# Important Aspects of Profit Maximization

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.

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...+67.5*23=2652.5
STC=2000+10Q = 2000+10*33=2330
And we can find with price discrimination, the profit is: Profit1=TR-STC=2652.5-2330=322.5

Without price discrimination, the monopolist charges P in both domestic and foreign markets. Then Q = Qd+Qf = (21-0.1P) + (50-0.4P) = 71-0.5P
TR = P*Q = P(71-0.5P)= 71P-0.5P^2
STC=2000+10Q =2000+10(71-0.5P)=2710-5P
Then Profit= TR - STC = 71P-0.5P^2-(2710-5P)=76P-0.5P^2-2710
To maximize profit, we use first order condition:
dProfit / dP = 76 -P = 0 then we can calculate P*=76
Then Qd=21-0.1P=21-0.1*76=13.4 and Qf=50-0.4P=19.6
Q*=71-0.5P=71-0.5*76=33, TR=P*Q*=76*33=2508
And STC=2000+10Q* = 2000+10*33=2330
So without price discrimination, the profit is: Profit2=TR-STC=2508-2330=178