301 Economics Fall 2006 PRELIM 2 MAKEUP - J. Wissink Friday November 3, 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 Each question is worth 20 points. 1. 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 well-behaved preferences who gets utility from Gas (G) and $aog. Much to Bushs dismay, his tax on gas raises very little revenue in terms of $aog. However, the tax does reduce gas consumption a great deal. a. In an "indifference curve-budget line" diagram illustrate that this could, indeed, happen. Please put gallons of gas on the horizontal axis. b. Given that Zac generates very little revenue for the government, is it fair to say that Zac is not hurt very much by this tax? Explain your position. c. 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). d. Suppose Zac is really angry with Bush over the gas tax. What, if anything, could Bush do to appease Zac, but also get one thing that he wanted that is for Zac to consume less gasoline?
2. (This should take VERY little work, but some good thinking.) What are the values of the two own price elasticities of demand and the two cross price elasticities of demand for the utility function: u = xy(1-) That is, get the following: 1) own-price elasticity of demand for x with respect to Px; 2) own-price elasticity of demand for y with respect to Py; 3) cross-price elasticity of demand for x with respect to Py; and 4) cross-price elasticity of demand for y with respect to Px. HINT: Do you recall the Cobb-Douglas system? demand This is what is the x* function and what is the y* function?
3. Bree is on the famous game show: Lets make a deal. The host of the show offers Bree the following options: Option 1: Choose one of two curtains. There is $X behind one of the curtains. There is nothing behind the other. Option 2: The host holds out $10,000 cold cash and tells Bree she can have it. Brees utility function for money is u=X. The producers of the show want to make sure Bree goes for Option 1: picking a curtain, since this makes viewing more fun. a. What is the minimum amount they have to put behind the winning curtain to get Bree to "play" Option 1? b. How would your answer change if we assumed that Bree was risk neutral, instead?
1
4. Consider the isoquant diagram for producing x with skilled and unskilled labor.
Unskilled Labor 12
a. What production function represents this particular set of isoquants? b. Given w = $2 = the price of unskilled labor and v = $20 = the price of skilled labor, determine the firms 3 long run cost curves; that is find 1) long run total cost; 2) long 4 run average total cost and 3) long run marginal cost. c. Suppose that you have CONTRACTED to pay for 4 units of skilled labor at a price of $20 per unit. What would your fixed costs be? What would your variable costs be in this short run situation?
x0 = 4 units x1 = 12 units
2
6
Skilled Labor
5. Illustrate how all four points, A, B, C, and D on the cost curve diagram below would be represented on an isocost/isoquant diagram. Assume the two factors of production to make x are S and T.
$ srtc1 srtc2 C
lrtc
D B
A x1 x2 widgets
EXTRA CREDIT PROBLEM 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? 2