10. Consider the labour/leisure choice problem where the utility function is: U(c,l) = c²l where c is consumption of goods and services, and l is leisure time. The constraint is: w(T – 1) + N = c, where w is the real wage, T is time available for work and leisure and N is income derived from non-labour sources (rents, profits etc). This is all spent on consumption c. (a) Form the Lagrangean, find optimal consumption (c*) and leisure (1*) in terms of w, and N. Do not check the second order conditions. (b) Labour time advanced (L*) is T– l*. Define this in terms of w,T and N. (c) Show that optimal L* change positively as the real wage (w) increases.

10. Consider the labour/leisure choice problem where the utility function is: U(c,l) = c²l where c is consumption of goods and services, and l is leisure time. The constraint is: w(T – 1) + N = c, where w is the real wage, T is time available for work and leisure and N is income derived from non-labour sources (rents, profits etc). This is all spent on consumption c. (a) Form the Lagrangean, find optimal consumption (c) and leisure (1) in terms of w, and N. Do not check the second order conditions. (b) Labour time advanced (L) is T– l. Define this in terms of w,T and N. (c) Show that optimal L* change positively as the real wage (w) increases.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter16: Labor Markets

Section: Chapter Questions

Problem 16.11P

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