Economics 11: Microeconomic Theory 1 Professor Christian Hellwig Practice Problems Week 5 1) A particular household consists of two individuals who are both potential workers and who pool their budgets. The household’s preferences are represented by a single utility function U(X0, X1, X2), where X1is the amount of leisure enjoyed by person 1, X2is the amount of leisure enjoyed by person 2, and X0is the amount of the single composite consumption good enjoyed by the household. The two members of the household each have 24 hours which can either be enjoyed as leisure, or spent in paid work. The hourly wage rates for the two individuals are w1and w2, respectively, and they jointly have non-wage income of M. The price of the composite consumption good is 1. a)Write down the household budget constraint b)The household utility function takes the form: U (X0, X1, X2) = β0log (X0- α)+ β1 log X1+ β2log X2Solve for the household’s optimal choice of X1,X2,X0c)Derive the household’s supply of the labor of individuals 1and 2.
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