Econ 301 - Homework #3 1. Deriving Labor Supply . Consider a consumer with preferences for consumption of a composite good (Y) and leisure (N) given by the following utility function: U ( Y,N ) = 2 Y 2 / 3 N 1 / 3 Denote the consumer’s wage rate by w and total time available for labor and leisure is 24 hours. The price of consumption is one. Denote the amount of labor supplied as N, so that N + H = 24. The consumer also receives an unearned income of I . a. Write out the budget constraint determining feasible allocations of leisure and consumption. b. Using substitution method to derive the optimal bundle of labor supply H ( w,I ) and optimal bundle of consumption Y ( w,I ) ( Hint , only need to solve the interior solution where labor supply and consumption are positive). c. Derive the consumer’s leisure consumption function: N ( w,I ). d. Optional (5 extra points) . Determine the eﬀect of increasing unearned income I on the supply
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