False -- an increase in the interest rate lowers the quantity of investment demanded. (See pages 717-9.)

True - If you give up one good now, you will get 1+r goods next year. (See page 705 and pages 706-8.)

True - The demand for loans increases, raising the real interest rate. However, if people save all the money from the tax cut, then the supply of loans increases by the same amount as demand, leaving the real interest rate unchanged. (See pages 737-41.)

True -- if you save all the money from the tax cut, then you will have just enough money to pay the higher taxes that the government will have to impose in the future (to repay its current loans). (See pages 740-1.)

False -- You can benefit by committing to future actions (even at the loss of flexibility to make a better choice later on) because your commitment can change other people's actions in a way that benefits you (see the examples on pages 430-432).

24 years = 72/3. (See page 675.)

A Nash equilibrium is a situation in which each player makes his or her best response.

A public good is a good that is nonrival and nonexcludable. (Nonrival means that when one person consumes more, the quantity of the good left over for other people does not fall (think of turning on your radio or television. Nonexcludable means that sellers cannot prevent people who don't pay for the good from using it (think of watching PBS television or listening to NPR radio).) The problem with public goods is that it is hard to get people to produce and sell them, because they cannot stop potential buyers from getting the good for free.

The Nash equilibrium is: Barney tells and Fred tells.

Egalitarianism is the view that fairness requires equal results. A simple version is that fairness requires everyone to have the same income. Another version of egalitarianism says that fairness requires that some people get more income than others to compensate them for other differences: perhaps a handicapped person or a person with greater medical needs should get more income than other people. Perhaps a person who is physically unattractive should get more income than a popular, good-looking person. Perhaps a person whose job is unpleasant should get more income than a person with a personally-satisfying job (such as an artist). Another version of egalitarianism, "From each according to his abilities, to each according to his needs," was advocated by Karl Marx.

Egalitarianism in some form has obvious appeal to many people. (That is, after all, one reason for giving every person one vote in an election.) But problems arise when one tries to decide which version of egalitarianism is best, or to design policies that would create an egalitarian society. The main problem is that egalitarian policies reduce incentives to work. If egalitarianism is desirable for its own sake, it may be worth sacrificing some economic efficiency to achieve a more equal distribution (according to whichever version of egalitarianism one chooses).

Many questions of policy arise from egalitarianism. What is the best tradeoff between equality and efficiency? Is it better to have a society in which half the people have 100 and half the people have 200, or a (more egalitarian) society in which everyone has 100? Is it just to punish a poor person who robs from a rich person? Or does the robbery contribute to justice? Should socially valuable behavior -- such as curing a disease, or producing a good that people want -- be rewarded with extra income? Should esteem (bestowed by other people) be equally distributed like income? Can it be? Should people with more esteem get less income? Can people give material (or physical) tokens of esteem in an egalitarian world, or do these tokens count as income?

Another set of issues arises when people become unequal through their actions. Suppose two people have the same wealth at age 20, but one saves more than the other. In later years, the saver will have investment income that the other person does not. Is this just? Is it consistent with egalitarianism?

One need not be an egalitarian to believe that a more equal distribution of wealth would be desirable. Nor need one be an egalitarian to believe that, regardless of the degree of income inequality, government policies to reduce poverty (defined in some way) are good. These views can be deduced from other views of justice that we now consider.

Utilitarianism is the view that justice consists of maximizing the total amount of human happiness.

Only total happiness matters to a utilitarian, not who is happy and who does not. In this sense, utilitarianism is very different from egalitarianism, which argues that distribution is important and should be equal. Despite its concentration on total happiness, utilitarianism provides an argument for redistributing income from the rich to the poor. The argument is that if you take a dollar from a rich person and give it to a poor person, the loss in happiness to the rich person is smaller than the gain in happiness to the poor person. The poor person, according to this argument, values money more than the rich person because he has less of it. The marginal utility (benefit) of the money is larger for the poor person than for the rich person, so redistributing income from the rich to the poor raises total utility (happiness). Critics of this argument say that it requires an impossible interpersonal comparison of utility -- that we cannot compare one person's happiness with another person's. For all we know, according to this criticism, redistributing income from the rich to the poor might actually reduce total happiness. A utilitarian might reply that while we can never be sure of these comparisons, it seems reasonable that poor people gain more happiness from an extra $10 than rich people lose when the government takes away $10, and that people make interpersonal comparisons of utility regularly when they decide to give money to charities.

There are many criticisms of utilitarianism. Many people find it objectionable because it does not consider the distribution of happiness important. A utilitarian would prefer a situation in which Jeremy has 10 units of happiness and John has 1 unit to a situation in which Jeremy and John each have 5 units of happiness; an egalitarian would prefer the latter situation.

A second criticism of utilitarianism is that it ignores peoples' fundamental rights. If someone needs an emergency kidney transplant to stay alive and no one offers to donate a kidney, a utilitarian might say that the government should force someone to donate (because the gain in happiness to the person who needs the transplant exceeds the loss in happiness to the donor, who can live with her remaining kidney). Some critics of utilitarianism say that, while the situation is unfortunate, forcing someone to donate a body part is a violation of her rights. Many philosophers believe utilitarianism has "morally monstrous" implications.

Justice as an Implicit Contract

Before you play a game with a friend, you agree on rules. Football teams agree on rules before they know the outcome of the "toss of the coin" which determines which team will receive the first kickoff.

Suppose people could meet with each other and agree on the rules of life before the "toss of the coin" (that is, luck) turns them into unique individuals living in diverse circumstances around the world. We can imagine that people meet together before they are born -- before they find out if they will be smart or dumb, beautiful or ugly, lucky or unlucky, whether they will have rich or poor parents, tastes for material goods or for spiritual fulfillment, and so on. This is called meeting in the original position or behind the veil of ignorance.

At this meeting, people would choose the legal rules and government policies that will affect their lives. They would decide whether the government should redistribute income from rich people to poor people, and how much they should transfer. They would decide what rights and obligations people have. Because people do not (yet) know their own individual circumstances when they make these decisions, they would not be able to make rules to give special benefits to themselves. Instead, they would presumably choose rules that benefit, in a sense, the whole society. In this sense the rules they choose would be fair and would give meaning to the concept of justice.

According to this view, only rules can be fair or just, not outcomes like who wins a game or how equally income is distributed. Rules are fair or just if everyone would agree to them at this magical meeting behind the veil of ignorance. But because this meeting is impossible to arrange, no one knows for sure what rules people would agree on. John Rawls, in his book A Theory of Justice, guessed that people would choose a system that involves considerable redistribution from the lucky to the unlucky -- from the rich to the poor -- to make certain that no one falls below a certain level of income. He argued that people in the original position would agree to redistribute income from whoever turns out to be rich, to those who turn out to be poor. Justice is then the enforcement of this agreement. Other proponents of the idea that justice is an implicit contract have other guesses about what rules people would choose.

The basic model of economic growth says that investment raises the capital stock over time, which raises real GDP, but that diminishing returns to capital create a long-run equilibrium in which economic growth stops. The equilibrium level of savings and investment determines how fast the economy adds to its capital, so it determines the equilibrium rate of economic growth. (Higher investment means faster growth.) As the

economy adds to its capital stock, the demand for investment falls (because of diminishing returns to capital). This lowers the equilibrium real interest rate over time.

The main problems with the model are: (1) the evidence does not support the model's prediction that long-term economic growth slows down over time; (2) the evidence does not support the model's prediction that real interest rates fall over time.