The market demand function for corn is Qd = 15 - 2P and the market supply functi
ID: 1124087 • Letter: T
Question
The market demand function for corn is Qd = 15 - 2P and the market supply function is Qs = 5P -2.5, both measured in billions of bushels per year. The initial equilibrium price is $2.50, and the initial equilibrium quantity is 10 billion bushels. Consumer surplus is $25, producer surplus is $10, and aggregate surplus is $35. Suppose the government gives corn farmers a subsidy of $0.70 per bushel of corn. What will be the effects on aggregate surplus, consumer surplus, and producer surplus? What will be the deadweight loss created by the subsidy?
Explanation / Answer
The subsidy will effectively lower the cost of production for firms, and supply will increase. New supply function is
Qs = 5(P + 0.7) - 2.5
Qs = 5P + 3.5 - 2.5
Qs = 5P + 1
Equating Qs with Qs,
15 - 2P = 5P + 1
7P = 14
P = $2 (Price paid by buyers)
Price received by sellers = $2 + $0.7 = $2.7
Q = (5 x 2) + 1 = 10 + 1 = 11 (billion)
From demand function, when Qd = 0, P = 15/2 = $7.5 (Reservation price)
New CS = Area between demand curve & price = (1/2) x $(7.5 - 2) x 11 = (1/2) x $5.5 x 11 = $30.25
New PS = Area between supply curve & price = (1/2) x $(2.7 - 0) x 11 = (1/2) x $2.7 x 11 = $29.7
Aggregate surplus = CS + PS = $(30.25 + 29.7) = $59.95
Deadweight loss = (1/2) x Unit subsidy x Difference in Quantity = (1/2) x $0.7 x (11 - 10) - $0.35 x 1 = $0.35
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