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3. Consider the production function y = f (L, K) = 2L§Ki. The output good is sold for
price p, the inputs are priced at w for Labour and r for Capital. (a) If K 2 K = 8 is fixed in the short run, derive the short-run demand for Labour.
(b) K : K = 8 is fixed in the short run. write out the short-run profits of the firm. (c) K = K = 8 is fixed in the short run. Determine the profit-maximizing amount of
Labour and the profit-maximizing level of output when the price of the output
good is p = 10 and the cost of labour is w = 2. (d) K = K : 8 is fixed in the short run, but the firm could avoid the cost associated
with capital (TK) if it were to choose to shut down production (Cost of Capital
is avoidable). For what prices of Capital (’3‘) wold the firm be better off shutting
down production?

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