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Could use some help working through the following problem, any help would be appreciated:
1. The manager of a national retailing outlet recently hired an economist to estimate the firm’s production function. Based on the economist’s report, the manager now knows that the firm’s production function is given by Q = K1/2L1/2.
a. Assuming capital is fixed at 4 units, calculate the average product of labor when 9 units of labor are utilized.
b. Assuming capital is fixed at 4 units, calculate the marginal product of labor when 9 units of labor are utilized.
c. Assume that capital is fixed at 4 units and that the firm can hire labor at a wage of $10 an hour and output can be sold at a price of $100 per unit. Determine the profit-maximizing levels of labor and output.