Question

Suppose that the demand curve for a particular commodity is P=17-2D, where D is the quantity demanded and P is the price. The supply curve for the commodity is P=2+S, where S is quantity supplied. (1)Find the equilibrium price and output. Suppose now that a unit tax of 3 dollars is imposed on the commodity. (2) Show the new equilibrium is the same regardless of whether the tax is imposed on producers or buyers of the commodity. (3) Calculate the deadweight loss.

Answer 1

(1) In equilibrium, Demand equals supply (and D = S = Q).

17 - 2Q = 2 + Q

3Q = 15

Q = 5

P = 2 + 5 = 7

(2)

(a) If tax is imposed on producers, supply curve shifts leftward and new supply function becomes

P - 3 = 2 + Q

P = 5 + Q

Equating with demand,

17 - 2Q = 5 + Q

3Q = 12

Q = 4

P = 5 + 4 = $9 (Price paid by buyers)

Price received by sellers = 9 - 3 = $6

(b) If tax is imposed on buyers, demand function shifts leftward and new demand function becomes

P + 3 = 17 - 2Q

P = 14 - 2Q

Equating with supply,

14 - 2Q = 2 + Q

3Q = 12

Q = 4

P = 2 + 4 = $6 (Price received by sellers)

Price paid by buyers = $6 + $3 = $9

Therefore, results are the same in case (a) and case (b).

(3) Deadweight loss = (1/2) x Tax per unit x Change in quantity = (1/2) x $3 x (5 - 4) = $1.5 x 1 = $1.5