1. Suppose that an individual in Japan has preferences represented by the following utility function:<\/p>
U <\/em>( C 0<\/sub><\/em> , C 1<\/sub><\/em> ) = l n ( C 0<\/sub><\/em> ) + (1\/1+rho) ln(C1<\/sub>)<\/p> 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 (\"rho\") is equal to 2%. Suppose the real interest rate in Japan is 2% per year.<\/p> <\/p> 1. Set up and solve this individual's utility maximization problem. Find the optimal amount of consumption for this individual in each period.<\/p> <\/p> 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?<\/p> <\/p> 3.Explain what has happened in terms of income and substitution effects.<\/p>",
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