Consider a firm that produces output according to the following production function: Q = K1/2L1/2 MPL= .5K1/2L-1/2= (1/2)(Q/L) MPK= .5K-1/2L1/2= (1/2)(Q/K) The demand curve for the firm's output is given by: Q = 300 - 10 P. Initially, the wage rate is $10 per labor-hour and the rental rate on capital is $2.50 per machine-hour. At these input prices, the firm optimizes by using 50 labor-hours and 200 machine-hours to produce 100 units of output that are sold at a price of $20. Suppose the wage rate rises to $22.50 per labor-hour. a. Find the firm's new profit-maximizing output level, mix of inputs, and price, and the amount of profit it earns in the long run. b. By how much has the increase in the wage rate changed the use of labor and capital? What part of each of these changes is due to the factor substitution effect and what part is due to the output effect? Is each input normal or inferior? How can you tell