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1. Suppose that an individual in Japan has preferences represented by the following utility function:U 0C 1C 01 ( C , ) = l n ( ) + (1/1+rho) ln(C)
Consumption is measured in yen, and the subscripts represent this period (0) and next (1). For simplicity, assume that the individual lives only two periods. She begins with wealth of 5 million yen, and has no labor income. Suppose this individual's rate of time preference ρ ("rho") is equal to 2%. Suppose the real interest rate in Japan is 2% per year.
1. Set up and solve this individual's utility maximization problem. Find the optimal amount of consumption for this individual in each period.
2. Suppose, instead, that the interest rate is 4%. What happens to the optimal value of C0? Therefore, what happens to the amount of the initial wealth that this person saves for period 1?
3.Explain what has happened in terms of income and substitution effects.
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