Suppose the competitive market price is $50, and a competitive firm’s total cost

Question

Suppose the competitive market price is $50, and a competitive firm’s total costs = 5q2 - 10q + 150 and marginal cost = 10q - 10.
a. Solve for the profit-maximizing (or loss minimizing) quantity (q*).
b. What is the market equilibrium price?
c. Should the competitive firm produce q*? Explain why using one of the four key questions and solutions.
d. Does the competitive firm make a profit? Explain why using one of the four key questions and solutions.
e. How much profit (or loss) does the competitive firm make?

Explanation / Answer

a. Profit = Total Revenue(TR) -Total Cost (TC)

= P.Q - TC

= 50*q - 5q2 - 10q + 150

d/dq = 50 - 10q - 10

Putting   d/dq = 0

50 = 10q - 10

q* = 6.

b. The market equilibrium price will be $50.

c. Yes the competitive firm should produce at q* = 6 as at q* , the marginal cost of the firm is equal to the price of the market price , so if he produces more than q* its profit will decrease.

d. Yes, the competitive firm does make a profit, Yes as for given the market Price, the Marginal cost is greater then the average cost , so the firm will make profits.

e. Profit = Total Revenue(TR) -Total Cost (TC)

= P.Q - TC

= 50*6 - 5(6^2) + 10*6 - 150

= 300 - 180 + 60- 150

= $30

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