This is a group assignment. One copy can be turned in for a team of up to four students.
Assignment 1: Retirement Saving and Consumption Smoothing
Consider trying to give Katniss advice about how much she should save when young.
Her life can be split into 3 periods:
- At \( t = 1 , \) her after-tax income is \( Y_1 = $100,000 \)
- At \( t = 2 , \) her after-tax income is \( Y_2 = $140,000 \)
- At \( t = 3 , \) she has no income, so \( Y_3 = $0 \)
Assume the market interest rate and the utility discount rate are equal to zero, which implies that savings earn no interest in the District that she lives in and she is relatively patient. In addition, Katniss is not very risk averse so she has utility \( U ( C_t ) = l n ( C_t ) \). Given her utility, the marginal value of an additional unit of consumption in any period of her life is \( U' (C_t) = \frac 1 {C_t} \) , where \( C_t \) is Katniss' consumption during period \( t \).
Answer the following questions:
- What are the best amounts of saving in the