Consider an economy with two goods, consumption c and leisure I, and a representativeconsumer. The consumer is endowed with 24 hours of time in a day. A consumer's dailyleisure hours are equal to 1 = 24 - h where h is the number of hours a day the consumerchooses to work. The price of consumption p is equal to 1 and the consumer's hourlywage is w. The consumer faces an ad valorem tax on their earnings of T percent. Theconsumer also receives some exogenous income Y that does not depend on how manyhours she works (e.g. an inheritance). The consumer's preferences over consumptionand hours of work can be represented by the utility function:U(C,h) = c-B- where ß> 0 and p > 0 are parameters.‚h¹- P1+ pa) What is this consumer's budget constraint?b) Solve for the consumer's utility maximizing hours of work h*(w, 1-T) andconsumption c* (w, 1 - T, Y).c) What is the compensated own-price elasticity for the supply of hours of work?For parts (d) - (h), assume the following: w = $50, Y = $100, ß = 0.5 and p = 2.(d) Suppose the income tax rate is initially zero (i.e. t = 0). Calculate the consumer'sutility at their utility maximizing consumption and labour supply bundle.(f) Calculate the change in the consumer's surplus (i.e. utility) following the tax change.i) Now suppose that p = 1 (instead of p = 2). Re-calculate the excess burden from thistax. Is your answer different than in part (h)? Explain why or why not in 4 sentences.(j) Suppose instead that the consumer's utility function was U(c, h) = min(c, -h). Wouldthe EB from a unit excise tax be larger or smaller compared with the original utilityfunction. Explain your answer in 4 sentences.

Given information Utility function U=c-βh1-ρ1+ρWhere β>0ρ>0c-- consumptionh--- hours of…

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 1 = 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 τ 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: n'+p 1+ P U(C,h) = c-B where ß> 0 and p > 0 are parameters. a) What is this consumer's budget constraint? b) Solve for the consumer's utility maximizing hours of work h*(w, 1-T) and ( 1

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 1 = 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 τ 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: n'+p 1+ P U(C,h) = c-B where ß> 0 and p > 0 are parameters. a) What is this consumer's budget constraint? b) Solve for the consumer's utility maximizing hours of work h*(w, 1-T) and ( 1

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter17: Capital And Time

Section: Chapter Questions

Problem 17.1P

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