Microeconomics, Module 3: "The behavior of Consumers"

: Landsburg, Chapter 3

(The attached PDF file has better formatting.)

Updated: October 12, 2013

Modules 3 and 4 deal with consumer behavior. We begin with indifference curves and their application to microeconomics.

We model consumers’ tastes with indifference curves. An indifference curve is the locus of points (combinations of goods or baskets of goods) that provide the same level of satisfaction (equal utility).

Definition: The marginal value of good A in terms of good B is the amount of good B that the consumer will trade to get one unit of good A.

This marginal value is the absolute value of the slope of the indifference curve passing through that point (i.e., the point of a given number of units of goods A and B). The indifference curve slopes downward, so its slope is negative; the marginal value is positive.

The simplest indifference curves have the form A × B = k, which has the proper downward slope and convex curvature.

Suppose there are only two goods in the economy: bread and wine. Jacob’s indifference curves are of the form W × B = k. Jacob gets the same utility from 8 loaves of bread and 2 flasks of wine, 4 loaves of bread and 4 flasks of wine, or 2 loaves of bread and 8 flasks of wine.

The budget constraint (budget line) is the locus of points (combinations of goods) that the consumer can purchase. The slope of the budget line reflects the relative prices of the two goods being considered; the consumer’s income determines the distance of the budget line from the origin.

A consumer has 1 budget line and an infinite number of indifference curves. The optimum (the point of maximum utility) is the point of tangency of an indifference curve to the budget line; this is the point where the marginal value of the good equals its relative price.

You will be given the type of indifference curve, such as A × B = k, and a budget line. The budget line may be given as the prices of goods A and B and the income of the consumer. You must find the equilibrium quantity of A and B that the consumer buys. We show the procedure in the practice problems and a homework assignment.

We can often predict consumer behavior by analyzing changes in the points where utility is maximized. Landsburg uses indifference curves to show that the standard indices of changes in the cost of living are biased.

Isn’t this true only if the consumer buys more of a good when its price declines and less of a good when its price rises?

Yes; we assume that consumers behave rationally; this is the law of demand.

The current edition of Landsburg’s textbook does not show the mathematics of inflation indices. The practice problems and many past exam problems test the math, but the final exam for this course does not test the mathematics. The CAS transition exam may test the math; candidates taking the exam should review the procedures.

A final example in Landsburg’s text uses indifference curves to show that an income tax lowers consumer welfare more than a head tax that raises the same revenue. This illustration is complex, and the final exam does not test the specifics of this illustration.

Why does an income tax reduce consumer utility? Is it because we transfer money to the government?

Transferring money to the government is a wealth transfer; economists do not say that it reduces social welfare. But an income tax distorts consumer incentives, leading them to work less. If the consumer paid the same tax to the government with a lump-sum tax instead of an income tax, the consumer would have incentives to work more, get more income, and enjoy higher utility.

A common theme of Landsburg’s text, Barro’s text, and much economic analysis is that most taxes distort consumers’ incentives, change their behavior, and reduce social welfare. This does not mean that taxes are necessarily bad; certain government services are essential and someone must pay for them. But some types of taxes reduce social welfare more than others. An economic goal is to obtain the benefits of government services with the least reduction in social welfare.

Does Landsburg say that a head tax is better than an income tax? But a head tax is regressive, whereas an income tax is progressive. A head tax which is the same for all citizens can’t raise much money, since most citizens are not that wealthy.

Landsburg is not comparing an income tax with a head tax that is the same for all citizens. He is comparing an income tax with a head tax that equals the income tax that citizen would pay if we used an income tax.

If the tax is the same, why is one better than the other?

With the head tax, consumers work more, since there is no disincentive to work.

Review exercise N1 on page 68. The exercise is simple for actuarial candidates, who use the mathematical curves, not tables. The final exam may gives a similar problem, where the utility is Y × Z (Y and Z are the two products).

Review problems 5 and 6 on page 69. The final exam may give two or more points on an indifference curve and ask if another point might lie on the same curve.

Review problems 12 and 13 on page 70. These problems deal with changes in both prices and income.

Review problems 16 and 17 on page 71. Some final exam problems ask which basket of goods is preferred.

Review problems 24 and 25 on page 72.

Review problems 27-30 on pages 72-3. Tax policy is hotly debated in all modern societies. Landsburg (and Barro in the macroeconomics course) and most economists say taxes affect workers' incentives. Higher marginal tax rates cause people to work less. Western European countries have such high tax rates that people prefer leisure to additional hours of work. The price tag for the misguided tax policy eventually comes due, as the countries are forced to cut spending.

The appendix to Chapter 3 is not required reading.