Question

A household's income is e₁ in the 1st period, e₂ in the 2 nd period, and e₃ in the 3rd period. They can only make a single borrowing choice b in the 1st period, and once they borrow, they have to repay at an interest rate of r in the 3rd period. In other words, they have to repay (1+r)b in the 3rd period. No financial transaction occurs in the 2nd period. Assume that their utility of consumption cᵢ in period i is ln(cᵢ), and that their discount factor is β. 1. Formulate the 3-period utility maximization problem. Hint: make sure that you include the discount factor for each period i as βᶦ⁻¹.

Answer 1

The 3-period utility maximization problem involves a household's income in three periods: e₁, e₂, and e₃. The household can make a single borrowing choice, b, in the 1st period and then has to repay it at an interest rate of r in the 3rd period. The goal is to formulate the problem in a way that maximizes utility across the three periods.

Step-by-step explanation:

The 3-period utility maximization problem involves a household's income in three periods: e₁, e₂, and e₃. The household can make a single borrowing choice, b, in the 1st period and then has to repay it at an interest rate of r in the 3rd period. The utility of consumption in each period is ln(cᵢ), and the discount factor is βᶦ⁻¹. The goal is to formulate the problem in a way that maximizes utility across the three periods.