Question

d) (7pts) Suppose that the production function is Y = 12K1/3 (EL)23 and capital lasts for an average of 10 years so that 10% of capital wears out every year (depreciate rate = 1/10 = 0.1 or 10%). Assume that the rate of growth of population is 4 percent, and the rate of technological growth is 2 percent. 1. (1pt) Derive the equation for output per effective worker y = Y/(EL) = f(k). 2. (3pts) Calculate the Golden Rule level of capital per effective worker and the saving rate associated with this steady state. (Hint: First Derive the MP) 3. (3pts) Calculate all of the following at their Golden rule levels: output per effective worker, saving and investment per effective worker, and consumption per effective worker.

Answer 1

B) 1) Y18 K 13 (EL) 2/3, 8-oj, y = 12 613 (EL)213 = n=.04 , g = .02 12 (1 ) '13 EL EL 2 at ỹ = f(K) = 12 13 Golden Rule Level, MPK = (stneg) MPG = aylak = 12 k-2/3 = (&tntg). 3 so as Golden Rule level is steady state 8 sy = (8tntg) k 56. (125 k 13 = 12 k-213 k. - SG = 1 k 13 x 188 = 113 Som = 33.33% Are

3.) $0 Page No : SG* = 13 Golden Rule level k ot t 4 R-db3 = (17.04 + 602) = (16) 4 = R213 = R1251 - Ang Now y= 12 k = 12 (125) 13 40> to e a = 12x 5 = 60. ů per effective worker = sy = x 60 = 20. = (&tntg k= .168.125 = 20 Ang C = (1-5) y = (1-1/3 60 gadta &*60 = 40. Ang Sper workere I x 60 = 20.