Question

1. Consider the following production functions. In each case determine if: • the function is Cobb Douglas (Y = AK 11-a). If the function is Cobb Douglas, what is the value of the parameter a? • Do capital and labor exhibit diminishing returns. Explain your thinking using algebra / calculus /a graph etc. (a) F(K, L) = 27K+15VL (b) F(KL) = 5K + 3L (c) F(KL) = K0.5 0.5 (a) F(KL) - VK2 + L2 2. Suppose that the production function is Cobb Douglas with parameter a = 0.5 and level of technology A - 1. The economy begins with 100 units of labor and 100 units of capital (a) How much output does the economy produce? (b) What are the real wage () and real rental rate of capital (3)? (c) What share of output does labor receive? (a) If half the population emigrates (leaves the country), what is the new level of output? (e) What is the new wage and rental price of land? (f) What share of output does labor receive now?

Answer 1

a The above MPK = FLK, L) = 2 JK above function +ISJE. is not cobb- Douglas function. Since ăn related the the input and a this, capital info it and marginal product are negatively, labor exhibit diminishing returns (6) FK L) = 5K+ 3L. No, it is not a 5 MP = 3. it is not cobb. Douglas function. MPx = Marginal product are constant and thus capital and abor do not exhibit diminishing retwins (C) F (K, L) = Kos Los This is the case of cobb- Douglas production function and L= o.s. Mix = o.sxjos MP = 0.5x(K) Thus, capital and labor have diminishing returns. d) FLK, L) = TK² + [2 No, it is not cobb Douglas function . M = I x 2xK 2 K Me = L & J K²+12 Jk²,2 J K²+ Siminishing returns do not exist .