5. (15 points) Suppose the total cost for a given firm is characterized by the f

Question

5. (15 points) Suppose the total cost for a given firm is characterized by the following cquation: TC q +10 (marginal cost is given by MC8+ 4). T'he firm operates on a perfectly competitive market with demand given by P 100 2Q, where Q- total quantity of production on this market. Assume that all the firms on this market are identical (i.e. having the same total cost function). Suppose the firm produces q-4. Given that it behaves rationally in the short-run what is inter of firms in the inarket? (Hint: Q = nq, where n-numler of firms in the nurket.) . Suppose the firm produces q 1. In the long run, what is the number of firms in the market? (Hint: look at the propertics of lougs run evquiirium)

Explanation / Answer

a)

TC = 4q2 + 4q +10

MC = 8q + 4  

since q = 4 given

so MC = 8(4) + 4

= 36

P = MC

p = 36

P = 100 - 2Q

2Q = 100 - P

Q = 50 - P/2

Q = 50 - 36/2

= 50 - 18

= 32

so number of firms n = Q/q

= 32/4

= 8

b)

MC = 8q + 4

q = 1

MC = 8(1) + 4

= 12

P = MC

P = 12

Q = 50 - P/2

= 50 - 12/2

= 50 - 6

= 44

Number of firms n = Q/q

= 44/1

= 44

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