3. A firm has a cost function of the form: C(21. 22. 9) = w25 0.25...

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3. A firm has a cost function of the form: C(21. 22. 9) = w25 0.25 0.25 0.25 qº where 21.24 are factor inputs, W₁.....w4 are factor wages, q is the firm's output, a is a positive constant, a > 0. (a) What are the conditional factor demands? Is the production function homothetic? (b) Set up the firm's maximization problem given the wages w and the price of the final output p. (c) Solve the firm's profit maximization problem. Indicate for what values of a this problem leads to a finite and unique profit-maximizing output (use second order conditions). Relate this problem to the returns to scale. (d) Write down the firm profit function (p, w) for the range of a found in (c). 3. A firm has a cost function of the form: C(21. 22. 9) = w25 0.25 0.25 0.25 qº where 21.24 are factor inputs, W₁.....w4 are factor wages, q is the firm's output, a is a positive constant, a > 0. (a) What are the conditional factor demands? Is the production function homothetic? (b) Set up the firm's maximization problem given the wages w and the price of the final output p. (c) Solve the firm's profit maximization problem. Indicate for what values of a this problem leads to a finite and unique profit-maximizing output (use second order conditions). Relate this problem to the returns to scale. (d) Write down the firm profit function (p, w) for the range of a found in (c).

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a The conditional factor demands are K 2124 L 22 The production function is homothetic since it has ... View the full answer