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An IT company called Zucchini has the following production function: y=16L^(1/4) K^(1/4). (A) Using the following two conditions for profit-maximizing in the long-run, show that the long-run demand functions for input labour is L=(4p/r)^(1/2) (4p/w)^(3/2)=(16p^2)/(r^(1/2) (w) ^(3/2) ) (1) p.mpL=w (2)p.mpK=r In the short-run, the level of capital is fixed at 256 units. The price of output is $10, the cost of labour is $20/unit and the cost of capital is $4/unit. (B) Find the value of short-run demand for labour (report all numbers until the second decimal). (C) Find the value of short-run profit for the firm. (D) Derive the two conditions (conditions 1 and 2) you used in part (A). [Hint: You need to show me using calculus where these two conditions come from. These two conditions are the result of maximizing profit by choosing labour and capital].
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