Suppose that the demand curve for wheat is q = 100 - 10p and the supply curve is q = 10p. the government imposes a price support at p = 6 using a deficiency payment program. What is the quantity supplied, the price that clears the market, and the deficiency payment? What effect does this program have on consumer surplus, producer surplus, welfare, and deadweight loss?

Solution:

In free trade equilibrium, quantity demanded equals quantity supplied:

100 - 10p = 10p

20p = 100

p = 5

q = 10 x 5 = 50

When p = 6, this is the market price for a price support program, since it is above equilibrium price and therefore, is binding.

Quantity demanded = 100 - (10 x 6) = 100 - 60 = 40

Quantity supplied = 10 x 6 = 60

Surplus = 60 - 40 = 20

Deficiency payment = 6 x 20 = 120

Since producers will sell only the quantity that consumers will buy, relevant quantity = 40.

From demand function, when q = 0, p = 100/10 = 10 (reservation price)

Consumer surplus (CS) = Area between demand curve and market price

CS before price floor = (1/2) x (10 - 5) x 50 = 25 x 5 = 125

CS after price floor = (1/2) x (10 - 6) x 40 = 20 x 4 = 80

Decrease in CS due to price floor = 125 - 80 = 45

When quantity supplied = 60, from demand function: 60 = 100 - 10p, or 10p = 40, or p = 4

Producer surplus (PS) = Area between supply curve and market price

PS before price floor = (1/2) x (5 - 0) x 50 = 25 x 5 = 125

PS after price floor = (1/2) x [ (6 - 0) + (6 - 4) ] x 40 = 20 x (6 + 2) = 20 x 8 = 160

Increase in PS after price floor = 160 - 125 = 35

Deadweight loss = (1/2) x (6 - 4) x (50 - 40) = (1/2) x 2 x 10 = 10