# imperfectly competitive firm

1) An imperfectly competitive firm has the following demand and cost functions:

P=230-20Q

C=50+30Q

a. What is optimum output?

b. What is equilibrium price of this output per unit?

c. What is optimal revenue?

d. What is total profit?

2) A firm in a perfectly-competitive industry where market price of output prevailing is $50 per unit has a cost function where:

C=40+5Q2

a. What is marginal cost in dollars?

b. What is marginal revenue in dollars?

c. What is optimal output in units?

d. What is maximal profit?

3) A monopolist facing a demand curve and cost function like the following:

P=72-6Q

C=15+6Q2

a. has what equation for marginal revenue?

b. What is the equation for marginal cost?

c. What is optimal output?

d. What is price per unit?

What is profit?

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#### Solution Preview

<br>1) An imperfectly competitive firm has the following demand and cost functions:

<br>P=230-20Q

<br>C=50+30Q

<br>

<br>a. What is optimum output?

<br>b. What is equilibrium price of this output per unit?

<br>c. What is optimal revenue?

<br>d. What is total profit?

<br>

<br>For optimum in an imperfectly competitive firm, MR = MC

<br>

<br>Total Revenue = TR = Price * Quantity = P*Q

<br> = (230-20Q)*Q = 230Q - 20Q^2

<br>MR = d(TR)/dQ = d(230Q - 20Q^2)/dQ = 230 - 40Q

<br>MC = dC/dQ = 30

<br>MR = MC ==> 230-40Q = 30 ==> ...

#### Solution Summary

Characterize an imperfectly competitive firm.