Consider a person who will live for two years (1 and 2). The real interest rate between the two periods is r. In period 1 any income they have to use, Y1, must be earned by working at wage w, denoted in period 1 dollars, for hours H1, which they can choose. In period 2 they cannot work, but they will be paid a stipend of Y2. Their intertemporal utility is defined over consumption of a composite in each period, q1 and q2, and leisure in each period, L1 and L2. You can assume that the price of consumption in each period is $1, denoted in that period's dollars. Given this information, state the person's utility maximization problem in full, and derive the first order conditions for an optimal solution. Give an economic interpretation of the conditions you derive (i.e., carefully describe the nature of the optimal choice).

Consider a person who will live for two years (1 and 2). The real interest rate between the two periods is r. In period 1 any income they have to use, Y1, must be earned by working at wage w, denoted in period 1 dollars, for hours H1, which they can choose. In period 2 they cannot work, but they will be paid a stipend of Y2. Their intertemporal utility is defined over consumption of a composite in each period, q1 and q2, and leisure in each period, L1 and L2. You can assume that the price of consumption in each period is $1, denoted in that period's dollars. Given this information, state the person's utility maximization problem in full, and derive the first order conditions for an optimal solution. Give an economic interpretation of the conditions you derive (i.e., carefully describe the nature of the optimal choice).

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter17: Capital And Time

Section: Chapter Questions

Problem 17.7P

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