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(3) Consider the firm of the previous question (with f(L,K) = 2K√L and with w =...

(3) Consider the firm of the previous question (with f(L,K) = 2K√L and with w = 1 and r = 4). For the following questions suppose that this firm currently uses K = 4 machine hours, and that this can’t be changed in the short-run.

f(L) = 8√L

L = Q^2/64

C= 16 + Q^2/64

AC = 16/Q + Q/64

MC = Q/32

(e) In one graph draw the average cost and marginal cost curves. The graph should show the relationship between these two curves – the exact shape of the curves is not important.

(f) What is the efficient scale of production? What is the average cost at the efficient scale of production?

(g) Assume that the r∗K = 4∗4 = 16 dollars that the firm pays for its capital are sunk. What is the profit maximizing quantity as a function of the market price p? Draw the supply curve of the firm. What are the firm’s profits (as a function of p)?

(h) How would the supply curve change if the fixed cost (of 16 dollars) is avoidable instead of sunk?

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Answer #1

e) Marginal Cast 32 Q +16 64 Q Average Cast MC, AC Marginal Cost Auerage Cast 32 aoantity production: 9tis the lowat can proc16 64 16 Q2 64x16-1024 +32 Output can not be So negatiue Q 32 Auenage cost ad of produchon. ficiend scale AC= +16 32 32 ProfeQ37P (Suupply Curve) Quantity Supply h.) Curve 8tays Same euen when the cast is auoidable

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