The demand for Derp is Q = 1200 – 2P. Suppose the supply of Derp is given by Q =

Question

The demand for Derp is Q = 1200 – 2P. Suppose the supply of Derp is given by Q = –600 +2P. What is the equilibrium price of Derp? What is the equilibrium quantity of Derp? What is the price elasticity of demand at the equilibrium price and quantity? What is the price elasticity of supply at the equilibrium price and quantity? For the next seven questions, suppose a per-unit excise tax of $50 per Derp is levied on the consumers. What price will sellers receive after the tax is levied? What price will consumers pay after the tax is levied? What percent of the tax will be paid by the consumers of Derp? (give an answer between 0 and 100) What percent of the tax will be paid by the suppliers of Derp? (give an answer between 0 and 100) How many Derps will be sold after the tax is imposed? How much consumer surplus do consumers get after the tax? What is the deadweight loss created by this tax?

Explanation / Answer

Demand: QD = 1,200 - 2P

Supply: QS = - 600 + 2P

(a) In equilibrium, quantity demanded equals quantity supplied.

1,200 - 2P = - 600 + 2P

4P = 1,800

P = $450

Q = 1,200 - (2 x 450) = 1,200 - 900 = 300

(b) Price elasticity of demand = (dQD/dP) x (P/QD) = - 2 x (450 / 300) = - 3

(c) Price elasticity of supply = (dQS/dP) x (P/QS) = 2 x (450 / 300) = 3

(d) Tax on consumers will decrease demand, shifting demand curve by $50 a every output level. New demand function becomes

QD = 1,200 - 2(P - 50) = 1,200 - 2P + 100 = 1,300 - 2P

Equating with QS,

1,300 - 2P = - 600 + 2P

4P = 1,900

P = $475 (Price paid by buyers)

Price received by sellers = $475 - $50 = $425

(e) Tax paid by buyers = After-tax price paid by buyers - Pre-tax price = $475 - $450 = $25

% of tax paid by buyers = $25 / $50 = 0.5 = 50%

(f) Tax paid by sellers = Pre-tax price - After-tax price received by sellers = $450 - $425 = $25

% of tax paid by sellers = $25 / $50 = 0.5 = 50%

(Note: An easier way to remember: Since demand and supply have equal absolute value of elasticity, buyers and sellers bear same % of tax)

(g) After tax, Q = - 600 + (2 x 425) = - 600 + 850 = 250

NOTE: As per Chegg Answering policy, first 8 parts are answered.

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