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ECON302_Assignment2_F11

ECON302_Assignment2_F11 - ECON 302 Macroeconomic Theory 2...

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Page 1 of 2 Pages ECON 302 Macroeconomic Theory 2 Instructor: Sharif F. Khan Department of Economics University of Waterloo Fall 2011 Assignment 2 (Optional) Total Marks: 50 Marks Read each part of the question very carefully. Show all the steps of your calculations to get full marks, unless it is mentioned otherwise. 1. [20 marks] Suppose that the representative consumer’s preferences are given by the utility function ( ) , ln ln , l C l C U α + = where C is consumption and l is leisure. The consumer’s budget constraint is given by ( ) T l h w C - + - = π , where w is the real wage, h is the quantity of time the consumer has available, π is dividend income, and T is the lump-sum tax. a) Set up the consumer’s optimization problem. b) Write down the Lagrangian associated with this consumer’s optimization problem. c) Assume that there is an interior solution to the consumer’s problem. Determine the consumer’s optimal choice of consumption and leisure.

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