. A firms technology is characterized by a Cobb-Douglas production function of the form = (, ) = 3 1/2 + 5 1/2

a. The output price is , and the input prices are and for and , respectively. Set up the problem for a profit-maximizing firm and solve for the factor demand functions for and .

b. Find the firms supply function.

c. Find the firms profit function.

dAssume now that = 2, = 1, and = 1. Using the functions you have found in parts (a), (b) and (c), calculate the profit-maximizing levels of the factors ( and ), the profitmaximizing output level ( ) and the maximum profit of the firm ( ).