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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?

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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