Question

A firm in a perfectly competitive constant cost industry has
total costs in the short run given by: TC = 2q^{2} + 2q +
72 q ≥ 2

where q is output per day and TC is the total cost per day in dollars. The firm has fixed costs of $54 (already included in the TC equation above). The TC equation generates minimum average costs of $26 (per unit) at q = 6. You are also told that this size firm generates minimum long run average costs (that is, minimum LAC occurs at q = 6, with min LAC = $26).

Suppose that the demand curve facing the industry is given by the equation P = 44 - .004Q where P is the price per unit and Q is the number of units demanded per day. suppose that we are now in the long run.

The number of firms in the industry, rounding to the nearest integer, is:

A) 0 B) 2917 C) 2417 D) 300 E) 750 F) 400

G) 1250 H) 292 I) 583 J) none of the above

Answer #1

Since this is a perfectly competitive firm, the firm should produce in the long-run where average cost (AC) becomes the minimum.

In the long-run, LAC is $26. This is to be placed as P in the industry demand equation in order to get Q.

Given,

P = 44 – 0.004Q

26 = 44 – 0.004Q

0.004Q = 44 – 26

0.004Q = 18

Q = 18 / 0.004 = 4,500

Now given, q at LAC is 6.

Number of firms = Q / q

= 4,500 / 6

= 750

Answer: E

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