Consider the overlapping generations model with Cobb-Douglas utility where ce is consumption when young and c++...

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Consider the overlapping generations model with Cobb-Douglas utility where ce is consumption when young and c++ is consumption when old. Workers earn wages in the first period and live off their savings in the second: a + 8 ≤w; 9+1 ≤ (1+7+1) 8 Factors earn their marginal products in the production process. The production function is: and capital accumulates as: Y₁ = K"N¹- K₁+1=1₁+(1-5)K, where the next period's capital stock is made up of the current generation's saving: Ki+1 = N181 a) Derive the Euler equation and the optimal consumption of c₁, Q+1 as well as optimal saving 84. 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 3 of let's say 0.9? Explain the meaning of in this intertemporal context. c) Derive the law of motion of capital per person (₁41 as a function of k, 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 for this economy. If the population 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 3=0.9, is the economy operating under dynamic efficiency? What is dynamic inefficiency? Explain. Consider the overlapping generations model with Cobb-Douglas utility where ce is consumption when young and c++ is consumption when old. Workers earn wages in the first period and live off their savings in the second: a + 8 ≤w; 9+1 ≤ (1+7+1) 8 Factors earn their marginal products in the production process. The production function is: and capital accumulates as: Y₁ = K"N¹- K₁+1=1₁+(1-5)K, where the next period's capital stock is made up of the current generation's saving: Ki+1 = N181 a) Derive the Euler equation and the optimal consumption of c₁, Q+1 as well as optimal saving 84. 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 3 of let's say 0.9? Explain the meaning of in this intertemporal context. c) Derive the law of motion of capital per person (₁41 as a function of k, 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 for this economy. If the population 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 3=0.9, is the economy operating under dynamic efficiency? What is dynamic inefficiency? Explain.

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a The Euler equation is ctgamma beta 1rt1ct1gamma The optimal consumption when young is ct wt The ... View the full answer