3. Consider a parent who is altruistic towards her child, but also cares about her own consumption. The parent's utility over her own consumption and that of her child is up log(co) + a log(c₁) where c₁ is the child's consumption, and a > 0 is the degree of parental altruism. Suppose that the parent can invest in the child's human capital by spending money (e) on her education; education generates human capital h = f(e) and human capital is paid at rate w. The parent has a total income of y. (a) Write down an expression for the child's future consumption in terms of the parent's choice of e. (b) Now write down the Lagrangian for the parent's decision problem.

3. Consider a parent who is altruistic towards her child, but also cares about her own consumption. The parent's utility over her own consumption and that of her child is up log(co) + a log(c₁) where c₁ is the child's consumption, and a > 0 is the degree of parental altruism. Suppose that the parent can invest in the child's human capital by spending money (e) on her education; education generates human capital h = f(e) and human capital is paid at rate w. The parent has a total income of y. (a) Write down an expression for the child's future consumption in terms of the parent's choice of e. (b) Now write down the Lagrangian for the parent's decision problem.

Principles of Microeconomics

7th Edition

ISBN:9781305156050

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter21: The Theory Of Consumer Choice

Section: Chapter Questions

Problem 11PA

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