2. Consider a market for a certain prescription drug where demand is Q2500 50P a
ID: 1127072 • Letter: 2
Question
2. Consider a market for a certain prescription drug where demand is Q2500 50P and supply is Qs-150P - 500. a. Calculate the equilibrium price and quantity. b. i, Calculate the own-price elasticity of demand and the elasticity of supply at equilibrium. ii. At what price is the elasticity of demand =-0.5? c. Calculate the consumer surplus and producer surplus at equilibrium. d. Suppose the government imposes a tax of $2 per unit. What are the new equilibrium price (paid by consumers) and quantity? e. What are producer and consumer surplus now? f. How much revenue is generated by the tax? g. What is the deadweight loss? h. Suppose instead the government introduced a subsidy of $3 per unit. What are the new equilibrium quantity, consumer price and producer price?Explanation / Answer
QD = 2500 - 50P
QS = 150P - 500
(a) In euilibrium, QD = QS
2500 - 50P = 150P - 500
200P = 3000
P = 15
Q = 2500 - (50 x 15) = 2500 - 750 = 1750
(b)
(i)
Elasticity of demand = (dQD/dP) x (P/QD) = - 50 x (15 / 1750) = - 0.43
Elasticity of supply = (dQS/dP) x (P/QS) = 150 x (15 / 1750) = 1.29
(ii)
- 0.5 = - 50 x [P / (2500 - 50P)]
0.5 = 50 x [P / (2500 - 50P)]
1250 - 25P = 50P
75P = 1250
P = 16.67
(c)
From demand function, when QD = 0, P = 2500 / 50 = 50 (Reservation price)
Consumer surplus = Area between demand curve and market price = (1/2) x (50 - 15) x 1750 = 875 x 35 = 30625
From supply function, when QS = 0, P = 500/150 = 3.33 (Minimum price)
Producer surplus = Area between supply curve and market price = (1/2) x (15 - 3.33) x 1750 = 875 x 11.67 = 10208
(d) The tax will shift the supply curve leftward by $2 at every output level and new supply function is
QS = 150(P - 2) - 500 = 150P - 300 - 500 = 150P - 800
Equating with QD,
2500 - 50P = 150P - 800
200P = 3300
P = 16.5 (Price paid by buyers)
Price received by sellers = 16.5 - 2 = 14.5
Q = 2500 - (50 x 16.5) = 2500 - 825 = 1675
NOTE: As per Chegg answering guidelines, first 4 parts are answered.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.