Assume a profit maximizing monopolist faces the following

Question

Q1. The demand and supply curves for beer are

Demand: Q_d = 50 - 2P_d

Supply: Q_s  = 2P_s

where Q_D is the quantity of beer demanded per year (in millions of cases), Q_S is the quantity of beer supplied (in millions of cases), and P is the price is of beer (in dollars per case).

a) Assume that the beer industry is perfectly competitive   Calculate the equilibrium quantity and price of beer. (Hint: Replace Qd = Q, Qs = Q, Pd = P and Ps = P in the demand and supply equations given above and then set demand = supply to solve for the equilibrium price and quantity).

b) If a tax of $5 per case is imposed, calculate;

i. the price the consumers pay.

ii. the price the sellers receive.

iii. the change in consumer surplus and producer surplus.

iv. the dead weight loss.

c) Starting with a perfectly competitive outcome (part a), assume now that the world price of beer is $8 per case and there is free trade in beer.  The government imposes an import quota of 10 million cases of beer.  

i. Explain why the government may want to impose a quota.

ii. Calculate the domestic price of beer after the quota is imposed.

Q2. Assume a profit maximizing monopolist faces the following demand, marginal revenue and cost functions:

Demand: P = 400 - 50Q

Total Cost: TC = 100Q

Marginal cost MC = 100

Marginal Revenue MR = 400 - 100Q

a) Find the monopolist's profit maximizing output level.

b) At this level of output what price will the monopolist charge?

c) What is the monopolists total profit?

d) If the monopolist were a revenue maximizer instead of a profit maximizer, what would be the monopolists output level?