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 , X 1 , X 2 ), where X 1 is the amount of leisure enjoyed by person 1, X 2 is the amount of leisure enjoyed by person 2, and X0 is 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 w 1 and w 2 , 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 , X 1 , X 2 ) = β0 log (X0- α )+ β 1 log X 1 + β 2 log X 2 Solve for the household’s optimal choice of X 1 ,X 2 ,X0 c)
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