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Question: 5 a consumer has the utility function u in cin...

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5. A consumer has the utility function U= In C+In (24-N), where C is consump- tion and Nis labor supply. Her budget constraint is pC MwN, where p is the price of the consumption good, w the wage rate, and M the consumers non- wage income. (a) Formulate the problem of utility maximization subject to the budget con- straint, and derive the first-order conditions, using the Lagrange multi- plier approach and ignoring the nonnegativity constraints. 80 1 Static optimization Find the demand function C-C(p, w, M) and the labor supply function N N*(p, w, M) (i.e. , express C and N in terms of p, w, and M). Show that N* and C are homogeneous of degree zero in (p, w, M) (b) and aU*/3p<0. Show that U* is concave in M and convex in p. What is the relationship between aU*/aM and the Lagrange multiplier?

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