Policy & the Perfectly Competitive Model: Consumer & Producer Surplus

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

Let’s 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.

As we increase the quantity & reduce the price, the total area of the consumer & producer surpluses increases, P S P2 D Q Q2

and increases, P S P3 D Q3 Q

until we reach the perfectly competitive equilibrium.
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. P S PS PD D Q4 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?
Calculate the welfare from situation 1 by summing its consumer surplus and producer surplus: W1 = CS1 + PS1. Calculate the welfare from situation 2 by summing its consumer surplus and producer surplus: W2 = CS2 + PS2. 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. Calculate the change in consumer surplus: ΔCS = CS2 – CS1 . Calculate the change in producer surplus: ΔPS = PS2 – PS1 . Add to get the total gain or loss in social welfare: ΔCS + ΔPS = (CS2 – CS1) + (PS2 – PS1)

Let’s explore the welfare effects of some government policies.

Price Ceilings P S P* D Q Q*
Without 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.
Q Qc

Consumers have lost area V but gained area U.
P S V U Pc D Q Qc

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. P S V U Pc D Q Qc

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 S V Pc U D Q Qc

Producers have lost areas U and W.
Pc U D Q Qc

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

Area V+W is the difference in the total consumer and producer surplus with and without the policy (CS2 + PS2) – (CS1 + PS1). P S V It is the deadweight loss to society that results from the policy. W Pc D Q Qc

Price Ceiling Example: Rent Controls Suppose in the absence of controls, equilibrium rent would be \$8,000 per year and quantity would be 2 million apartments. Rent (thousands of dollars per year) S 9 8 7 D 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 D Quantity of apartments (millions)

U = (1. 8 million) (8,000 – 7,000) = \$1,800 million V = (1/2)(0
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 million Rent (thousands of dollars per year) S 9 8 7 V W U D Quantity of apartments (millions)

Consumers gain U – V = \$1,800 million - \$100 million = \$1,700 million
Consumers gain U – V = \$1,800 million - \$100 million = \$1,700 million. Producers lose U + W = \$1,800 million + \$100 million = \$1,900 million Rent (thousands of dollars per year) S 9 8 7 V W U D Quantity of apartments (millions)

Producers lose \$200 million dollars more than consumers gain
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) S 9 8 7 V W U D Quantity of apartments (millions)

Are the effects of price floors similar to those of price ceilings
Are the effects of price floors similar to those of price ceilings? Let’s see.

Once again without the floor, consumer & producer surpluses are as shown by the purple & green areas. S D P Q P* Q*

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

Consumers lose areas U & V.
P S Pf U V D Q Qf

Producers gain area U & lose area W.
Pf U W D Q Qf

Again the deadweight loss is area V+W .
P S Pf V W D Q Qf

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 S Pf D Q Qf

However, it doesn’t always work that way
However, it doesn’t 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 S Pf P* T D Q Qd Qs

Consumer surplus also falls by area U + V.
So consumers lose a total of T + U + V . P S Pf P* U V T D Q Qd Qs

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 S Pf P* D Q Qf

The increase in producer surplus is the pink area.
Pf P* D Q Qf

That gain to producers is much smaller than the loss to consumers (T + U + V).
Pf P* U Therefore, as a result of the price floor, total social welfare falls. V T D Q Qd Qs

Next, we’ll examine the effect of a sales tax.

Suppose a tax of \$0.25 per unit is imposed on an item.
From the consumer’s perspective, it is as if the supply curve has shifted up vertically by the tax amount of \$0.25. S’ P S \$0.25 1.50 D Q 50

The equilibrium quantity falls & the equilibrium price rises.
Although the price rises, it does not rise by the full amount of the tax. S’ P S \$0.25 1.50 \$0.25 D Q

The buyer pays (in this example) 15 cents more than before
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. S’ P S \$0.25 1.65 1.50 1.40 D Q

Consumer surplus falls by area U + V.
1.65 1.50 1.40 U V D Q

Producer surplus falls by area X + W.
1.65 1.50 1.40 W X D Q

Tax revenues equal the tax per unit times the number of units sold
Tax revenues equal the tax per unit times the number of units sold. The area U + X is the government tax revenue. S’ P S 1.65 1.50 1.40 U X D 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) . S’ P S 1.65 1.50 1.40 U V The negative sign in front of the V + W indicates that it is a loss of V + W. W X D Q

So area V + W is deadweight loss.
P S 1.65 1.50 1.40 V W D Q

Next, we’ll 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
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.
SD P1 O DD Q1 quantity

Without trade: consumer surplus is area A ...
price SD P1 O A DD Q1 quantity

... and producer surplus is area B.
price SD P1 O B DD Q1 quantity

Total Supply Curve (ST ): Supply of Cars to U. S
Total Supply Curve (ST ): Supply of Cars to U.S. Consumers by All Producers price SD P1 O ST DD Q1 quantity

With trade: price is P2 and quantity purchased by U.S. consumers is Q2.
SD ST DD Q1 Q2 quantity

The quantity sold by U.S. producers is Q0 and the quantity of imports is Q2 – Q0.
price P1 P2 O SD ST DD Q0 Q1 Q2 quantity

With trade: Consumer Surplus is area C
price P1 P2 O SD C ST DD Q0 Q1 Q2 quantity

Recall: Without trade, consumer surplus was area A.
Consumers have gained area C-A from trade. price P1 P2 O SD A ST C – A DD Q0 Q1 Q2 quantity

Suppose we are viewing this issue from the perspective of the U. S
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.
price P1 P2 O SD ST D DD Q0 Q1 Q2 quantity

Recall: Without trade, producer surplus was area B.
price P1 P2 O SD ST B DD Q0 Q1 Q2 quantity

Producers have lost area B – D from trade.
price P1 P2 O SD ST B - D DD Q0 Q1 Q2 quantity

So consumers have gained area C – A ...
price P1 P2 O SD ST C – A DD Q0 Q1 Q2 quantity

... and producers have lost area B – D.
price P1 P2 O SD ST B - D DD Q0 Q1 Q2 quantity

So for U.S. citizens, there is a net gain from trade of area G.
price P1 P2 O SD ST G DD Q0 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.
Let’s look now at the effect that quotas & tariffs have on consumer & producer surplus. In the analysis that follows, we assume that a single country’s 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.

SD price P2+ t ST P2 O DD quantity
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. SD price t P2+ t ST P2 O DD Q Q Q2 quantity

SD price P2+ t P2 ST O DD 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’. SD price P2+ t P2 O ST DD Q0 Q0’ Q Q2’ Q2 quantity

How will consumer & domestic producer surplus change?

Consumer surplus will fall from this area
SD price P2+ t P2 O ST t DD Q0 Q0’ Q Q2’ Q2 quantity

to this area SD price P2+ t P2 O ST DD Q0 Q0’ Q Q2’ Q2 quantity

which is a loss of consumer surplus of this area.
SD price P2+ t P2 O ST t DD Q0 Q0’ Q Q2’ Q2 quantity

Domestic producer surplus rises from this area
SD price P2+ t P2 O ST DD Q0 Q0’ Q Q2’ Q2 quantity

to this area SD price P2+ t P2 O ST DD Q0 Q0’ Q Q2’ Q2 quantity

which is an increase in domestic producer surplus of this area.
SD price P2+ t P2 O ST DD Q0 Q0’ Q Q2’ Q2 quantity

SD price P2+ t P2 ST O DD quantity
Government revenues from the tariff are the number of imports times the tariff per import, which is this area. SD price P2+ t P2 O ST t DD Q0 Q0’ Q Q2’ Q2 quantity

SD price P2+ t P2 ST O DD quantity
The deadweight loss from the tariff is the change in consumer surplus + the change in domestic producer surplus + the government tariff revenue. SD So the deadweight loss is the area of these two triangles. price P2+ t P2 O ST DD Q0 Q0’ Q 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. SD price P3 P2 O ST DD Q0 Q0’ Q Q2’ Q2 quantity

Again consumer surplus falls by this area.
SD price P3 P2 O ST t DD Q0 Q0’ Q Q2’ Q2 quantity

Domestic producer surplus increases by this area.
SD price P3 P2 O ST DD Q0 Q0’ Q Q2’ Q2 quantity

SD price P3 P2 ST O DD 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. SD price P3 P2 O ST DD Q0 Q0’ Q 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.

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