Question

Suppose a consumer values income (m) and leisure (l) with utility function U(m,l)=ml. The consumer has T hours per week to allocate between labor and leisure with an hourly wage rate of w. The consumer's weekly time constraint is (m/w)+l=T. Use a Lagrangian to maximize the consumer's utility subject to the weekly time constraint. What is the optimal amount of leisure? what is the optimal amount of labor (L=T-l)

Answer 1

Anawer L= T- mwT- T wL m = Ym T Maximize U= Sbjcct ml LT Lagramge Ast Oder Condidion m (3 о 1 from (2) and (8) we get wl m (1). T wwt + T Hence L+ T 2- LeisueT/2 Optimal amouut =T-1-0T Hence, ptimal pont LaloAIhows