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Consider a special case of SP under uncertainty: Take SP2 under uncertainty and assume the following: utility is CRRA with 1 as the coefficient of
Consider a special case of SP under uncertainty:
Take SP2 under uncertainty and assume the following: utility is CRRA with 1 as the coefficient of relative risk aversion. Production is linear (i.e. = 1), and the production function reads f(kt) = Atkt. Depreciation is (0,1). Assume further that productivity {At} is independent and identically distributed (iid). Hence, (At+1 | At) = (At+1). Furthermore,E[(1+At )1]<1
- Write down the full problem in sequence notation.
- Calculate the FOC(s).
- Guess ct = c(kt,At) = c (1 + At )kt, where c is a constant. What does that imply for the policy function of kt+1?
- Find a recursive solution to the FOC(s), i.e. determine c .
- Argue that solving the FOC(s) is sufficient to find the solution to the original
- problem.
- Does this problem exhibit precautionary savings/investment? What would be the case for log-utility?
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