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# Important Aspects of Profit Maximization

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1. A monopolist has the possibility of price discriminating between domestic and foriegn markets for a product. The demands are Qd = 21-0.1P in the domestic market and Qf = 50-0.4P in the foriegn market. The monopolist's short-run total cost function is STC = 2000+10Q, where Q = Qd+Qf.

a. Calculate the profit-maximizing, price-quantity combination for the monopolist with the price discrimination in each market and without price discrimination.

c. Compare the profit differential between price discrimination and no price discrimination. Does it make any economic sense for this firm to engage in price discrimination? Why or why not?

2. Larry, Curly and Moe run the only saloon in town. Larry wants to sell as many drinks as possible without losing money. Curly wants the saloon to bring in as much revenue as possible. Moe wants to make the largest possible profits. Using a single graph of the saloon's demand and marginal revenue curves and its marginal cost and average cost curves, where MC = AC, show the price quantity combination favored by each of the three partners.

3. The monopolist's total revenue function is TR = 1400Q-7Q^2. His short-run total cost function is STC = 1500+140Q.

a. Calculate the profit-maximizing, price quantity combination.
b. Calculate the revenue-maximizing, price-quantity combination.

##### Solution Summary

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1.a) with the price discrimination, the monopolist charges Pd in the domestic market and Pf in the foreign market. Then Q = Qd+Qf = (21-0.1Pd) + (50-0.4Pf) and Total revenue is
TR = Pd Qd+ Pf Qf = Pd(21-0.1Pd) + Pf (50-0.4Pf) = (21 Pd -0.1Pd^2) + (50Pf -0.4Pf^2).
And STC = 2000+10Q = 2000+10 (21-0.1Pd + 50-0.4Pf) = 2710 - Pd - 4Pf
Profit = TR - STC = (21 Pd -0.1Pd^2) + (50Pf -0.4Pf^2) - (2710 - Pd - 4Pf)
To maximize profit, we use first order condition:
dProfit / dPd = 21 - 0.2 Pd +1 = 0 (1)
and dProfit / dPf = 50 - 0.8 Pf +4 = 0 (2)
from (1) we can get Pd* = 110, substitute it into Qd* =21-0.1Pd* = 21-0.1*110=10
and from (2) we can get Pf* = 67.5, substitute it into Qf* =50-0.4Pf*=50-0.4*67.5 = 23
Then Q*= Qd*+Qf* =10+23=33, So TR= Pd Qd+ Pf ...

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