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Problem Set 2.

Econ 100B. Winter 2023

January 26, 2023

Each problem is 5 points. Only one problem will be randomly selected and graded. Please, make sure to attempt and solve all of them!

Reminder: There will be a total of four problem sets. Two of them, those for which you get the lowest scores, will not count towards the final grade.

1. Consider a firm operating in the short-run using a technology q = f (L,K) where K is fixed at 10, w = 5, and r = 2.  What is the marginal cost if:

(a) f (L,K) = L K 

(b) f (L,K) = min{L,K}

(c) f (L,K) = 2L + K

2. Suppose a firm’s cost function is c(q) = q2 + 100. Compute the average cost, marginal cost, and average variable cost functions. Also compute the quantity at which average cost is minimized and compute the minimum average cost. Finally, compute the firm’s supply curve (in the short and long run).

3. Suppose that a firm has the production function f(L,K) = 5L + 3K − 2^LK .

(a) In the long run, what is the optimal way for the firm to produce q = 150 units?

Give the optimal values of L and K and explain how these depend on the wage rate w and rental rate r .

(b) Calculate the long-run cost function of the firm, explaining how it depends on the

wage rate w and rental rate r .