Suppose that the production function is given by: ? = ?(?, ?) = ?(?)^1/3(?)^1/3 where ?...

Suppose that the production function is given by: ? = ?(?, ?) = ?(?)^1/3(?)^1/3

where ? > 0 is total factor productivity, ? indicates the amount of capital employed and ? the amount of labor employed. Wages are ? and the rental cost of capital is ?. Suppose that in the short run capital is fixed, i.e., ? = ?bar. Moreover, the firm must pay ??bar regardless of the production level

a) Solve the cost minimization problem. That is, determine the amount of capital and labor that THE firm employs in the short run. Hint: Capital is trivial because it is fixed.

b) Compute the short run cost function. Also indicate variable and a fixed cost, and compute average variable cost, marginal cost and average total cost.

c) Suppose that the price of ? is ?. Compute the level of output that maximizes the profits of the firm. Also compute the corresponding level of ?.

d)Explain how the supply curve of the firm is affected by the following variables: the wage rate ??, the rental cost of capital ?, the fixed capital ?bar, and total factor productivity ?. Hint: You only need to check if the quantity supplied at each price (that is, the supply curve) increases or decreases with each variable.

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Expert Solution

Rahul Sunny answered 1 week ago

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