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You are a manager in a perfectly competitive market
You are a manager in a perfectly competitive market. The price in your market is $35. Your total cost function is: C(Q) = 30Q^2 + 5(Q) + 80. Please identify the price you will charge, the output that you will produce, the profit/loss that you will make, and what you would expect to happen to your firm in the long-run. NOTE: Assume this is a service and fractional output levels are possible.
Expert Solution
a. If the total cost is given, take the derivative of the cost function to determine the marginal cost. In perfect competition, price is equal to marginal cost. Set price equal to marginal cost and solve for quantity to find the equilibrium quantity in perfect competition.
if C(Q) = 80 + 5Q + 30Q^2 find the MC
MC(Q) = 5 + 60Q
in perfect competition set P = MC
35 = 5 + 60Q
60Q = 30
Q = 0.5
The firm should produce 0.5 units.
b. In perfect competition the price is the market price which is $35.
c. The total revenue is equal to the equilibrium price multiplied by the equilibrium quantity. Plug the equilibrium price into the cost function and solve for the total cost. The profit or loss is equal to total revenue minus total cost
TR = P*Q = 35 * 0.5 = 17.5
C(0.5) = 80 + 5(0.5) + 30(0.5^2) = 80 + 2.5 + 7.5 = 90
Profit = 17.5 - 90 = -72.5
The firm loses 72.5
d. In the long run because the firm is not profitable the firm will exit the market.
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