3 Overlapping Generations Question 3.[20pt] Consider the overlapping generations model with Cobb-Douglas utility U = c t c 1 t+1 where ct is consumption when young and ct+1 is consumption when old. Workers earn wages in the first period and live off their savings in the second: ct + st wt ; ct+1 (1 + rt+1)st Factors earn their marginal products in the production process. The production function is: Yt = KN 1 and capital accumulates as: Kt+1 = It + (1 )Kt where the next periods capital stock is made up of the current generations saving: Kt+1 = Ntst a) Derive the Euler equation and the optimal consumption of ct , ct+1 as well as optimal saving st . b) Compare your Euler equation to the one derived in class with log utility. What value should take to get a reasonable time preference parameter of lets say 0.9? Explain the meaning of in this intertemporal context. c) Derive the law of motion of capital per person (kt+1 as a function of kt and exogenous parameters). Show graphically that it converges to a steady state and calculate the steady state capital per person k . d) Derive the golden rule capital stock and saving rate for this economy. If the population 3 grows a 3%, capital depreciates at 10%, the capital share of income in the economy is 1/3 and with a value of that is consistent with a discount factor of = 0.9, is the economy operating under dynamic inefficiency? What is dynamic inefficiency? Explain.

3 Overlapping Generations Question 3.[20pt] Consider the overlapping generations model with Cobb-Douglas utility U = cc where ct is consumption when young and C++1 is consumption when old. Workers earn wages in the first period and live off their savings in the second: a +8+