Profit Maximization for Perfect Competition and Monopolies
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1. In a competitive market at a price of $50 and cost function of C=50+5Q2 what is the maximum profit? Show how the solution was reached.
2. In a competitive market at a price of $60 and cost function of C=50+3Q2 what is the maximum profit? Show how the solution was reached.
3. In a competitive market with a price of $14 and total cost curve of
C(Q)=10+4Q+0.5Q2, what price should be charged in the short-run? Show how the solution was reached.
4. In a monopoly with a demand curve of P=85-5Q and cost of C=20+5Q, what is the profit maximizing output? Show how the solution was reached.
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Solution Summary
The solution discusses profit maximization for perfect competition and monopolies.
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1. Profit is maximized when MC=P in perfect competition.
We can find the marginal cost by differentiating the cost function:
dC/dQ = 10Q
Set this equal to price:
50 =10Q which gives us a quantity of 5.
Revenue is then PQ, which is 250.
Profit is revenue minus cost, or 250-(50+5Q^2) = 200-5 ...
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