Question: 1) A firm's production function is q = F(L, K) = L + K The wage rate of labor is w equal to $ 2

1) A firm's production function is q = F(L, K) = L + K

The wage rate of labor is w equal to $ 2 and the rental rate of capital is r equal to $8.

a)Suppose capital is fixed at a level 2 in the short run, that is, K = 2.

(i)How many units of labor, if any, is the firm going to use to produce q = 1 unit of output? How many units of labor, if any, is the firm going to use to produce q= 5 units of output? In general, how many units of labor is the firm going to use to produce q units of output?

(ii)What is the short-run average variable cost? What is the short-run average fixed cost?

b)In the long run, capital is no longer fixed.

(i)Suppose the firm wants to produce q= 1 unit of output: how many units of labor and how many units of capital should the firm use if it wants to minimize its cost?

(ii)Suppose the firm wants to produce q= 5 units of output: how many units of labor and how many units of capital should the firm use if it wants to minimize its cost?

(iii) In general, how many units of capital and how many units of labor is the firm going to use to produce units of output at minimum cost?

(iv) What is the long-run cost function? Are there economies of scale? Why or why not?

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