Final answer:
The conditional factor demand functions for a zero fixed-cost firm with a Cobb-Douglas production function demonstrate how labor and capital demanded change with output level and input prices, given by L(q, w, r) and K(q, w, r), scaled by functions of wage and capital rental rates.
Step-by-step explanation:
A zero fixed-cost firm with a Cobb-Douglas production function F(L,K) = LαKβ and positive exponents α and β can derive its conditional factor demand functions based on the production levels (q), wage rate (w), and rental rate of capital (r). Assuming that the firm is operating to maximize profit, it will choose quantities of labor (L) and capital (K) that minimize the cost for a given output level. The cost-minimizing input choices are described by the conditional factor demand functions, which are functions of q, w, and r, and should satisfy certain properties due to the Cobb-Douglas production function characteristics.
The firm's conditional factor demand functions can be written as L(q, w, r) = r1(w,r)q1/α+β and K(q, w, r) = Yk(w, r)q1/α+β, for some functions r1(w, r) and Yk(w, r) that depend positively on w and r, demonstrating how the quantities of labor and capital demanded change with output and input prices.