

Therefore, as a result of the price floor, total social welfare falls.

D Qd Qs Q

Next, well examine the effect of a sales tax.

Suppose a tax of $0.25 per unit is imposed on an item. From the consumers perspective, it is as if the supply curve has shifted up vertically by the tax amount of $0.25.

P$0.25

S

S

1.50

D50

Q

The equilibrium quantity falls & the equilibrium price rises. Although the price rises, it does not rise by the full amount of the tax.

P$0.25$0.25

S

S

1.50

D40 50

Q

The buyer pays (in this example) 15 cents more than before. The seller gets 25 cents less than the buyer pays. So the seller gets 10 cents less than before.

P$0.25

S

S

1.65 1.50 1.40

D40 50

Q

Consumer surplus falls by area U + V.

P1.65 1.50 1.40U

S

SV

D40 50

Q

Producer surplus falls by area X + W.

P1.65 1.50 1.40X W

S

S

D40 50

Q

Tax revenues equal the tax per unit times the number of units sold. So the area U + X is the government tax revenue.

P1.65 1.50 1.40U X

S

S

D0 40 50

Q

The total change in social welfare is the change in consumer surplus [-(U + V)] plus the change in producer surplus [-(X + W)] plus the government revenue (U + X), which equals [-U - V] + [-X - W] + (U + X) = V W or (V + W) .

P1.65 1.50 1.40U X

S

SV WThe negative sign in front of the V + W indicates that it is a loss of V + W.

D0 40 50

Q

So area V + W is deadweight loss.

P1.65 1.50 1.40V W

S

S

D0 40 50

Q

Next, well examine the effects of international trade and of tariffs & quotas.

Domestic Demand Curve (DD ): Demand for Cars by U.S. Consumers

price

DD quantity

Domestic Supply Curve (SD ): Supply of Cars to U.S. Consumers by U.S. Producers price SD

DD quantity

Without trade: price is P1 & quantity is Q1.

priceP1

SD

DD O Q1 quantity

Without trade: consumer surplus is area A ...

priceA

SD

P1 DD

O

Q1

quantity

... and producer surplus is area B.

priceP1

SDB

DD

O

Q1

quantity

Total Supply Curve (ST ): Supply of Cars to U.S. Consumers by All Producers

priceP1

SD

STDD

O

Q1

quantity

With trade: price is P2 and quantity purchased by U.S. consumers is Q2. priceP1 P2 SD

STDD

O

Q 1 Q2

quantity

The quantity sold by U.S. producers is Q0 and the quantity of imports is Q2 Q0.

priceP1 P2

SD

STDD

O

Q 0 Q1 Q2

quantity

With trade: Consumer Surplus is area C

priceP1 P2C

SD

STDD

O

Q 0 Q1 Q2

quantity

Recall: Without trade, consumer surplus was area A. Consumers have gained price SD area C-A A from trade. P1 C A ST P2DD

O

Q 0 Q1 Q2

quantity

Suppose we are viewing this issue from the perspective of the U.S. government.

Our concern is the welfare of U.S. consumers and U.S. producers (not foreign producers). Domestic producer surplus is the area above the domestic supply curve and below the price.

With trade: (Domestic) Producer Surplus is area D. priceP1 P2 D SD

STDD

O

Q 0 Q1 Q2

quantity

Recall: Without trade, producer surplus was area B. priceP1 P2 B SD

STDD

O

Q 0 Q1 Q2

quantity

Producers have lost area B D from trade.

priceP1 P2B-D

SD

STDD

O

Q 0 Q1 Q2

quantity

So consumers have gained area C A ...

priceP1 P2CA

SD

STDD

O

Q 0 Q1 Q2

quantity

... and producers have lost area B D.

priceP1 P2B-D

SD

STDD

O

Q 0 Q1 Q2

quantity

So for U.S. citizens, there is a net gain from trade of area G.

priceP1 P2G

SD

STDD

O

Q 0 Q1 Q2

quantity

Putting it all together: Relative to the no-trade situation, when there is free trade,the price paid by U.S. consumers is lower. the quantity purchased by U.S. consumers is higher. there is a gain in consumer surplus. there is a loss of producer surplus. there is a net gain to U.S. citizens or a gain in total social welfare.

The net gain we just found was the gain from free trade, that is, trade without tariffs or quotas.Lets look now at the effect that quotas & tariffs have on consumer & producer surplus. In the analysis that follows, we assume that a single countrys production of a good is small relative to total world production. Therefore, the equilibrium price of the good in the world as a whole is not changed by the policy of a single country. Suppose a tariff of t dollars is imposed on cars imported to the U.S.

Suppose a tariff of t dollars is imposed on cars imported to the U.S. The price of domestic cars in the U.S. will rise so that the new price equals the pre-tariff price + the tariff t.

price

SD

P 2+ t P2

t

ST DD

O

Q0

Q1

Q2

quantity

The total number of cars purchased by U.S. consumers will fall to Q2, the number of domestic cars purchased will rise to Q0, and the number of imported cars will fall to Q2 Q0.

price

SD

P2+ t P2

ST DD

O

Q0 Q0 Q1

Q2 Q2

quantity

How will consumer & domestic producer surplus change?

Consumer surplus will fall from this area

price

SD

P2+ t P2

t

ST DD

O

Q0 Q0 Q1

Q2 Q2

quantity

to this area

price

SD

P2+ t P2

ST DD

O

Q0 Q0 Q1

Q2 Q2

quantity

which is a loss of consumer surplus of this area.

price

SD

P2+ t P2

t

ST DD

O

Q0 Q0 Q1

Q2 Q2

quantity

Domestic producer surplus rises from this area

price

SD

P2+ t P2

ST DD

O

Q0 Q0 Q1

Q2 Q2

quantity

to this area

price

SD

P2+ t P2

ST DD

O

Q0 Q0 Q1

Q2 Q2

quantity

which is an increase in domestic producer surplus of this area.

price

SD

P2+ t P2

ST DD

O

Q0 Q0 Q1

Q2 Q2

quantity

Government revenues from the tariff are the number of imports times the tariff per import, which is this area.

price

SD

P2+ t P2

t

ST DD

O

Q0 Q0 Q1

Q2 Q2

quantity

The deadweight loss from the tariff is the change in consumer surplus + the change in domestic producer surplus + the government tariff revenue.

price

SD

So the deadweight loss is the area of these two triangles.

P2+ t P2

ST DD

O

Q0 Q0 Q1

Q2 Q2

quantity

What is the effect of an import quota instead of a tariff?Suppose the government establishes a quota of q . Then the price of cars will rise until the quantity supplied by domestic producers + the import quota = the quantity demanded by U.S. consumers.

Suppose the quota is q = Q2 Q0. The new price will be P3.

price

SD

P3 P2

ST DD

O

Q0 Q0 Q1

Q2 Q2

quantity

Again consumer surplus falls by this area.

price

SD

P3 P2

t

ST DD

O

Q0 Q0 Q1

Q2 Q2

quantity

Domestic producer surplus increases by this area.

price

SD

P3 P2

ST DD

O

Q0 Q0 Q1

Q2 Q2

quantity

However there is no additional government revenue. So the deadweight loss from a quota is this area which is greater than the deadweight loss from a comparable tariff.

price

SD

P3 P2

ST DD

O

Q0 Q0 Q1

Q2 Q2

quantity

We have shown that a perfectly competitive economy maximizes the total net gain of consumers & producers. We saw that deadweight losses (reductions in economic efficiency) resulted if the government imposes a price ceiling, price floor, import tariff or quota, or sales tax. The general theme seems to be that the economy would be better off if the government quit meddling & let competitive markets alone. This is frequently sound advice but not always. There are often other objectives besides economic efficiency to be considered (for example, equity or fairness). Also, there may be externalities involved. In addition, sometimes markets are not competitive.