Suppose that the production function for iPhones is Q = 20K^0 · 5 x L^0 · 5 . The marginal product of labor is lO(K/ L)^0.5, and the marginal product of capital is lO(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 iPhones. Fractional units of labor and capital are permissible. c. What is the minimum cost of producing 49 iPhones? d. Suppose that the firm has exactly $300 to spend on producing iPhones. What is the maximum number of iPhones it can produce?
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