S17_PS4Part2.pdf - Ec 21 Problem Set 4 Part 2 Due Monday...

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Page 1 of 13 Ec 21 – Problem Set 4, Part 2 Due Monday April 24, Midnight (No need to hand in) You do not need to hand-in this part of the problem set, but you are of course expected to do it. Doing this by Monday midnight will enable you to ask questions about it during extra office hours that I will hold on Tuesday. Moreover, doing these problems will be very good practice for the Quiz on Wednesday. Solutions will be posted on Canvas on Tuesday morning. Please check your answers carefully after the solutions are posted. This problem set is literally Quiz 2 of Ec21 in 2012. This year’s quiz will roughly follow the same format, so it should give you some guidance on the level of difficulty, format, and types of questions you can expect on the quiz. There are optional practice questions at the end, and the solutions to the optional practice questions have been posted (but try to do the problems without looking at the solutions). ============================================================================
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Page 2 of 13 1. Short Answer Questions (16 points) a. Give the definition of a normal good. b. Give the definition of “revealed preference” in the sentence “bundle A is revealed preferred to bundle B.” c. Consider a country (say, some welfare state in northern Europe) where monthly welfare payments are adjusted so that the utility of a typical welfare recipient is always equal to a certain level. A typical welfare recipient purchases 20 subway rides per month when the price per ride is 2.00 but only 17 rides when the price of price per ride is 2.50 (after his welfare payments have been adjusted). What is the compensated (Hicksian) elasticity of demand for subway rides for a typical welfare recipient? d. Recall that the Slutsky equation (in derivative form) for the number of Skiway tickets (subscript “T”) is given by: h T / p T = x T / p T + x T x T / y where p T denotes the price of tickets, denotes h T the compensated quantity of tickets demanded, x T denotes the uncompensated quantity of tickets demanded, and y denotes income. A change in the price of Skiway tickets also has an effect on the compensated quantity of books demanded: h B / p T . Please give an equation (a modified version of the Slutsky equation) that expresses h B / p T in terms of quantities and derivatives of the uncompensated demand curves, and explain in words how you arrived at this equation. Note: please use the subscript B for books. h B / p T = Explanation:
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Page 3 of 13 2. HOP Tickets and Mountain Dew (14 points) Suppose a Tuck student derives utility from just two goods, HOP Tickets (“T”) and Mountain dew (“M”) according to the utility function: U(T, M) = 2T + ln(M) The price of Tickets is p T and the price of Mountain dew is p M . Denote utility by U and income by Y. a. Use the method of Lagrange to find the compensated (Hicksian) demand function for Tickets and the compensated (Hicksian) demand function for Mountain dew.
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