In Exercises 28 through 30, let Q(x, y) be a production function, where x and y represent units of labor and capital, respectively. If unit costs of labor and capital are given by p and q, respectively, then px + qy represents the total cost of production.

Show that the inputs x and y that maximize the production level Q(x, y) subject to a fixed cost k satisfy

(Assume that neither p nor q is 0.) This is called a fixed-budget problem.

Transcribed Image Text:

Qx P Qy 9 with px + qy = k