ECO 110 – Introduction to Economics



ECO 220 – Intermediate Microeconomics

Professor Mike Rizzo

Third COLLECTED Problem Set – This is an assignment that WILL be collected and graded. Please feel free to talk about the assignment with your friends or with your group and I strongly encourage you to submit your assignment as a group.

Assigned: Monday, April 25th

Due: Monday, May 2nd

These following questions are for a review of your notes – you should study these, but do not report the answers to me:

1. Why must a signal between potential adversaries be costly to fake?

2. What causes the used car market to “unravel”?

3. What causes the dating service market to “unravel”?

4. What might cause an insurance market to “unravel”?

5. Explain why it makes sense to self-insure against minor losses.

6. How might statistical discrimination affect the distribution of insurance premiums within a group?

7. How might statistical discrimination affect the average insurance premium paid by members of different groups?

Problem Set Questions:

1. Suppose the messiness of an apartment is measured on a scale of 0 to 100, with 0 being the cleanest and 100 being the messiest. Suppose that 10% of the apartments fall between 0-20, 20% between 20 and 40, 40% between 40 and 60, 20% between 60 and 80 and 10% between 80 and 100.

Suppose that all parents tried to teach their parents never to let anyone in to see their apartments if they were over 80 on the messiness scale. If such a rule of thumb were widely observed, what would your best estimate of the messiness index of someone who said, “You can’t come in now, my place is a pit?” In a world in which everyone makes use of all available information, would you expect this rule of thumb to be stable? What do you conclude from the fact that people really do sometimes refuse admission on the grounds that their apartments are too messy?

We never talked directly about the next two questions, but THINK about them – they are related to everything we’ve talked about during the past week:

2. Why should you EXPECT that all WWF wrestling matches are fixed but expect that fewer prize fights are rigged and far fewer baseball games are rigged?

3. What grounds are there for assuming that a randomly chosen social worker is less likely to cheat you in cards than a randomly chosen person is?

4. A new motorcycle sells for $9,000, while a used motorcycle sells for $1,000. If there is no depreciation and risk-neutral consumers know that 20% of all new motorcycles are defective, how much do consumers value a non-defective motorcycle?

5. What is the expected value of a random toss of a die (fair and six sided)?

6. Suppose your current wealth is $100 and your utility function is U(w) = w2. You have a lottery ticket which pays $10 with probability 0.25 and $0 with probability 0.75. What is the minimum amount for which you would be willing to sell this ticket?

7. Joe has an investment opportunity that pays $33 with probability ½ and loses $30 with probability ½.

a. If his current wealth is $111 and his utility function is U(w) = w ½ , will he make this investment?

b. Will he make it if he has two equal partners? (Be sure to calculate the relevant expected utilities to at least two decimal places)

8. Given a choice between A (a sure win of $100) and B (an 80% chance to win $150 and a 20% chance to win 0), you pick A. But when you are given a choice between C (a 50% chance to win $100 and a 50% chance to win 0) and D (a 40% chance to win 150 and a 60% chance to win 0), you pick D. Are your choices consistent with expected utility maximization?

9. Suppose Jones gets a disease with probability ½ and that his wealth is $9 million. If he gets the disease, it costs $5 million to cure.

a. If his utility function is U(w) = w ½ , will he purchase a government insurance policy that $2.6 million?

b. Now, suppose that there is a diagnostic laboratory that offers him a test. The test costs $D if it says that you will get the disease later in life and it costs $N if you will not get the disease. Further, assume that it costs a hospital $1,000 to administer the test and that the testing industry is perfectly competitive. What are the equilibrium values of D and M if the test gets it right 100% of the time? Interpret the meaning of this answer. To help you answer the question, you need to consider the following information:

i. What is the budget constraint faced by a competitive firm (i.e. if it charges two different prices for the test, what must the expected value of the prices be in a long-run perfectly competitive equilibrium)?

ii. If Jones discovers from the test that he will get the disease, he will want to purchase the insurance.

iii. If Jones discovers from the test that he will not get the disease, he will not want to purchase the insurance.

iv. You don’t need to use the utility function directly to compute the answer, but realizing what form the utility function takes should tell you what Jones’ wealth should be like in all states of the world.

10. There are two groups, each with a utility function given by U(w) = w ½. Suppose initial wealth levels for all individuals equals 100. Each member of group 1 faces a loss of 36 with probability 0.5. Each member of group two faces the same loss with probability 0.1.

a. What is the most a member of each group would be willing to pay to insure against the loss?

b. In part (a), if it is impossible for outsiders to discover which individuals belong to which group, will it be practical for members of group 2 to insure against this loss in a competitive insurance market? (For simplicity, you may assume that insurance companies charge only enough premiums to cover their expected benefits payments). Explain.

c. Now suppose that the insurance companies in part (b) have an imperfect test for identifying which persons belong to which group. If the test says that a person belongs to a particular group, the probability that he really does belong to that group is x < 1.0. How large must x be in order to alter your answer to part (b)?

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