301 Economics Fall 2006 PRELIM 2 - J. Wissink Thursday November 2, 2006 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 90 minutes. Total points on test = 100 ANSWER ALL THE QUESTIONS. See point scores by each question. 1. (20 points) The Bush administration has decided to follow the lead suggested by our very own Robert Frank and get people to conserve gasoline. Bush also wants to shore-up the federal budget. Suppose Bush decides to place a per unit tax on gas. This tax raises the price consumers pay from P 0 to P1. Assume the supply curve for gas is horizontal. Suppose Zac is a representative consumer with very well-behaved preferences who gets utility from Gas (G) and $aog. Much to Bushs dismay, even though the tax on gas raises revenue in terms of $aog, the tax leads to absolutely NO CHANGE in the observed 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" diagram illustrate that this could, indeed, happen. Please put gallons of gas on the horizontal axis. c. Given that Zac consumes the same amount of gas as before the tax, is it fair to say that Zac is not hurt by this tax? Explain your position. d. Using the concept of change in Marshallian/Dupuit consumers surplus, what, if any, is the excess burden (,,ala 101) associated with this tax? Illustrate your answer in the graph you drew for part (a). e. Using the concept of equivalent variation, what, if any, is the excess burden (,,ala 301) associated with this tax? Illustrate your answer in the graph you drew for part (a) OR on the graph you drew in part (b). f. Suppose Zac is really angry with Bush over the gas tax. What, if anything, could Bush do to appease Zac, but also get what he wanted that is for Zac to consume less gasoline?
2. (12 points) 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 = $3, he chose the bundle X = 10 and Y = 0. a. Graph Manfreds implied budget lines with the bundles he selected indicated. Please put X on the horizontal and Y on the vertical. b. Do Manfreds choices satisfy the weak axiom of revealed preference, and why or why not? c. Propose a pair of bundles on Manfreds August and September budget lines that would satisfy the weak axiom of revealed preference. d. Based on what you proposed in your answer to (c), can you necessarily say that Manfred was better off or worse off in August as compared to September? Or is there insufficient evidence to tell? Explain briefly.
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3. (15 points) Ruth is an ordinary well-behaved utility maximizer with the utility function: u=($M) where $M is money. Ruth is on the game show "Let's Make a Deal" starring as host the stunning, Ivanna DuEconomics. Ivanna offers Ruth two options: Option A is $500 in cash; Option B is a gamble in which Ruth would take home $2500 if the (fair) she coin flips comes up heads and $225 if the coin toss comes up tails. a. b. c. d. e. What is the expected utility of Option B? What is the expected value of Option B? What is the certainty equivalent of Option B? Should Ruth take Option A (the cash) or Option B (the gamble)? Explain/defend your answer. If instead Ruth were offered the expected value of the gamble as the sure amount of cash in Option A would she take the chance or take the sure money? Explain/defend your answer.
4. (17 points) Illustrate how all four points, E, F, G & H on the isoquant/isocost diagram would be represented on a diagram representing average total cost functions, both long-run and short-run. Assume T and S are the only two inputs in the production function for x. When considering the short run, assume S is the fixed input. Make sure to use the numbers in the graph, not just any old numbers.
x=200 S
tc=$6800 F G tc=$6000 S1 tc=$5000 H E tc=$5400 x=100 T
S0
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5. (18 points) Greg and Christine are both delft vase makers and buy labor and capital at the same market prices. They have the following delft vase production functions:
xChristine = KL and xGreg = K1/2L1/2.
a. Without doing the full-blown problem and all the arithmetic involved, qualitatively describe how Gregs long run total cost curve compares to Christines long run total cost curve? Briefly defend your answer/description. b. This time, do the full-blown problem and all the arithmetic involved, and show how Gregs short run total cost curve compares to Christines short run total cost curve assuming KGreg=KChristine=9? c. Would you rather have Greg or Christines production function in the short run situation described in the previous part? 6. (18 points) Backpacks are produced by Wissport with fabric included sewing machines and labor. Suppose you are responsible for making the labor and kaptial (that is the fabric included sewing machines) decision for Wissport. The labor-kapital technology of backpack production is described by the isoquant diagram below. Assume that the price of labor is $40/unit and that the price of kapital is $200/unit. a. What production function is illustrated by this particular isoquant diagram? b. Determine your long run total cost function, assuming you produce backpacks efficiently. c. Suppose Wissport is deliberating signing a contract for K=2, taking Wissport from a long run situation into a short run situation. What would Wissports short run total cost function be if they signed such a contract?
K
isoquant for x = 2 backpacks
helping line with slope 1/3
2
isoquant for x = 1 backpack
1 3 6 L
(5 points) EXTRA CREDIT PROBLEM 7. Professor Ima Payne is searching for a utility function that will make it so that when she does surplus and burden measures for the good "X" she can safely use the market or Marshallian demand curve and will not have to worry about the difference between equivalent variation and change in consumers surplus or equivalent variation and consumers surplus since this always gives her a headache. Do you have a suggestion for her? If so, what explicitly is the form of this utility function and why do you suggest it? 3