Reference no: EM131167342
Q1. Consider the production function f(L, K) = 2LK + 5K1/3, where L is the amount of labor and K is the amount of capital. Calculate the average product of labor and the marginal product of capital. Is the marginal product of capital diminishing?
Q2. Consider the production function f(L, K) = 3L2 + 4K1/3. Calculate the isoquant for production level q- = 10 and express this in the form of K as a function of L.
Q3. Consider the production function f(L, K) = √3(K1/2L2/3). Find the level of production q- for which the MRTS equals -16 when L = 1.
Q4. Consider the production function f(L, K) = (max{3L, K})3/4 (min{√L, 5√K})x, where x > 0. Is this production function homogeneous of any degree? If so, what value of x makes it exhibit constant returns to scale?
Q5. Suppose that the short-run cost function of a firm is cSR(q) = 100 + 3q + q2. Calculate the average cost, the average variable cost, and the marginal cost at production level q = 10.
Q6. Consider a firm operating in the short run and using the production function f(L, K) = min{3√L, K2}. Suppose that the wage rate is w = 2 and the rental rate is r = 1.
(a) What is the maximal level of output qmax that the firm can produce in the short run when the capital is fixed at level K-?
(b) Suppose that capital is fixed at K- = 5 in the short run. Calculate the function L(q, K-) that gives the quantity of labor required to produce any level of output q that the firm can actually produce.
(c) Calculate the short-run cost function of the firm and draw it in a graph.
(d) Calculate the average cost, the average variable cost, and the marginal cost of the firm.
Q7. A firm operates in the long run using the production technology f(L, K) = 3√(LK) + L + 4K.
(a) Calculate the marginal product of labor and capital.
(b) For each level of output q ≥ 0, derive the level of inputs L∗(w, r, q) and K∗(w, r, q) that allow the firm to produce q at the lowest cost in the long run, given that the prices of labor and capital are w = 20 and r = 80.
(c) Calculate the long-run cost function of the firm.
(d) Suppose that the firm expects that, in three years, the price of its product will be p = 10 and the prices of labor and capital will continue to be w = 20 and r = 80. Would it make sense for the firm to invest over the next three years so as to grow and achieve a level of output q = 140?
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