Policy & the Perfectly Competitive Model: Consumer & Producer Surplus

1. Policy & the Perfectly Competitive Model: Consumer & Producer Surplus

2. 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*

3. 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*

4. 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.

5. Let’s look at the sizes of the consumer & producer surpluses at various output levels.

6. At quantity Q1 & price P1, consumer surplus is the purple area & producer surplus is the green area. P S P1 D Q Q1

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

8. and increases, P S P3 D Q Q3

9. until we reach the perfectly competitive equilibrium. P S P* D Q Q*

10. 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 Q Q4

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

12. 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.

13. 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)

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

15. Price Ceilings Without the ceiling our consumer & producer surpluses are as shown by the purple & green areas. P S P* D Q Q*

16. With price ceiling, Pc , the consumer & producer surpluses are as shown. P S Pc D Q Qc

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

18. 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

19. 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

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

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

22. 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

23. Price Ceiling Example: Rent ControlsSuppose 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 D Quantity of apartments (millions) 0 2.0

24. 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 D Quantity of apartments (millions) 0 1.8 2.0

25. 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) 0 1.8 2.0

26. Recall that consumers gain area U and lose area V.Producers lose areas U and W. Rent (thousands of dollars per year) S 9 8 7 V W U D Quantity of apartments (millions) 0 1.8 2.0

27. U = (1.8 million) (8,000 – 7,000) = $1,800 million V = (1/2)(0.2 million)(1,000) = $100 millionW = (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) 0 1.8 2.0

28. 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) 0 1.8 2.0

29. 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) 0 1.8 2.0

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

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

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

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

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

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

36. 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

37. 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.

38. 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

39. 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

40. 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

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

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

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

44. 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

45. 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 40 50

46. 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 40 50

47. Consumer surplus falls by area U + V. S’ P S 1.65 1.50 1.40 U V D Q 40 50

48. Producer surplus falls by area X + W. S’ P S 1.65 1.50 1.40 W X D Q 40 50

49. Tax revenues equal the tax per unit times the number of units sold. So the area U + X is the government tax revenue. S’ P S 1.65 1.50 1.40 U X D Q 0 40 50

50. 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 0 40 50