ECONOMICS 108

Fall, 1998
Third 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.

PRINT NAME

SIGN NAME

Soc. Sec. #

page 2 ________________

page 3 ________________

page 4 ________________

page 5 ________________

page 6 ________________

TOTAL___________________________________

1. 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. (8)

SEE FIGURE 2 ON PAGE 470

2. (a) What is a non-rival good? (3)

A NON-RIVAL GOOD IS A GOOD FOR WHICH THE QUANTITY AVAILABLE FOR OTHER PEOPLE DOES NOT FALL WHEN ONE PERSON CONSUMES MORE.

(b) What is a non-excludable good? (3)

A GOOD IS NON-EXCLUDABLE IF IT IS PROHIBITIVELY COSTLY TO PROVIDE THE GOOD TO PEOPLE WHO PAY FOR IT WHILE PREVENTING NON-PAYERS FROM OBTAINING IT.

A PUBLIC GOOD IS A GOOD THAT IS NON-RIVAL AND NON-EXCLUDABLE.

(d) Why can public goods provide a rationale for government actions? What actions might they justify? (3)

PUBLIC GOODS CREATE FREE-RIDER PROBLEMS. PEOPLE WANT TO CONSUME THE GOOD (WITHOUT PAYING) WHILE LETTING OTHER PEOPLE PAY FOR IT. AS A RESULT, IF ONLY A FEW PEOPLE ARE WILLING TO PAY FOR IT, THE EQUILIBRIUM QUANTITY OF THE PUBLIC GOOD MAY BE LESS THAN THE ECONOMICALLY-EFFICIENT LEVEL. THIS CAN PROVIDE A RATIONALE FOR GOVERNMENT TO COLLECT MONEY, THROUGH TAXES, TO PAY FOR THE PUBLIC GOOD.

3. Comment: "Committing yourself to a future action is never a good idea because it takes away your flexibility to respond to a situation in whatever way is best at the time." (4)

FALSE. YOU MAY BE ABLE TO CHANGE THE BEHAVIOR OF OTHER PEOPLE, IN WAYS THAT BENEFIT YOU, BY COMMITTING YOUR SELF TO A FUTURE ACTION. FOR EXAMPLE, THE GOVERNMENT COMMITS NOT TO DEAL WITH TERRORISTS WHO TAKE HOSTAGES (EVEN THOUGH, AFTER TERRORISTS HAVE ALREADY TAKEN HOSTAGES, THE BEST COURSE OF ACTION MIGHT BE TO COMPROMISE WITH TERRORISTS TO GAIN THEIR RELEASE). BY COMMITTING NOT TO DEAL WITH TERRORISTS UNDER ANY CONDITIONS, THE GOVERNMENT REDUCES TERRORISTS' INCENTIVES TO TAKE HOSTAGES IN THE FIRST PLACE.

4. (a) Explain "moral hazard." (5)

MORAL HAZARD OCCURS WHEN AN AGENT LACKS AN INCENTIVE TO ACT IN THE BEST INTERESTS OF THE PRINCIPAL (WHO HAS HIRED THE AGENT), AND THE PRINCIPAL CANNOT OBSERVE THE ACTIONS OF THE AGENT. FOF EXAMPLE, A REAL ESTATE AGENT MAY EARN A COMMISSION EQUAL TO 6% OF THE PRICE OF A HOUSE HE SELLS. IF HE WORKS HARD TO FIND A BUYER WILLING TO PAY AN ADDITIONAL $1000 FOR THE HOUSE. THE AGENT EARNS ONLY $60 OF THAT MONEY. AS A RESULT, THE AGENT MAY NOT WORK AS HARD AS HE COULD TO FIND SUCH A BUYER -- EVEN THOUGH THE PRINCIPAL (THE PERSON SELLING THE HOUSE) WOULD WANT HIM TO DO SO.

(b) How does moral hazard apply to insurance? (4)

WHEN A PERSON HAS INSURED A PRODUCT AGAINST THEFT, HE HAS LESS INCENTIVE TO TAKE ACTIONS TO PREVENT THEFT. WHEN A PERSON HAS HEALTH INSURANCE, HE HAS LESS INCENTIVE TO TAKE ACTIONS THAT CAN HELP AVOID MEDICAL EXPENSES.

ADVERSE SELECTION REFERS TO A SITUATION IN WHICH SOME SELLERS HAVE RELEVANT INFORMATION THAT BUYERS LACK (OR VICE-VERSA) ABOUT SOME ASPECT OF PRODUCT QUALITY. 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 -- SINCE BUYERS KNOW THAT PEOPLE ARE MORE LIKELY TO TRY TO SELL THEIR CARS IF THEY HAVE PROBLEMS THAN IF THEY ARE VERY RELIABLE, BUYERS EXPECT LOW QUALITY. THEREFORE, SOMEONE TRYING TO SELL A HIGH-QUALITY CAR MAY BE UNABLE TO FIND BUYERS WILLING TO PAY THE HIGHER PRICE THAT SUCH A CAR WOULD OTHERWISE BRING.

(d) How does adverse selection apply to insurance? (4)

WHEN INSURANCE COMPANIES OFFER POLICIES, PEOPLE WITH THE HIGHEST RISKS HAVE MORE TO GAIN FROM INSURANCE THAN PEOPLE FACING LOWER RISKS. CONSEQUENTLY, THE PEOPLE WHO CHOOSE TO BUY (THE MOST) INSURANCE TEND TO BE HIGH-RISK PEOPLE -- WHICH RAISES THE COST TO THE INSURANCE COMPANY OF PROVIDING INSURANCE. IF THIS FACT LEADS INSURANCE COMPANIES RAISE PRICES, THIS TENDS TO DRIVE AWAY MOSTLY LOW-RISK CUSTOMERS, WITH HIGH-RISK PEOPLE CONTINUING TO BUY INSURANCE. THIS FURTHER RAISES THE INSURANCE COMPANY'S COSTS.

5. Fred and Wilma can each choose "action 1" or "action 2." They each must choose without knowing what the other person will choose. The table below shows their payoffs from each possible combination of actions. (8 points)

Fred

Action 1 Action 2

Action 1 Fred gains 10 Fred gains 12

and Wilma gains 10 and Wilma gains 4

Wilma

Action 2 Fred gains 4 Fred gains 5

and Wilma gains 12 and Wilma gains 5

(a) What is the Nash equilibrium of this game?

FRED AND WILMA EACH CHOOSE ACTION 2; FRED GAINS 5 AND WILMA GAINS 5.

(b) Explain why your answer to part (a) might change if Fred and Wilma played this same game repeatedly (e.g. every day).

FRED AND WILMA COULD EACH GAIN IF EACH WERE TO CHOOSE ACTION 1. IN A REPEATED GAME, WILMA AND FRED MIGHT LEARN TO TRUST EACH OTHER TO COOPERATE, PLAYING STRATEGIES LIKE TIT-FOR-TAT, THAT COOPERATE IF THE OTHER PERSON COOPERATES, AND BRIEFLY PUNISH THE OTHER PERSON FOR NOT COOPERATING.

6. A lake is a common resource with many fish that can be sold for $5 each. If only one person fishes on the lake, that person can catch 15 fish on an average day. If two people fish on the lake, they each catch 14 fish on an average day. The table below shows how the number of fish caught per person depends on the number of people fishing. The opportunity cost of each person's time is $50 per day, and alternative jobs are exactly as much fun as fishing.

number of fish caught

people fishing per person

1 15

2 14

3 13

4 12

5 11

6 10

7 9

8 8

9 7

10 6

(a) How many people fish in equilibrium, when the lake is a common resource? (4)

IF THE LAKE IS A COMMON RESOURCE, 6 PEOPLE WILL FISH ON IT (SINCE A SIXTH PERSON CATCHES 10 FISH, SELLING THEM FOR $5 EACH AND EARNING $50, WHICH IS ALL HE COULD EARN IN THE OTHER JOB).

(b) What is the economically efficient number of people fishing on the lake? (4)

3 PEOPLE, BECAUSE (1) A THIRD PERSON INCREASES THE TOTAL NUMBER OF FISH CAUGHT BY 11, FROM 2*14=28 TO 3*13=39, RAISING THE TOTAL VALUE OF THOSE FISH BY $55, WHICH EXCEEDS THE $50 OPPORTUNITY COST OF THAT PERSON'S WORK. HOWEVER, (2) A FOURTH PERSON WOULD INCREASE THE TOTAL NUMBER OF FISH CAUGHT BY 9, FROM 3*13=39 TO 4*12=48, RAISING THE TOTAL VALUE OF THOSE FISH BY $45, WHICH IS LESS THAN THE $50 OPPORTUNITY COST OF THAT PERSON'S WORK.

(c) If the lake were private property and the lake’s owner maximized profit from the lake, what price would the owner charge each person to fish? How many people would fish on the lake? (8)

THE OWNER COULD MAXIMIZE PROFIT BY CHARGING AN $15 PER DAY FEE TO FISH ON THE LAKE. WITH THAT $15 FEE, 3 PEOPLE WOULD FISH (BECAUSE A THIRD PERSON WOULD CATCH 13 FISH, SELLING THEM FOR $65, WHICH LEAVES $50 AFTER THE $15 FEE -- AND THIS PERSON CANNOT DO BETTER BY SWITCHING TO THE OTHER JOB, WHICH PAYS $50).

7. Cho produces unique outdoor sculptures at a cost of $40 each. (His marginal and average costs are $40 per sculpture.) He faces the demand schedule in the table below. His sculptures have positive externalities; the third column in the table shows the marginal benefit to other people (that is, the benefit to people other than the buyers).

quantity

price demanded MB to other people

$200 1 $60

$180 2 $50

$160 3 $45

$140 4 $40

$120 5 $35

$100 6 $30

$80 7 $25

$60 8 $20

$40 9 $15

$20 10 $10

(a) Find the equilibrium price and level of production of these sculptures when Cho maximizes his profit. (3)

HE MAXIMIZES PROFIT BY PRODUCING 5 UNITS (SO THAT MR=MC=$40) AND CHARGING A PRICE OF $120.

(b) What is the economically efficient level of production? (3)

9 UNITS. THE MARGINAL SOCIAL BENEFIT OF THE 9^TH UNIT IS $55, WHICH EQUALS THE MARGINAL PRIVATE BENEFIT, TO BUYERS, OF $40, PLUS THE MB TO OTHER PEOPLE OF $14. SINCE THIS EXCEEDS THE MC OF PRODUCING THAT UNIT, $40, IT IS ECONOMICALLY EFFICIENT TO PRODUCE THE 9^TH UNIT. HOWEVER, IT WOULD NOT BE ECONOMICALLY EFFICIENT TO PRODUCE THE 10^TH UNIT, BECAUSE ITS MARGINAL SOCIAL BENEFIT IS ONLY ($20+$10=) $30, WHICH IS LESS THAN ITS $40 MARGINAL COST.

(c) If the local government decided to tax or subsidize purchases of Cho's art to achieve an economically efficient level of production, would it choose a tax or a subsidy? What level of tax or subsidy would it choose? (8)

CHO WOULD NEED A SUBSIDY OF $160 TO BE WILLING TO PRODUCE THE 9^TH UNIT, SINCE ITS MARGINAL COST IS $40 AND ITS MARGINAL REVENUE IS -$120. THE GOVERNMENT COULD EITHER PROVIDE A $160 SUBSIDY ON EACH UNIT PRODUCED, OR A SUBSIDY OF $40 TO PRODUCE THE 6^TH UNIT, PLUS A SUBSIDY OF $80 TO PRODUCE THE 7^TH UNIT, PLUS A SUBSIDY OF $120 TO PRODUCE THE 8^TH UNIT, PLUS A SUBSIDY OF $160 TO PRODUCE THE 9^TH UNIT.

8. (20) You (the "principal") have a new company and hire an agent to work for you. The agent should try to convince a major corporation to sign a contract to buy products from your company. If you get the contract you earn a $400,000 profit; otherwise your profit is zero.

The following table shows how the chances (probabilities) of winning the contract depend on whether the agent works very hard, works normally, or shirks.

Chance of Winning the Contract

	Agent's action
Result:	Work Very Hard	Work Normally	Shirk
$400,000 profit	6/10	5/10	4/10
Zero profit	4/10	5/10	6/10

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

Assume: (1) No one will accept the job as the agent unless they have an expected salary of $60,000 and a guarantee of at least $40,000 regardless of the whether the firm makes a profit or not. (2) An agent will work normally, rather than shirk, if normal work raises his expected salary by at least $20,000 (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 $20,000 (above his expected salary if he works normally).

(a) What is the minimum amount you can pay a person to become an agent, and how does the agent's pay depend on whether you get the contract?

YOU MUST PAY AT LEAST $40,000 NO MATTER WHAT HAPPENS (EVEN FAILURE TO WIN THE CONTRACT) AND YOU MUST PAY AN EXPECTED SALARY OF $60,000. IF THE AGENT SHIRKS, THEN HE WOULD HAVE A 6/10 CHANCE OF GETTING $40,000, SO YOU WOULD NEED TO PAY HIM $90,000 IF HE WINS THE CONTRACT. THE CALCULATION IS (SOLVING FOR X IN THE EQUATION BELOW):

(4/10) X + (6/10)($40,000) = $60,000,

or X = (10/4)($60,000-$24,000) = (10/4)($36,000) = $90,000.

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

TO GET HIM TO WORK NORMALLY, RATHER THAN SHIRK, HE WOULD NEED TO SEE AN EXPECTED BENEFIT OF $20,000 FROM THAT NORMAL WORK. SO YOU WOULD NEED TO PAY HIM Y dollars if he succeeds in winning the contract, and $40,000 if he fails, where Y is the solution to:

(5/10) Y + (5/10)($40,000) = {(4/10) Y + (6/10)($40,000)} + $20,000

The left hand side of the equation above shows the expected salary if the agent works hard (giving a 5/10 chance of winning the contract and a 5/10 chance of failing). This expected salary must be $20,000 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)($40,000) from both sides, we get:

(1/10) Y = (1/10)($40,000) + $20,000

or Y = $40,000 + $200,000

or Y = $240,000.

The answer is the same as in part (b).

By going through the same reasoning as in part (b), you can show that if you offer to pay the agent (a) $40,000 for failure and (b) $240,000 for success, then the agent will take the job and work hard.

(If you pay at least $90,000 but less than $240,000 for success, and $40,000 for failure, the agent will take the job and shirk. If you pay less than $90,000 for success or less than $40,000 for failure, then the agent will not take the job at all.)