Econ 633/733: Advanced Microeconomics Midterm Exam, Autumn 2004 Professor Kosteas

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1 Econ 633/733: Advanced Microeconomics Midterm Exam, Autumn 2004 Professor Kosteas Name: Instructions: You will be assigned a number. Write this number in the top right corner of every page. Do not write your name on any other page except for the cover page. You have 1:50 to complete the exam. Take your time and show your work. Good Luck. Short Answer Multiple Choice Short Essay Total

2 Short Answer (50 points): Show your work and label any graphs. α 1 α 1. Given the utility function U = x y, derive the Marshallian demand functions for x and y and the indirect utility function. (12 points)

3 m 2. Given the indirect utility function V =, derive the Hicksian demand γ γ p x + p y functions for x. (3 points) Explain why we call the Hicksian demand function a compensated demand function. (3 points) α α px p y 3. Given x =, what is the income effect of a change in p x? From the income m effect, what can we say about good x. (6 points)

4 α β γ 4. Given the demand function y = p p m, crosss-price and income elasticities for good y? If β>0, how are goods y and x related? (5 points) x y 5. Illustrate the income and substitution effects for a decrease in p x on good x, given that x is a giffen good. (5 points)

5 6. Define compensating and equivalent variation. Illustrate an example of equivalent variation. (7 points)

6 7. Draw the game tree for the following scenario. Matt, an actor, has two options for the future of his career. He can sign on to do a spin-off of his previous television series or he can pursue a film career. If he tries the TV series, there is a 0.2 probability of success, with a payoff of $8,100,000. If the series fails, he receives $400,000. If he pursues a film career, there is a 0.5 probability he will have a good career and make $2,500,000, and a 0.5 probability he has mediocre career, making $900,000. Draw the game tree and M determine which path Matt should choose if his utility is given by U =. What 100,000 M should he choose if his utility isu ' = 100, ? (9 points)

7 II. Multiple Choice (2 points each): Circle the correct answer. 1. If Laura is a saver, then a decrease in interest rates means: A) the substitution effect on savings will be positive B) the substitution effect on savings will be negative C) the income effect on savings will be negative D) Both A and C are correct 2. If Rachel earns $2000 this year and $1100 next year, the present value of her endowment, if the interest rate is 10% is: A) $3000 B) $3100 C) $2110 D) $ In diagram 6.2, suppose that the budget constraint above reflects an actuarially fair gamble. If so, which of the following odds for A and B respectively, is possible? A) A = 25% ; B = 75% B) A = 50% ; B = 50% C) A = 40% ; B = 60% D) A = 10% ; B = 90%

8 4. James wants to invest in a lemonade stand. He wants to add cherry flavor as well. If this new product sells, he will make back $20. If it does not sell, he will make only $12. James' utility function is U = (I 2 ). If the odds of selling well are 50/50, James' expected utility is: A) 256 B) 272 C) 236 D) none of the above 5. Which of the following does not support the notion that people are risk averse? A) people buy actuarially unfair insurance B) the existence of risk premia C) the existence of diversified mutual funds D) the popularity of state lottery games 6. The substitution effect for the labor market means that as wages, the number of hours worked. A) increases; increases B) increases; decreases C) decreases ; increases D) None of the above 7. Richard and Susan are both in the running for class president. Polls say that Susan has a 70% chance of winning. Richard offers her this bet. If she wins, she gets $2. If she loses, she must pay Richard $3. This bet: A) is actuarially fair B) is unfair for Susan C) is unfair for Richard D) has an expected value of zero for Susan 8. Suppose you roll a six-sided die and the payoff in dollars is equal to the face of the die. So rolling a 1 pays $1. Assuming you were risk adverse, if it cost $2 to play, you would: A) be willing to play B) not be willing to play C) be indifferent to playing D) cannot tell from information given

9 9. The substitution and income effects of a wage change have the opposite sign if: A) the wage in increasing B) the wage is decreasing C) work is a normal good D) leisure is a normal good 10. If Charlie works 10 hours a week for $10 an hour, but would not work at all if the wage fell to $5 an hour, Charlie's producer surplus from working is: A) $100 B) $25 C) $50 D) $0

10 Short Essays (10 points each): Answer each question in 2-3 paragraphs. 1. According to Auten and Joulfian, how do bequest taxes affect charitable contributions by parents? What other factors affect charitable giving?

11 2. How does experimental economics address the debate between economic theorists and psychologists?

12 3. Why should age and experience have different impacts on wage profiles?