Question

Suppose the demand for and supply of ethanol in a small town are as follow:

Qd = 9,000 - 1,000P
Qs = 2,000P - 3,000

● Where Q measures gallons per day and P represents price per gallon. The current equilibrium price $4, and the current equilibrium quantity is 5,000 gallons per day.
● Now suppose that the government wants to create a subsidy of $0.375 per gallon to encourage the use of ethanol.

a. What will happen to the price buyers pay per gallon, the price sellers receive per gallon, and the number of gallons consumed each day?
b. How much will this subsidy cost the government?

Answer 1

In free market equilibrium, Qd = Qs.

9,000 - 1,000P = 2,000P - 3,000

3,000P = 12,000

P = 4

Q = 9,000 - 4 x 1,000 = 9,000 - 4,000 = 5,000

(a)

The subsidy will shift supply curve rightward by $0.375 at every quantity, and new supply function is

Qs1 = 2,000 x (P + 0.375) - 3,000

Qs1 = 2,000P + 750 - 3,000

Qs1 = 2,000P - 2,250

Equating Qd and Qs1,

9,000 - 1,000P = 2,000P - 2,250

3,000P = 11,250

P = $3.75 (Price paid by buyers)

Price received by sellers = $3.75 + $0.375 = $4.125

Q = 9,000 - 3.75 x 1,000 = 9,000 - 3,750 = 5,250

So,

Price paid by buyers decreases by $(4 - 3.75) = $0.25.

Price received by sellers increases by $(4.125 - 4) = $0.125.

Quantity increases by (5,250 - 5,000) = 250.

(b)

Cost of subsidy = Unit subsidy x Quantity after subsidy = $0.375 x 5,250 = $1,968.75