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

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