Beta industries manufactures floppy disk that consumers perceive as identical to
ID: 1101169 • Letter: B
Question
Beta industries manufactures floppy disk that consumers perceive as identical to those produced by numerous other manufacturers. Recently, Beta hired an econometrician to estimate its cost function for producing boxes of one dozen floppy disks. The estimated cost function is C=20+2Q^2.
a. What are the firm's fixed costs?
b. What is the firm's marginal cost?
From question c to f, assume many other firms in the market sell the product at a price of $10
c. How much should this firm charge for the product?
d. What is the optimal level of output to maximize profits?
e. How much profit will be earned?
f. In the short run, should this firm continue to operate or shut down? why?
Explanation / Answer
a. Firms fixed costs are the one that do not depend on Q. Hence,
fixed costs = 20
b. MC = dC/dQ = d(20 + 2Q^2)/dQ = 4Q
c. Many firms means that the market is perfectly competitve. The firm is a price taker in such a market and must charge the same price of $10 as other firms in the market to sell its goods.
d. Many firms means that the market is perfectly competitve. Hence, MR = Price = $10.
At profit max: MC = MR, hence
4Q = 10 => Q = 10/4 = 2.5
Optimal level of output to maximize profits = 2.5 units
e. Profits = Revenue - Costs
= price * Q - (20 + 2Q^2)
= 10 * 2.5 - 20 - 2*(2.5)^2
= 25 - 32.5
= -7.5
Hence profits are - $7.5 (loss of $7.5).
f. The firm should continue to operate in short-run as losses of $7.5 is less than the fixed costs which is $20. In other words, the firm is able to cover more than its variable costs of production and hence must continue to operate in the sort-run.
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