Question

Suppose the aggregate demand for honey in a small country is given by Q^D = 100 − P and the aggregate supply is Q^S = P. The international price of honey is P^I = 60, and the world market is willing to buy or sell any amount at that price. Let all quantities be given in gallons and all prices in dollars per gallon. Suppose the country initially starts out with closed borders, and cannot import or export at all.

(a) What is the equilibrium price of honey in the domestic market?

(b) How much consumer surplus, producer surplus, and total welfare is generated by the honey market? Suppose the government recognizes how delicious honey is and decides to subsidize its purchase. They offer consumers a $5 rebate on every gallon of honey purchased.

(c) Find the new equilibrium price and quantity with the rebate.

(d) How would this answer change if the subsidy were given to producers instead of consumers?

(e) Compute the consumer surplus, producer surplus, transfers, and social welfare generated by the subsidy. Depict these graphically. How does each piece of social welfare compare to the competitive equilibrium?

(f) What is the deadweight loss of the subsidy? Propose a set of transfers in the competitive equilibrium such that everyone in the economy would be at least as well off as they are under the subsidy.

Answer 1

(a)

In equilibrium, QD = QS.

100 - P = P

2P = 100

P = $50

Q = P = 50

(b)

From demand function, when QD = 0, P = 100 (Vertical intercept of demand curve).

Consumer surplus (CS) ($) = Area between demand curve & price = (1/2) x (100 - 50) x 50 = 25 x 50 = 1,250

From supply function, when QS = 0, P = 0 (Vertical intercept of supply curve).

Producer surplus (PS) ($) = Area between supply curve & price = (1/2) x (50 - 0) x 50 = 25 x 50 = 1,250

(c)

The subsidy will decrease effective cost of production, so producers will increase supply. The supply curve will shift rightward by $5 at every output and new supply function will be

QS = P + 5

Equating with QD,

100 - P = P + 5

2P = 95

P = $47.5 (Price paid by buyers)

Price received by sellers = $47.5 + $5 = $52.5

Q = 100 - 47.5 = 52.5

(d)

If subsidy was given to consumers, effective price paid by buyers will fa,, so consumers will increase demand. The demand curve will shift rightward by $5 at every output and new demand function will be

QD = 100 - P + 5 = 105 - P

Equating with QS,

105 - P = P

2P = 105

P = $52.5 (Price received by sellers)

Price paid by buyers = $52.5 - $5 = $47.5

Q = P = 52.5

Therefore the outcome would be the same as in part (c).

NOTE: As per Answering Policy, 1st 4 parts are answered.