Suppose that the production function for iPods is Q = 20 K0.5L0.5. The marginal product of labor is 10(K/L ) 0.5, and the marginal product of capital is 10(L/K ?)0.5
a. Suppose that labor can be hired for $6, and capital can be hired for $9. When the firm is producing 49 units at lowest cost, what will the firm's marginal rate of technical substitution be?
b. Solve for the lowest-cost combination of labor and capital that will allow the firm to produce 49 iPods. Fractional units of labor and capital are certainly permissible.
c. What is the minimum cost of producing 49 iPods?
d. Suppose that the firm has exactly $300 to spend on producing iPods. What is the maximum number of iPods it can produce?