1. A firm can price discriminate between two markets. Assume that its TR functions are
Market 1 TR_1 = 25Q_1 - 2Q_1^2
Market 2 TR_2 = 17Q_2 - Q_2^2
and its TC function is TC = 2 + 5Q_1 + 5Q_2
a. Find the firm’s profit function.
b. Find the output levels needed to maximise profit.
Use the second-order derivatives to test for a maximum.
What is the maximum profit?
What price will the firm charge in each market to maximise its profit?
Profit = TR - TC
b.
Find the marginal costs/revenues by differentiating the total costs/revenues with respect to the output level of the relevant good.
Find maximum profit by equating marginal cost = marginal revienue in each market
Market 1:
market 2
I assume you know what a second derivative is so you should be able to do the rest yourself.
To get the price, use the fact that (Total Revenue / Quantity) = Price.
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