Consider a following problem with a utility function with taste shocks u(c) = oln(c), where c...
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Consider a following problem with a utility function with taste shocks u(c) = oln(c), where c is consumption, o is taste shock (how much we value consumption), production function is f(k) = 0ka, where output depends on technology and capital k with a € (0, 1], feasibility condition k 0 + c≤ f(k) and taste shock o 0 =(1-po) o + poo + 0.0< po<1 and 20 is a shock to taste with a mean zero and variance of one. • A. (10 points) Write down the Bellman equation • B. (10 points) Which are the states, and which are the controls? . C. (10 points) Take necessary first order conditions (remember you need to take focs with respect to the states too!) Interpret what they mean! • D. (10 points) Find the Euler equation. What is different in this Euler equation from a standard Euler equation? • E. What does a positive current taste shock do to optimal consumption path? • F. (10 points) What do you think, can these taste shocks cause business cycles we observe in the data? Consider a following problem with a utility function with taste shocks u(c) = oln(c), where c is consumption, o is taste shock (how much we value consumption), production function is f(k) = 0ka, where output depends on technology and capital k with a € (0, 1], feasibility condition k 0 + c≤ f(k) and taste shock o 0 =(1-po) o + poo + 0.0< po<1 and 20 is a shock to taste with a mean zero and variance of one. • A. (10 points) Write down the Bellman equation • B. (10 points) Which are the states, and which are the controls? . C. (10 points) Take necessary first order conditions (remember you need to take focs with respect to the states too!) Interpret what they mean! • D. (10 points) Find the Euler equation. What is different in this Euler equation from a standard Euler equation? • E. What does a positive current taste shock do to optimal consumption path? • F. (10 points) What do you think, can these taste shocks cause business cycles we observe in the data?
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