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

Question: 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

Consider a following problem with a utility function with taste shocks u(c)

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

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