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# Profit Maximization

A firm has the following short-run demand and cost schedule for a particular product: Q=100+2P and Total Cost (TC)=200+2Q.

a. Determine the firm's profit-maximizing Quantity Q, Price P, and economic profits or losses.

b. If this firm operates in a monopolistically competitive market, what will happen in the long-run to Q, P and profits?

c. What are two strategies that you would implement to increase your profits?

#### Solution Preview

a. Determine the firm's profit-maximizing Quantity Q, Price P, and economic profits or losses.

I think the demand curve should be Q=100 - 2P
Then, the demand curve can be written into:
2P = 100 - Q
P = 50- 0.5Q
Then total revenue is TR = P*Q = (50 - 0.5 Q)Q = 50Q - 0.5 Q^2
The marginal revenue is MR = dTR/dQ = 50 - Q

From the total cost function, we know marginal cost is MC = dTC /dQ = 2

The first order condition for the firm to max its profit is: MR = MC, i.e.,
50 - Q = 2
Q = 48
Substitute back ...

#### Solution Summary

The solution answers the question below.

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