Consumer Choices

This is Unit Five of Principles of Microeconomics, part one of two: how a consumer with a fixed budget picks a bundle, and what happens to that choice when income or a price changes. Carry one idea. At the best bundle the last dollar buys the same satisfaction wherever it is spent. That rule finds the bundle, tests a bundle, and, when a price moves, splits the response into two effects that the exam asks you to name. By the end you will be able to define total and marginal utility and compute marginal utility from a table. To say what utility numbers can and cannot mean. To apply the utility-maximizing rule to find a bundle or test one. To read an income change off two bundles and classify each good. And to separate the two effects of a price change and classify a described response.

Four entries on utility: what the theory explains, the two measures of satisfaction, reading them from a table, and what the numbers can mean.

What the theory explains.

MIC 0401 What Consumer Theory Explains

Consumer theory explains how a household with a fixed budget and given prices picks the bundle of goods it prefers. Tastes are personal; the constraint is not, so two shoppers with the same income and prices fill different carts. The course treats a household as one decision maker; who inside it decides is a real question the model sets aside.

The two measures of satisfaction.

MIC 0402 Total Utility and Marginal Utility

Total utility is the satisfaction from a whole quantity of a good. Marginal utility is the change in total utility from one more unit, and it falls as the quantity rises: the sixth film in a month adds far less than the first did. Total utility keeps rising while marginal utility is positive, so falling marginal utility does not mean falling total utility.

Reading both from a table.

MIC 0403 Computing Marginal Utility from a Table

Given total utility at each quantity, marginal utility is the difference between consecutive rows: the total at this quantity minus the total at the one before. List the differences and check that they fall as quantity rises. Going the other way, total utility at any quantity is the sum of the marginal utilities up to it, so each column rebuilds the other. A student's total utility from coffees runs zero, twenty, thirty-five, forty-five, fifty, fifty-two, so the marginal utilities are twenty, fifteen, ten, five and two, each cup adding less than the one before; and twenty plus fifteen plus ten returns forty-five, the total at three cups. Marginal utility belongs between two rows, not on one, and a small marginal utility is not a reason to stop: it need only stay positive for the total to rise, and the budget decides where to stop.

What the numbers can and cannot mean.

MIC 0404 Utility Is Not Comparable Across People

Utility numbers are a device. Nobody can measure satisfaction, and one person's forty is not another's; all the theory needs is that a person can rank any two bundles. Saying which of two menus you prefer is enough, and a score is not required. The conclusions that survive without the numbers, such as the demand curve, are the ones the course keeps.

Four entries on the rule: the number that decides a purchase, the rule it leads to, finding the bundle, and testing one.

The number that decides a purchase.

MIC 0405 Marginal Utility per Dollar

Marginal utility per dollar is a good's marginal utility divided by its price: what one more dollar spent on it buys, and the number to compare across goods. Twenty utils at five dollars is four per dollar; nine at three dollars is three. Compare per dollar, never raw marginal utilities; a higher marginal utility can still be the worse buy if it costs more.

The rule the comparison leads to.

MIC 0406 The Utility-Maximizing Rule

Spending the whole budget, a consumer maximizes utility when marginal utility per dollar is equal across goods; if one is higher, moving a dollar there raises utility until the ratios meet. At the best bundle the last dollar buys the same satisfaction anywhere. Equal per dollar, not equal marginal utility: a good costing twice as much must give twice the utility.

Finding the bundle.

MIC 0407 Finding the Best Bundle

With two goods, a budget and each good's marginal utility at every quantity, spend the budget one purchase at a time: compute marginal utility per dollar for the next unit of each good, buy the higher, recompute, and repeat until the budget is gone. At the finish the two ratios should match as nearly as whole units allow. With twelve dollars, sandwiches at four dollars with marginal utilities of forty, thirty-two, twenty and twelve, and juices at two dollars with sixteen, twelve, eight and four: the first sandwich gives ten per dollar and the first juice eight, so buy the sandwich; the second sandwich gives eight and the first juice eight, so buy both, ten dollars spent; the third sandwich gives five and the second juice six, so buy the juice. The bundle is two sandwiches and two juices. Lumpy goods rarely equalize the ratios exactly, and a bundle that leaves money unspent is never best while any marginal utility is positive.

Testing a bundle you did not build.

MIC 0408 Is the Consumer at Equilibrium?

Given the marginal utility and price of each good at a consumer's current bundle, compute marginal utility per dollar for each. If they are equal, the consumer is at equilibrium and should change nothing. If they differ, buy more of the good with the higher ratio and less of the other; the higher ratio falls and the lower rises until they meet. Pizza has a marginal utility of thirty at ten dollars a pie, three per dollar, and salad eight at two dollars, four per dollar: not equilibrium, so more salad and less pizza. After the shift, pizza's marginal utility rises to thirty-six, three point six per dollar, and salad's falls to seven point two, also three point six: equilibrium. The direction is toward the higher ratio, not the higher marginal utility; pizza had the larger marginal utility and was still the good to cut.

Two entries on income: what it does to the budget line, and reading which good is inferior.

What income does to the line.

MIC 0409 An Income Change Shifts the Budget Line

Higher income shifts the budget line out, parallel, since prices and so the slope are unchanged; twice the income doubles both intercepts and leaves the slope alone. The new bundle usually holds more of both goods, and less of one means that good is inferior. A parallel shift is the signature of income; a change of slope is a price change.

Reading which good is inferior.

MIC 0410 Reading an Income Change

From a consumer's bundles before and after an income rise, classify each good: if the quantity rose the good is normal for this consumer, and if it fell it is inferior. Check the budget first, since both bundles should exhaust their budgets at the same prices, confirming that only income moved; then compare good by good, because one bundle can hold a normal and an inferior good at once. With forty dollars, bus fares at two dollars and taxi rides at eight, a commuter takes twelve bus rides and two taxi rides, forty dollars exactly. With eighty dollars she takes eight bus rides and eight taxi rides, eighty exactly. Bus rides fell as income rose, so they are inferior for her; taxi rides are normal. Inferior describes this consumer's response, not the good's quality, and the class is read from quantity, not spending.

Four entries on a price change: what it does to the line, the substitution effect, the income effect, and telling them apart.

What a price does to the line.

MIC 0411 A Price Change Rotates the Budget Line

A higher price for one good rotates the budget line inward around the other good's intercept, since that price did not change; the affordable set shrinks and the slope steepens. Dearer movies pull the movie intercept in and leave the T-shirt intercept fixed. A rotation changes what is affordable and what each good costs in the other, and both effects follow.

The first of them.

MIC 0412 The Substitution Effect

When a good's price rises it becomes dearer relative to other goods, so the consumer shifts toward substitutes. That change, holding purchasing power fixed, is the substitution effect: dearer oranges send a fruit buyer toward apples. The substitution effect always moves quantity opposite to the price, for every good, normal or inferior.

The second effect.

MIC 0413 The Income Effect

A higher price also cuts the buying power of a fixed income, so the consumer is poorer in real terms. The quantity change from that lost purchasing power is the income effect: after a rent rise a tenant cuts back on many things. The income effect needs no change in income; money income is fixed, and real income fell because prices rose.

Telling the two apart.

MIC 0414 Substitution or Income?

To classify a described response to a price change, ask which mechanism the description names. If it says the good became relatively dearer and the consumer moved toward alternatives, that is the substitution effect. If it says real income or purchasing power fell and quantity fell as a result, that is the income effect. Both happen at once, so a description picks one out by what it emphasizes. When the price of a product rises, a consumer's real income falls, causing the consumer to buy less of it: that names real income, so it is the income effect. Coffee gets dearer, so the consumer drinks more tea and less coffee: relative prices and a move to an alternative, the substitution effect. Each extra cup satisfies less: diminishing marginal utility, neither effect. The trap is the word income; the income effect is about purchasing power, not a pay change, and income elasticity is a distractor from unit four.

Look at what you can now do. You can define total and marginal utility and read marginal utility as the difference between rows of a table. You can say that utility numbers are a device, that ranking is enough, and that the demand curve survives without them. You can apply the rule, marginal utility per dollar equal across goods, to build a bundle one purchase at a time or to test one and say which way to move. You can read an income change as a parallel shift and classify each good by whether its quantity rose or fell. And you can separate a price change into the substitution effect, always opposite to price, and the income effect, a loss of purchasing power, and name the one a description points at. Part two derives the demand curve from all of this, adds consumers together, and gives the same choice a second language.