Answer each of the following questions as either true or false. For a statement to be "true," it must
always be true. If there is at least one case where the statement is not true (or if you need more
information to be sure), answer "false." You must justify each answer with an appropriate explanation
or counterexample (which may include a relevant diagram).
(a) (4) Consider two firms, Airbus and Boeing, with the following two production functions: fa(L,K) =
min{L,K} and fb(L,K) = [min{L,K}]^2. If both firms face the same inputs costs (wage w and
rental rate r), then the ratio of capital to labor (K/L) that each firm uses will be the same.
(b) (4) A perfectly competitive firm has marginal cost function MC(q) = 6 + 4q, faces an output
price of p = $26, and chooses to produce q∗= 6 units. In order to maximize profits, this firm
would increase output.
(c) (4) A firm can make widgets using capital and labor according to the production function
f(K,L) = 2L + 5K. Denote the wage w and the rental rate on capital r. If w is sufficiently
high, the firm will not hire any labor, no matter how many widgets it wants to produce.
(d) (4) Heather consumes running shoes and packs of energy gel. If energy gel is an inferior good and
becomes cheaper, then the income effect of that price change would induce Heather to consume
more energy gel.