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2. Suppose that a firm’s production function is Q = 10 L½ K½ and the unit...

2. Suppose that a firm’s production function is Q = 10 L½ K½ and the unit cost of labor is $20, capital is $80, and the product price is $12 per unit. The firm is currently producing 100 units of output and has determined that its cost minimizing quantities of labor and capital usage for this level of output is 20 and 5 respectively. The product price is $12 per unit.

a. Determine the current total cost for 100 units, the average cost per unit, and total profit.

b. The firm now wants to increase output to 150. Capital is fixed in the short run. How much labor is required to produce 150 units, and what is the average cost and total profit at this level of labor usage?

c. Use the optimality condition for long run L & K usage to prove that usage in "b." is not optimal.

d. Determine the optimal long run level of L & K to produce 150 units. What is the average cost and total level of profit?

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