Question

Problem 1. Consider the Cobb-Douglas production function f(x, y) = 12x 0.4y 0.8 .

(A) Find the intensities (λ and 1 − λ) of the two factors of production. Does this firm have decreasing, increasing, or constant returns to scale? What percentage of the firm’s total production costs will be spent on good x?

(B) Suppose the firm decides to increase its input bundle (x, y) by 10%. That is, it inputs 10% more units of good x and 10% more units of good y. What is the percent increase in output?

(C) Suppose the firm has a production quota of q = 1000 units, and the firm inputs x = 100 units of the first good. How many units of the second good does it need to use to meet the quota?

(D) Assume the firm has a production quota of q = 2000 units, and the input prices are (px, py) = (7, 19). Find the minimized cost C(2000) and the conditional factor demands (x ∗ , y∗ ).

Answer 1

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