Answers to questions as questions were in July,
2006
1. Much of economic theory is based on the belief that even if individuals do not always act rationally, enough of them do enough of the time so that the assumption that people are rational is a reasonable approximation of reality. What do economists mean when they say people are rational? Are you rational? Are most of the people you know rational?
Answers will vary. This question and the following may make good discussion questions.
2. One of the ways of stating the rationality assumption is, "There are no bozos." What does this statement mean? Did P.T. Barnum accept it when he said, "There is a sucker born every minute?"
People are rational; no.
3. Use an internet search engine to find the strange story involving "Meiwes" and "Brandes." What did they do that made them newsworthy? Can you argue that Meiwes was rational? How about Brandes? If what they did is rational, what does it take for behavior to irrational?
Answers will vary.
4. Roughly one in 50,000 people who run a marathon dies as a result. Is this evidence that people are irrational? Explain your answer.
Not necessarily--it depends on the benefits of running and the value a person puts on life. If a person values life at $5,000,000, then it is worth running if the value of the race exceeds $100.
5. People pay for bottled water when the alternative is safe and pure tap water that is free. Does the market for bottled water indicated that people are irrational? Explain your answer.
I do not understand why people buy bottled water--so I do not know how to answer this.
6. What is spite? Can acting spitefully be rational? Defend your answer.
Answers may vary; but economists tend to assume that people do not get enjoyment from the sufferings of others.
7. Some students are not familiar with the term "guns and butter" or "guns versus butter." Search for the internet for these terms. What issues are being addressed with this term today?
Answers will vary.
8a. Crusoe is the sole resident of Biosphere 28. He will spend two years alone in it. In each year he can grow 100 bushels of grain. Grain stores quite well, but 5% of it rot from the first year to the second. Draw his budget constraint. (Hint: the axes are consumption in year one and consumption in year two.)
100, 100 is possible. Theoretically, so is nothing in the first year and 195 in the second year.
8b. Now suppose that Crusoe is living in a primitive barter economy. The only way to store his grain is in the local warehouse, which charges him 5% of what he has to store. However nothing spoils. He can also borrow against next years crop, but at a 10% interest rate (payable in grain.) Draw his new budget line on a separate graph. (Hint: Make the axes consumption in year one and consumption in year two.)
(There is a slight kink in the line. It goes from 190, 0 to 100, 100 to 0, 195.)
9. (Now JavaScript) Joe likes Tom Thumb's Tiny Burgers. For him, they satisfy an important want. The schedule below shows how much "want-satisfying" power they have:
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a) If Tom Thumb's Tiny Burgers are free, how many should Joe take?
Five. Maximize benefits.
b) Suppose that for every Burger Joe buys, he must give up something that has 2.5 units of want-satisfying power. How many should he buy?
Three. Adding the third adds 3 in benefits at a cost of 2.5. Adding the fourth adds 2 in benefits but costs 2.5.
10. Have you ever wondered why there is so much spam in your e-mail? What do you think the marginal cost curve for spam looks like from the point of view of the spammer? What does the marginal benefit curve look like to the spammer?
The marginal cost curve is pretty much flat and just a tad above zero. The marginal cost of another spam message is a tiny fraction of a cent.
11. You are a farmer and there has been a moderate drought. What would a graph showing the marginal benefit of rain look like? (Hint: the horizontal axis measures the amount of rainfall.)
It should rise for a little bit because a tiny amount of rain has no effect. Then it should decline, eventually hitting zero and becoming negative. When it is negative, more rain is doing damage.
12 A housewife is buying four 12 ounce cans of peas for $.60 each and three 16 ounce cans for $.72 each. Using the equimarginal principle, determine if she is minimizing her costs of buying peas. If she is not, explain how she can shift her money to increase the amount of peas without spending more.
This illustrates a simple use of the equimarginal principle. You are interested in ounces of peas per dollar. (12 ounces )/$.60 = 20 ounces per dollar. (16 ounces)/$.72 = 22.22 ounces per dollar. Hence, you are getting more ounces of peas per dollar with the big cans. She is spending $2.40 on 12 ounce cans to get 48 ounces of peas. She gets 48 ounces of peas in the 16 ounce cans for $2.18. If she stops buying the four small cans and instead buys three more large cans, she gets the same amount of peas and saves $.22 cents.
If this example makes sense, then so should all other equimarginal reasonings.
13. Hans Fruehstueck has $1.00 to spend on breakfast. He must decide how many donuts and cups of coffee to buy. The utility these items give him is shown in the table below:
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a) Construct a table showing the utility function similar to that in the readings, and decide what Hans should do if coffee and donuts both cost $.25.
4 16 26 29 31 32 3 14 24 27 29 30 2 10 20 23 25 26 1 5 15 18 20 21 0 0 10 13 15 16 0 1 2 3 4 Number of
Coffees
Utility is maximized at 24, 3 donuts and 1 coffee.
b) If coffee and donuts both cost $.25, construct a table showing costs and benefits similar to that in the readings and find how many donuts he will buy by computing the marginal cost and marginal benefit of buying donuts.
c) Construct a table similar to that which the readings used to illustrate the equimarginal principle and show how it tells you what Hans should do.
Price of Donuts
Price of Cofee
Buy coffee, donut, donut, donut. Money gone, stop.
d) How will you find Hans' new best position using the methods of parts a, b, and c if the price of donuts rises to $.50? If he only has $.75 to spend?
For donuts costing $.50 cents, you get these:
4 16 26 29 31 32 3 14 24 27 29 30 2 10 20 23 25 26 1 5 15 18 20 21 0 0 10 13 15 16 0 1 2 3 4 Number of
Coffees
2 coffee, 1 donut. is best.
Buy the first donut, but not the second. Hence $.50 cents left for coffee, which buys two coffees.
Price of Donuts
Price of Cofee
Buy coffee, coffee, donut. Money gone. Answer one donut and two coffee.
For donuts costing $.75 cents, you get these:
4 16 26 29 31 32 3 14 24 27 29 30 2 10 20 23 25 26 1 5 15 18 20 21 0 0 10 13 15 16 0 1 2 3 4 Number of
Coffees
4 coffee is best because it gives 16 units of satisfaction.
Not even the first donut is worth buying because you must sacrifice the second, third, and fourth cups of coffee.
Price of Donuts
Price of Cofee
Buy coffee, coffee, coffee. If one could spend the last $.25 on donuts to get a quarter of a donut, that would be better than spending the last quarter on another coffee. The advantage of the equimarginal approach is that it leads one to see the fractional solution.
14. Suppose that Robinson Crusoe, isolated on his island, has figured a way to measure his utility. He has only two goods to consume, Bananas and Fish. (Ignore Coconuts for this part of the questions.) The table below show how bananas and coconuts provide him utility:
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a) Each item costs him two hours of effort and he has ten hours of effort to spend. How many of each will he consume? Explain how you get your answer.First two hours he uses to get the first fish; the next two he uses to get the second fish because both have a higher return than the first banana. The third fish gives him only a return of 1 util per hour, while the next four bananas give a higher return. Hence he will uses the next three hours to get bananas. Now he is out of hours, and has produced 2 fish and 3 bananas.
b) Suppose he now discovers that coconuts grow on his island. The utility they provide is shown above. Gathering a coconut also takes two hours and he still has ten hours of effort to spend. How many of each will he consume? Explain how you get your answer.
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Because the prices are the same, we want to pick the biggest five numbers, which are 5, 5, 4.5, 4, 3.5. That gives 2 fish, 2 coconuts, and 1 banana.
c) Suppose bananas drop in price so they only require one hour of effort to obtain. How will he now use his time to maximize his utility? Explain how you get your answer.
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We adjust the table to show the new prices. Now we start picking the biggest numbers and continue until we run out of hours:
7 - 1st banana--1 hour
6 - second banana - 2 hours
6 - third banana- 3 hours
5 - first fish - 5 hours
5 - second fish - 7 hours
4.5 first coconut - 9 hours
4 - either fourth banana or one half of the second coconut - 10
hours
so either four bananas, two fish, and one coconut. OR 3 bananas, two fish, and one and a half coconuts.
15. The average number of yards gained on a pass play in the NFL is greater than the average number of yards gained on a rushing play. Does this indicate that teams should use more passing and less running than they are currently using? Explain.
What matters is the marginal number of yards gained, not the average.
16. Aristotle argued that virtue was the middle way. For example, too little courage was bad (cowardice) as was too much courage (foolhardiness). Similarly, too little generosity was undesirable, but a person could also err by too much generosity. How would an economist recast Aristotle's theory of virtue in terms of marginal costs and benefits?
As we acquire more of a quality, the marginal benefit declines and/or the marginal cost rises. After some point the additional benefit of more of the quality is less than the additional cost.
17. We can take Aristotle's approach to areas that Aristotle might not have considered. For example, good athletes train. Better athletes usually train more than the good athletes. An economist would say that the best amount of training is where the marginal benefit of training just equals the marginal cost of training. Based on your experience, draw what you think the marginal benefit and marginal cost curves of athletic training look like, and explain why you drew them as you did. (Hint: time should be on the horizontal axis, and cost/benefit on the vertical.) How would these curves differ for a high school athlete and a professional athlete?
Hopefully the student will find that the marginal benefit falls and the marginal cost rises. The marginal benefit curve of a professional should be higher than for an amateur, so the optimal amount of training is greater.
18. How would you use this approach to determine the amount of time you should spend studying economics?
After some amount of studying, the benefit of additional study is less than the cost.
19. We can also take Aristotle's approach to areas that probably would have appalled Aristotle. For example, what are the marginal benefits of making the environment cleaner? What are the marginal costs of making the environment cleaner? Explain why it is best for society to stop environmental cleanup before it reaches zero pollution. Could this argument work as well for any other social bad such as crime?
If there is a limit to the amount of time people should study economics, there is a limit to anything else. What most people ignore is that there are costs to additional pollution reduction or crime reduction.
20. Can we also use this approach with terrorism? In the 2004 presidential campaign John Kerry said, "We have to get back to the place we were, where terrorists are not the focus of our lives, but they're a nuisance." The Bush campaign immediately attacked that statement with a commercial suggesting that Kerry was too weak against terrorism. Does Kerry's position seem reasonable in terms of economic analysis? Why or why not? (Explain using marginal cost and marginal benefit to define the optimal amount of terrorism.)
Economists would be sympathetic to the Kerry position.
21. Does Aristotle's approach suggest that one can be too rational?
Yes
(Aristotle would approve the economic assumption that people are rational. It is very much like his view that everything (not just people) has a goal (or purpose) and strives to attain it. However, he would not like the economic vision of spontaneous order that comes with the invisible-hand concept. For Aristotle order implied an orderer.)
Extra Stuff . . Chapter 7 . . Chapter 8
1.. Richard Thaler is an economist who has argued that people are not rational in the way that economic theory assumes that they are.
a) Find out who he is by searching on the internet.
b) Two concepts that he has help publicize are the "status quo bias" and "loss aversion." Search the internet to discover how these concepts are defined and, if possible, give examples.
c) Why do these concepts present problems for the way economists usually develop the theory of rational consumer choice?
Answers will vary. However, economics has long assumed that people are completely rational, and it has not yet come to terms with the idea that they may be predictably irrational. It will with time.
2 Some instructors give exams that tell the student how many points each question is worth. For example, on a test of five questions, three may be worth 20 points, one worth 10, and the last worth 30. When the author was a graduate student at the University of Wisconsin, one of the professors empowered students by letting them choose how important each questions was. For example, on a five question exam, a student might be able to assign any weight from 5 to 50 to a question, with the condition that the total for all five add up to 100. If a student was confident he had a really good answer for one question, he could assign it 50 and put less weight on answers he was less sure about.
Since students had more options, they should have been better off and therefore happy about this way of weighting test questions. In fact, many students did not like the system. Speculate on why more choices did not make them happier.
Here are some speculations:
a. There may be costs to making
decisions; more options may not better.
b. The element of risk may be involved. People may not be completely
rational under conditions of risk. Richard Thaler has argued this in
his work on quasi-rationality. The fear of making a bad choice may
have more emotional impact than the hope of making a correct one.
c. The situation in the example is a competition. The options makes
the competition more complex, but does not make the overall outcome
better. If some gain, some will lose. It may be that each would like
the option of choosing weights only for himself, but sees no gain
when others also have the option. If they fear that others may be
better at making choices of this sort, they will oppose
them.
3. Can you have too many choices? Would you be better off with 500 channels on your television rather than 100? How about 5000 rather than 500? Can you have too many channels to choose from?
Answers will vary. But if there are costs to making choices, at some point additional options will reduce value.
4. The April 1972 issue of Consumer Reports suggested that a home buyer purchase a washing machine, dishwasher, and clothes dryer from a department store, which charges $675 plus 15% interest each year for two years, rather than having the builder install them. The builder, in this example, could get the appliances for $450, but he would add this amount on to the mortgage. If the mortgage matured in 27 years (the national average in 1972) and if the mortgage rate of interest was 7.75%, the appliances would cost a total of $1075. The total cost of the appliances purchased at the department store on a two-year contract would be $785. Explain why the advice of Consumer Reports is bad advice in this case.
Consumer Reports ignored the concept of the time value of money. Money paid 26 years in the future cannot be considered as equivalent to a dollar today.
If a person set aside $675 in a savings account in year zero, and that savings account earned 5% interest, one would earn almost $33.75 in interest for the first year. That would almost be enough to pay the first year of the extra mortgage charge of $39.81 ($1075/27). If one deducted $39.81 from this account each year for the 27 years, one would still have money left in it at the end.
By the logic of Consumer Reports, almost every large corporation is throwing away stockholder money by issuing bonds. If the interest rate is 8%, a corporation will borrow $1000 today, pay $80 per year each year for 20 years, and then repay the $1000 at the end of 20 years. The corporation is giving out, by the logic of Consumer Reports, $2600 to get $1000. Capitalism certainly is doomed to failure by such stupidity of its business leaders.
This article is not one of the high points in the history of Consumer Reports.
5. JavaScript
6. JavaScript
7. The website humanforsale.com claims to determine your value in dollars. Having looked at some of their computations, I suspect that their way of obtaining that value does not follow good economic procedures. When economists value people (yes, they do that!), they use the technique of present value, basically considering a person as a bond or a machine. What information would you need to estimate the value of a person?
The stream of future earnings and the interest rate.
When we answer these questions for bonds or machines, we can check our answers against the price of machines in the marketplace. Although it is currently against the law to buy and sell humans, the prohibition on selling people is recent in terms of human history, and some of the past societies that had slavery left records. Economists who examined these records for the U.S. found that slaves on average gained value until they were in their twenties, then slowly lost value. Why should this pattern have been there?
The value of work done by a slave typically rose until the 20s, then leveled off before declining. As for a young slave, the peak years are distant so the present value of them is low. As the slave ages and uses the peak years, the present value of the future stream decreases. It is pretty much what happens to many people, but we cannot check their value because there is no market for people.
Age was only one factor that determined the value of a slave. What other things should have mattered and why? (One of the classics of cliometrics, the study of the past using statistics, is Time on the Cross by Robert Fogel and Stanley Engerman (1974). If you want to know more about the economics of slavery, it is a good place to start.)
The same things that matter for free people--special skills, disposition, character.
8. We no longer have a market for humans, but we sometimes need to compute their value. One situation in which we do this in computing awards in wrongful death lawsuits. If you kill someone by negligence, you may be liable to that person's heirs. The amount you will owe them will depend on who it is that you killed.
a) Will you have to pay more if you killed a 25-year-old medical doctor who is just starting a practice or a 25-year-old unemployed high school dropout? Explain you answer.Typically in wrongful death lawsuits, the awards are tied to future earnings. The MD has higher expected earnings so the award to heirs will usually be much more.
b) Will you have to pay more if you killed a 35-year-old MD making $250K a year of a 65-year-old MD making $250K a year? Explain your answer.The older MD has many fewer productive years ahead of him than the 35-year-old, so the award given the younger man's heirs should be larger.
9. When economists are looking at people as machines, they talk about the concept of "human capital." Look up the term on the internet and see what definition you get.
Internet exploration--answers will vary.
a) The obvious thing you can do to increase your human capital is to get more education. What other things can you do to increase your human capital?
On the job training, any kind of self-improvement to improve skills.
b) As you get older, your human capital may increase but its value may decrease. How can this be?
On the job training
c) Does rapid technological change increase or decrease human capital? For example, from 1960 until the present the computer field has seen enormous change. Every few years old operating systems and old hardware are obsolete, replaced with newer and different operating systems and hardware. If you have training in existing hardware or operating systems, what happens to the value of your human capital as technology changes?
Your human capital becomes obsolete. On the other hand, if people know that their skills may soon be obsolete, fewer will want to get them and the market will compensate by paying those with these short-lived knowledge very well.
d) Can you think of other fields in which technology alters the value of human capital?
Answers will vary.
e) How do people cope when technology threatens their human capital? Give examples.
Answers will vary.
10. (Now JavaScript) Ann, Betty, and Carol are three buyers of shoes. Their demand curves are shown below in terms of their willingness to pay.
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a. If the price of shoes is $15, how many pairs will Ann buy? Betty? Carol? How many will be bought in total?
2, 3, 2, 7
b. What will Ann's consumer surplus be at this price? What will the
total consumers' surplus be?
$120-$30=$90.
$90+$105+$90=$285
11. The market for widgets has three potential buyers and three potential sellers. Once a person has a widget, there is no use for another. The willingness to pay and willingness to sell tables are as follows:
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Potential Buyers |
Highest price each will pay |
Potential Sellers |
Lowest price each will accept |
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Jack |
$100 |
Mark |
$10 |
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Jim |
$75 |
Mike |
$25 |
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Joe |
$51 |
Mort |
$49 |
a) If the price in this market is $55, will the market clear, or will there be potential transactions left that could make someone better off?It will not clear; two willing buyers, 3 willing sellers.
b) If the price of all transactions is known in the market, what will tend to happen to the price in this market if it begins at $55?
It will drop.
c) If the price in the market is $45, will the market clear? If knowledge of prices is known, what will happen to price?
It will not clear; two willing sellers, 3 willing buyers.
d) If the price in the market is $50, will the market clear? What is the total surplus (producer plus consumer surplus) that exchange will generate?
yes. Consumer surplus = 50+25+1=76; producer surplus = 40+25+1=66; total =142
e) If prices below $55 are illegal, how how many will be exchanged? What is the largest the surplus can be with this price floor?
2 exchanged; largest surplus is 45=20+45+30=140. If Joe and Mort could now make a secret, private exchange, both could be made better off the surplus would rise by 2.
f) Could the three sellers get together and think of a way to make themselves better off by colluding? What would they do? What would happen to the surplus of the buyers? Of the sellers? To total surplus?
Pay Mort to leave the market and raise price to $74. CS= 26+1=27; Producer surplus = 64+49=113. By colluding they transfer surplus from buyers to sellers. They can easily pay off Mort in this example.
g) Suppose there are three hundred Jacks, Jims, Marks, etc. Will collusion be more or less likely than with there are only three buyers and three sellers? Explain.
Less likely; harder to negotiate and enforce the agreement among sellers.
h) Does the size of the surplus depend on whether the good being exchanged is socially acceptable or not? For example, if widgets are a form of pornography, do the answers change?
Not in economics. All wants are created equal for most economists. They do not know how to judge some wants better than others.