ECONOMICS  108

                                                                     Fall, 2000

                                              Second Midterm - with ANSWERS

There are 100 points on this exam; the number of points appears in parentheses near each question.

Print your name AND sign your name in the spaces provided below.  Also write your social security (University ID) number. 

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1. (8 points)  A firm’s factory pollutes the air. Draw a diagram to show (a) the marginal private cost of the good that the firm produces, (b) the marginal social cost of the good, (c) the marginal private and social benefit of the good, (d) the economically efficient quantity of the good, (e) the equilibrium quantity, (f) the equilibrium price, and (g) the deadweight social loss from allowing pollution.

 Draw a graph like this one.

(a) MPC

(b) MSC

(c) D

(d) 8,000 in this example 

(e) 10,000 in this example

(f) PA

(g) shaded pink area

(i)-(iv) – see graph

If the monopolist can perfectly price discriminate, then the graph looks like the following, with no deadweight social loss.

3. (5 points) Discuss, and give an example: "Committing yourself, in advance, to some future action is a bad idea because it takes away your flexibility to respond, in the best way, to changes in situations." 

False.  By committing to a future action, you can change incentives for other people so that they behave in ways that are more beneficial to you.  For example, if a government can commit never to negotiate with terrorists who take hostages, it can reduce the incentives of terrorists to take hostages in the future.

4. (a) Explain "moral hazard."  (4 points)

Moral hazard occurs when two people, a principal and an agent, are engaged in some transaction (or other relationship), and the principal cannot observe the agent’s actions, and the principal wants to change the agent’s incentives.

(b) How does moral hazard apply to insurance?  How does moral hazard apply to conflicts between a firm’s stockholders and its bondholders? (6 points)

Examples: If insurance covers your car in the event of damage, you have less incentive to be careful to prevent damage.  (You would have greater incentive to be careful if you had to pay for damage out of your own pocket.)  Similarly, when a person has insurance against theft, he has less incentive to take actions to prevent theft.  And when a person has health insurance, he has less incentive to take actions that can help avoid medical expenses. 

            After bondholders lend money to a firm, the stockholders may want the firm to choose some risky business actions, because the stockholders share the losses with the bondholders if the firm is unlucky, but the stockholders get all the gains if the firm is lucky.

(c) Explain " adverse selection." (4 points)

Adverse selection occurs when two people are engaged in some transaction (or other relationship), but one of the people has relevant information that the other person lacks.  For example, someone who sells a used car may know more about its reliability and potential problems than someone who seeks to buy a used car.  This creates a problem because buyers know that sellers are more likely to get rid of (sell) bad cars than reliable cars.  Consequently, buyers expect the typical used car to have low quality.  Therefore, someone trying to sell a high-quality used car may be unable to find buyers who are willing to pay the higher price that such a car would otherwise bring.

(d) How does adverse selection apply to insurance?   How does adverse selection apply to interest rates that banks charge on their credit cards? (6 points)

Examples:  People with greater risks of becoming ill are generally willing to pay more for health insurance than people with lower risks of becoming ill.  Consequently, whatever the price of health insurance, the people who choose to buy it tend to be those people with the relatively higher risks.  People who borrow money on credit cards (by not paying their full balances each month) tend to be people who are higher credit-risks – that is, they are more likely not to repay their loans on time.  (People with lower credit risks can generally borrow money at lower interest rates in other ways.)

5. (17 points) A forest is a common resource with many berries that can be sold for $10 per basket. If only one person picks berries in the forest, that person picks 10 baskets on an average day. If two people pick berries in the forest, they each pick 9 baskets on an average day. (The problem is that each person spends more time looking for berries that have not already been picked by the other person.) The table below shows how the number of baskets of berries picked per person depends on the number of people picking berries. The opportunity cost of each person's time is $40 per day, and alternative jobs are exactly as much fun as picking berries.

(a) How many people pick berries in equilibrium, when the forest is a common resource?  Why? 

Seven (7) people – because the marginal private benefit of the seventh person, $40, equals the marginal private cost (the $40 opportunity cost of the person’s time). 

(6 people is also a correct answer, since the 7th person is indifferent between picking berries and doing something else.)

(b) What is the economically efficient number of people picking berries in the forest?  Why?

Four (4) peo`ple – because the marginal social benefit of the fourth person, $40, equals the marginal social cost (the $40 opportunity cost of the person’s time). 

(3 people is also a correct answer, for similar reasons as above.)

(c) If the forest were private property and its owner maximized profit from the forest, what price would the owner charge each person to pick berries?  Why? How many people would pick berries in the forest?  Why? How much profit would the owner of the forest earn?  Why?

The owner would charge each person $30 to pick berries in the forest.  Consequently, four (4) people would pick berries. 

This maximizes the owner’s profit – because the marginal social benefit of the fourth person, $40, equals the marginal social cost (the $40 opportunity cost of the person’s time). 

6. (6 points) Explain, with an example, the paradox of voting (the Arrow impossibility theorem).

The simple logic of the median-voter model applies well to some political situations. However, many others give rise to strange and surprising equilibrium results. Suppose that three voters will evaluate three possible government actions, as in Table 1. Alan favors Policy A, considers Policy B second best, and thinks Policy C is the worst policy. Bill favors Policy B, thinks Policy C is second best, and thinks Policy A is the worst choice. Cindy thinks that Policy C is best, Policy A is second best, and Policy B is the worst option. If they vote on Policy A versus Policy B, Policy A wins because Alan and Cindy vote for A over B, and only Bill votes for B over A. Policy A beats Policy B in an election. If, instead, they vote on Policy B versus Policy C, Policy B wins because Alan and Bill vote for B and only Cindy votes for Policy C. Policy B beats Policy C in an election.

You might think that Policy A would beat Policy C in an election because A beats B, and B beats C. However, if the three people vote between Policies A and C, Policy C wins! Bill and Cindy vote for C and only Alan votes for A. Such an election produces strange results: A beats B, B beats C, and C beats A! Even if every voter makes a rational choice in the sense that each has a clearly defined first, second, and third choice, voting by society as a whole produces no clearly defined first, second, or third choice. This example illustrates the Arrow impossibility theorem.

The Arrow impossibility theorem states that, under very general conditions, voting can produce inconsistent results (in the sense that A can beat B in an election while B beats C, but A does not beat C) even if all voters make consistent choices.

If a majority of voters prefer Policy A to either Policy B or Policy C (or any other policy), then Policy A may seem, in one sense, to coincide with the public interest. The Arrow impossibility theorem shows that it is usually impossible to define the public interest in this way. One generally cannot combine the preferences of individual people, expressed by voting, into a consistent set of preferences for society as a whole.

This result also shows the importance of setting an agenda for voting. The outcome of voting between several alternatives can depend on the order in which people consider those alternatives. If people must choose first between A and B, and then between C and the winner in the first election, Policy C wins. If people first choose between B and C, then choose between A and the winner in that election, Policy A wins. If people first choose between A and C, then between B and the winner in that election, Policy B wins. This example illustrates that a political equilibrium can depend crucially on factors other than the views or preferences of voters.

7. (10 points) A dentist and a writer live next door to each other, and each has her office at home. Screams of pain from the patients in the dentist's office interfere with the writer's creativity, causing her to write inferior novels and lose $800 per year in income. It would cost $600 for the dentist to install sound-absorbing material on her office walls, and this material would have to be replaced each year. (it is a rowdy dentist office.) The writer sues the dentist. The court can rule in favor of the author and require the dentist to soundproof her walls, or it can rule in favor of the dentist and dismiss the case. Explain what would happen under each ruling if:
  a. The dentist and the writer are on speaking terms (small transactions cost, ignoring court fees).
  b. They are not speaking to each other under any circumstances (large transactions costs).

(a) If they are on speaking terms, then:

If court rules in favor of writer, then dentist spends $600 to sound-proof walls.

If court rules in favor of dentist, then writer pays dentist $600 to sound-proof her walls.

(b) If they are NOT on speaking terms, then:

If court rules in favor of writer, then dentist spends $600 to sound-proof walls.

If court rules in favor of dentist, then the dentist loses $800 per year in income.

8. (4 points)  What is a sub-game perfect Nash equilibrium?

A subgame perfect Nash equilibrium is a Nash equilibrium in which every player’s strategy is credible (no player makes incredible threats).  A strategy is credible if a player would have an incentive to carry out that strategy.
9.  (20 points) You (the "principal") have a company that hires an agent to work for it.  The agent should try to convince a corporation to buy products from your company.  If it does, then you earn a $600,000 profit; otherwise your profit is zero.  The table shows how the chances (probabilities) of making the sale depend on whether the agent works very hard, works normally, or shirks.

Chance of Making the Sale

You can pay the agent a salary that depends on whether you get the contract.   Also assume:

(1)   No one will accept the job as the agent unless they have an expected salary of $30,000, including a guarantee of at least $20,000 regardless of whether the firm makes the sale.  

(2)   An agent will work normally, rather than shirk, if normal work raises his expected salary by at least $10,000 (above his expected salary if he shirks).   

(3)   An agent will work hard, rather than normally, if hard work raises his expected salary by at least $10,000 (above his expected salary if he works normally).

(a) What is the minimum amount that you can pay a person to become an agent, and how does the agent's pay depend on whether your company makes the sale?  Explain your answer.

YOU MUST PAY AT LEAST $20,000 NO MATTER WHAT HAPPENS (EVEN FAILURE TO WIN THE CONTRACT) AND YOU MUST PAY AN EXPECTED SALARY OF $30,000.  IF THE AGENT SHIRKS, THEN HE WOULD HAVE A 6/10 CHANCE OF GETTING $20,000, SO YOU WOULD NEED TO PAY HIM $45,000 IF HE WINS THE CONTRACT.  THE CALCULATION IS (SOLVING FOR X IN THE EQUATION BELOW):

(4/10) X + (6/10)($20,000) = $30,000,

or X = (10/4)($30,000-$12,000) = (10/4)($18,000) = $45,000.

(b) What is the minimum amount you can pay an agent to get that agent to work normally? Explain your answer.

 TO GET HIM TO WORK NORMALLY, RATHER THAN SHIRK, HE WOULD NEED TO SEE AN EXPECTED BENEFIT OF $10,000 FROM THAT NORMAL WORK.  SO YOU WOULD NEED TO PAY HIM Y dollars if he succeeds in winning the contract, and $20,000 if he fails, where Y is the solution to:

(5/10) Y + (5/10)($20,000) = {(4/10) Y + (6/10)($20,000)}  +  $10,000

The left hand side of the equation above shows the expected salary if the agent works normally (giving a 5/10 chance of winning the contract and a 5/10 chance of failing).  This expected salary must be $10,000 more than the term in squiggly brackets on the right-hand side of the equation above, which shows the expected salary if the agent shirks (giving a 4/10 chance of winning the contract and a 6/10 chance of failing). 

Solving for Y, by subtracting (4/10)Y from both sides and subtracting (5/10)($20,000) from both sides, we get:

(1/10) Y  = (1/10)($20,000)  +  $10,000

or Y  = $20,000  +  $100,000

or Y = $120,000.

(c) What is the minimum amount you can pay an agent to get that agent to work hard?  Explain your answer.

THE LOGIC IS THE SAME AS IN PART (B).  TO GET HIM TO WORK HARD, RATHER THAN NORMALLY, HE WOULD NEED TO SEE AN EXPECTED BENEFIT OF $10,000 FROM THAT HARD WORK.  SO YOU WOULD NEED TO PAY HIM Z dollars if he succeeds in winning the contract, and $40,000 if he fails, where Y is the solution to:

(11/20) Z + (9/20)($20,000) = {(10/20) Z + (10/20)($20,000)}  +  $10,000

The left hand side of the equation above shows the expected salary if the agent works hard.  This expected salary must be $10,000 more than the term in squiggly brackets on the right-hand side of the equation above, which shows the expected salary if the agent works normally (giving a 10/20 chance of winning the contract and a 10/20 chance of failing). 

Solving for Z, by subtracting (10/20)Y from both sides and subtracting (9/20)($20,000) from both sides, we get:

(1/20) Z  = (1/20)($20,000)  +  $10,000

or Z  = $20,000  +  $200,000

or Z = $220,000.