202_finalQu - Fall 2003 F INAL E XAM D ECEMBER 8 2003...

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Fall, 2003 ARE202A F INAL E XAM D ECEMBER 8 2003 Tackle first the question you think is the easier one. It’s always a good strategy to make attempts at all parts of the question, because then you always have a chance at partial credit. If you omit a part, then you lose that chance! Don’t attempt either bonus part till you’ve done what you can on the non-bonus parts of both questions. Problem 1 . (60 points) Consider a consumer with Cobb-Douglas preferences: U = A . Q α L β with A > 0, α = 1 / 3 and such that β = 1 / 2, and where Q is a composite consumer good and L is leisure (not labor). The consumer maximizes his utility subject to non-negativity constraints ( Q 0, L 0), a time constraint L T (where T is the total time available) and subject to his budget constraint: pQ ( 1 - τ ) w ( T - L )+ Y where p is the price of the composite commodity, τ is the tax rate on wage income ( τ [ 0 , 1 ) ), w is the wage rate per unit of labor time, and Y is other non-taxed income. We assume that the consumer’s other income represents a small share of his maximum wage budget, i.e., that Y < w ( 1 - τ ) T 2 . (a) Write the utility maximization problem in the usual form. (b) Draw the feasible set. (c) On a graph, identify geometrically a segment representing the set of points that could potentially satisfy the Mantra (i.e., be candidates for solution), given what you know about the utility function.
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