3. A firm has a cost function of the form: C(z1,z2,q)=w10.25w20.25w30.25w40.25qa where z1,,z4 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(z1,z2,q)=w10.25w20.25w30.25w40.25qa where z1,,z4 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)