Question

The demand and supply conditions of market for beer are given by the following equations: Qd = 72 - P and Qs = -18 + P a) Find the initial equilibrium price and quantity. b) Calculate the consumer surplus and producer surplus for the equilibrium. c) Suppose that government impose a price floor at P=66 to control the consumption of beer. Is this policy effective? What are price and quantity consumed after this intervention of government? d) Going back to equilibrium in part a), suppose now that government restricts the production of the beer and set a quota of 20 in this market. What are price and quantity consumed after this intervention of government? Going back to equilibrium in part a), suppose now that the government imposes a tax of $10 per unit on producers and the producers adjust the supply function to include the tax when t-10. Illustrate with a diagram how the producer tax of 10 will affect the market demand and supply curves. Find the new equilibrium price and quantity after the tax. Show the initial and after tax equilibrium on your graph. Who gets the higher burden of the tax? Calculate the percentage tax share paid by consumers and producers. Also, calculate the deadweight loss associated with the tax policy. f) Going back to equilibrium in part a), suppose now that the government imposes a tax of $10 per unit on consumers. Show that your findings are equivalent to results you found for the case of producer tax.

Answer 1

(a)

In equilibrium, Qd = Qs

72 - (2P/3) = - 18 + P

5P/3 = 90

P = 54

Q = - 18 + 54 = 36

(b)

When Qd = 0, P = (72 x 3)/2 = 108

CS = (1/2) x (108 - 54) x 36 = 18 x 54 = 972

When Qs = 0, P = 18

PS = (1/2) x (54 - 18) x 36 = 18 x 36 = 648

(c)

When P = 66, it is higher than equilibrium price and so is effective.

Market price = 66

Qd = 72 - (2 x 66/3) = 72 - 44 = 28

Qs = - 18 + 66 = 48

Market quantity = min(Qd, Qs) = 28

(d)

When Qs = 20,

Quantity consumed = 20

From supply function,

20 = - 18 + P

P = 38 (market price)

NOTE: As HOMEWORKLIB Answering Policy, 1st 4 parts are answered.