tute_3(1).pdf - Macroeconomic Policy ECON2040 Tutorial 3 Week 4 Problem 1 The Household’s Problem Consider a representative consumer whose preferences

# tute_3(1).pdf - Macroeconomic Policy ECON2040 Tutorial 3...

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Macroeconomic Policy - ECON2040 Tutorial 3 Week 4 Problem 1: The Household’s Problem Consider a representative consumer whose preferences can be represented by the utility function U ( C, l ) , where C is consumption and l is leisure. U satisfies the standard assumptions discussed in class, e.g. U C > 0, U l > 0 and U is concave. Suppose the consumer has a total of h hours to distribute between leisure and labor supply ( N s ). Let w be the hourly wage and assume that the consumer pays a lump sum tax T to the government. Finally, let π be the amount of profits (or dividends) that the consumer receives from a firm that he owns. 1. Write the consumer’s budget constraint. 2. Write the consumer’s optimisation problem. 3. Show that the marginal rate of substitution between l and C , MRS l,C , is equal to U l /U C . 4. Show that at the optimum the marginal rate of substitution equals the wage rate. Interpret. 5. Suppose π - T > 0 . Draw the budget constraint on the ( l, C ) plane, and a typical optimal choice for consumption and leisure.

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