Economics 313 - Fall 2005 – PRELIM 1 - J. Wissink – Monday Oct. 3 Directions: Answer all questions. Write legibly, concisely, and coherently. Be sure to label all axes, functions, and variables you use. READ QUESTIONS CAREFULLY. Draw pictures whenever possible. Show all your work! Total time for the test is 50 minutes. Total points on test = 100 Part I. Short essay: Answer the following three questions for 15 points each. 1. Alfie consumes only X and Y and part of his indifference curve map is illustrated below. a. Write down a utility function that would be an acceptable representation of his preferences. b. Reproduce the diagram in your exam booklet and illustrate an optimal bundle for Alfie assuming that Px=$1 and Py=$1 and Income=$6.00. Add or subtract any lines/curves you need. c. In general, i.e., for any values of Px, Py and I, what is the function for the optimal amount of X in Alfie’s utility maximizing bundle? That is, what is Alfie’s demand function for X? 2. Suppose Marc gets utility from only X and Y. His “Slutsky Equations” are thus: (Note: M refers to the market/Marshallian demand responses where SSE refers to the Slutsky/compensated substitution effect responses. (∂X/∂Px)M = (∂X/∂Px)SSE – X(∂X/∂I)M (∂X/∂Py)M = (∂X/∂Py)SSE – Y(∂X/∂I)M (∂Y/∂Px)M = (∂Y/∂Px)SSE – X(∂Y/∂I)M (∂Y/∂Py)M = (∂Y/∂Py)SSE – Y(∂Y/∂I)M If Marc’s utility function is: U(X, Y) = min{2X, 3Y} then what are the algebraic signs of the following terms in his Slutsky Equations. NOTE: you can choose + or – or 0 or “can’t know without more info” a. (∂X/∂Px)M b. (∂X/∂Px)SSE c. (∂X/∂Py)M d. (∂Y/∂Px)SSE 3. In August, when prices for X and Y were Px = $4 and Py = $6, Manfred chose the bundle X = 6, Y = 6. In September when prices for X and Y were Px = $6 and Py = $3, he chose the bundle X = 10 and Y = 0. XY61224IC1IC0a. Graph Manfred’s implied budget lines with the bundles he selected indicated. Please put X on the horizontal and Y on the vertical. b. Do Manfred’s choices satisfy the weak axiom of revealed preference, and why or why not? c. Propose a pair of bundles on Manfred’s August and September budget lines that would satisfy the weak axiom of revealed preference. d. Based on your answer to (c), can you necessarily say that Manfred was better off or worse off in August as compared to September? Or is there insufficient evidence to tell? Explain briefly. Part II. Problems: Answer both at 27.5 points each 1. Consider Albert who has Cobb-Douglas preferences that can be described by the following utility function: u = xy2 a. What are Albert’s demand functions for x and y, that is find the functions x*( ) and y*( )? No detailed derivation necessary. b. Illustrate and label/identify the total effect, Hicksian substitution effect and income effect on an “indifference curve-budget line” diagram that reflects Albert’s specific utility function. Assume that the price of “x” increases. Put “x” on the horizontal and “y” on the vertical axes. c. On a separate diagram, illustrate what Albert’s market/Marshallian demand curve looks like for good x. Does it satisfy the law of demand and very briefly why? d. Will Albert’s Hicksian/compensated demand curve for good x at the original level of utility be steeper or flatter than the market/Marshallian demand curve you drew and very briefly why? e. What is the value of the “own price elasticity of demand for x” at $Px = 123.45? (THINK about PS#3 FIRST, then act.) f. What is the value of the “cross price elasticity of demand for x with respect to the price of y”? (THINK FIRST, then act.) 2. The Bush administration has decided it needs revenue fast to shore up the federal budget and it also needs people to conserve gasoline. Suppose Bush decides to place a tax on gas. This tax raises the price consumers pay from P0 to P1. Suppose Zac is a representative consumer with reasonably well-behaved preferences who gets utility from Gas (G) and $aog. Much to Bush’s dismay, even though the tax on gas raises revenue in terms of $aog, the tax leads to absolutely NO CHANGE in the market amount of gas Zac consumes. a. Draw a market demand curve for gas that would illustrate such a situation/outcome. b. In an “indifference curve-budget line” illustrate that this could, indeed, happen. Please put gas on the horizontal axis. c. Using the concept of change in Marshallian/Dupuit consumer’s surplus, what, if any, is the excess burden associated with this tax? Illustrate your answer in the graph you drew for part (a). d. Using the concept of equivalent variation, what, if any, is the excess burden associated with this tax? Illustrate your answer in the graph you drew for part (a) OR on the graph you drew in part (b). e. Based on Zac’s behavior, what can we conclude about whether G is a normal or inferior good and about Zac’s income and substitution effects when the price of gas changes? RETURN THIS EXAM QUESTION PAPER WITH YOUR ANSWER BOOKLETS. Print your name: