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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.

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