Consider an economy with two goods, consumption c and leisure I, and a representative consumer. The consumer is endowed with 24 hours of time in a day. A consumer's daily leisure hours are equal to l = 24 - h where h is the number of hours a day the consumer chooses to work. The price of consumption p is equal to 1 and the consumer's hourly wage is w. The consumer faces an ad valorem tax on their earnings of T percent. The consumer also receives some exogenous income Y that does not depend on how many hours she works (e.g. an inheritance). The consumer's preferences over consumption and hours of work can be represented by the utility function U(c, h) = c-
Consider an economy with two goods, consumption c and leisure I, and a representative consumer. The consumer is endowed with 24 hours of time in a day. A consumer's daily leisure hours are equal to l = 24 - h where h is the number of hours a day the consumer chooses to work. The price of consumption p is equal to 1 and the consumer's hourly wage is w. The consumer faces an ad valorem tax on their earnings of T percent. The consumer also receives some exogenous income Y that does not depend on how many hours she works (e.g. an inheritance). The consumer's preferences over consumption and hours of work can be represented by the utility function U(c, h) = c-
Economics Today and Tomorrow, Student Edition
1st Edition
ISBN:9780078747663
Author:McGraw-Hill
Publisher:McGraw-Hill
Chapter7: Demand And Supply
Section7.1: Demand
Problem 4R
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Transcribed Image Text:Consider an economy with two goods, consumption c and leisure l, and a representative
consumer. The consumer is endowed with 24 hours of time in a day. A consumer's daily
leisure hours are equal to l = 24 – h where h is the number of hours a day the consumer
chooses to work. The price of consumption p is equal to 1 and the consumer's hourly
wage is w. The consumer faces an ad valorem tax on their earnings of T percent. The
consumer also receives some exogenous income Y that does not depend on how many
hours she works (e.g. an inheritance). The consumer's preferences over consumption and
It
hours of work can be represented by the utility function U(c, h) = c-
(a) What is this consumer's budget constraint?
(b) Solve for the consumer's utility maximizing hours of work h*(w, 1 - T, Y) and con-
sumption c*(w, 1 - T, Y).
(c) Repeat part (b) for a consumer with the utility function U(c, h) = alog(c) - Blog(h).
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