Consumer Choices

This is Unit Five of Principles of Microeconomics, part two of two: from the consumer's rule to the demand curve, and from one consumer to the market. Carry the same idea as part one: the last dollar buys the same satisfaction anywhere. This part shows that following that rule as a price changes traces a demand curve, that adding every consumer's curve gives the market's, and that a diagram with no utility numbers reaches the same choice. By the end you will be able to say how the two effects combine for a normal good and for an inferior one. To derive points of an individual demand curve from the best-bundle rule. To build market demand as a horizontal sum. To state the tangency rule and decompose a price change on the indifference diagram. And to report the behavioral findings as attributed refinements, and run the whole chain.

Three entries on the road to demand: when the two effects agree, where the demand curve comes from, and deriving three points.

When the two effects agree.

MIC 0415 Normal, Inferior and the Two Effects

For a normal good the income effect reinforces substitution: a price rise cuts quantity through both. For an inferior good it pulls the other way, since being poorer raises demand for it, so inferior goods respond less to price than normal goods. Only if the income effect overpowered substitution would demand slope up, and evidence for such a good is rare and contested.

Where the demand curve comes from.

MIC 0416 From Utility to the Individual Demand Curve

Change one good's price, keep income and other prices fixed, and find the best bundle at each price. Plotting each price against the quantity chosen traces the consumer's demand curve for that good: three prices, three best bundles, three points on one curve. Utils are never observed; prices and quantities are, which is why the demand curve survives doubts about measuring utility.

Deriving three points.

MIC 0417 Deriving Three Points of a Demand Curve

Hold income and the other price fixed, then repeat the best-bundle method at each of three prices for the good: recompute marginal utility per dollar, spend the budget by the rule, and record the quantity bought. The three price and quantity pairs are three points on the demand curve, and quantity should fall as price rises. With twelve dollars, drinks at two dollars with marginal utilities of twelve, ten, eight, six, four and two, and snacks with marginal utilities of thirty, eighteen, nine and six: at six dollars a snack the rule buys one snack and three drinks; at three dollars, two snacks and three drinks; at two dollars, three snacks and three drinks. The points are six dollars and one, three dollars and two, two dollars and three, a downward-sloping demand curve. Change only the one price, since changing income or the other price would shift the curve rather than move along it.

Two entries on adding consumers together: the horizontal sum, and doing it.

Adding consumers together.

MIC 0418 Market Demand Is the Horizontal Sum

The market demand curve adds the individual demand curves horizontally: at each price, sum the quantities every consumer would buy. The result slopes down because each part does. At two dollars, three buyers wanting five, three and eight pounds make sixteen. Sum quantities at a price, never prices at a quantity; adding vertically gives a curve that means nothing here.

Doing the sum.

MIC 0419 Summing Individual Demands

Given two or more individual demand schedules, build the market schedule row by row: pick a price, read each consumer's quantity at that price, add them, and repeat for every price. A consumer whose quantity is zero at a high price contributes nothing at that row and something below it, which is why the market curve is flatter and further right than any individual's. For apples at three dollars, Ana wants two pounds, Ben zero and Cal four, so the market wants six; at two dollars, five, three and eight, sixteen; at one dollar, nine, seven and twelve, twenty-eight. Two errors: averaging instead of adding, which understates the market by the number of buyers, and adding the prices each buyer would pay for a given pound, a willingness-to-pay stack with a use in unit twelve and none here.

Four entries on the second language: indifference curves, their slope, the tangency rule, and separating the two effects on the diagram.

A second route to the same choice.

MIC 0420 Indifference Curves

An indifference curve shows every bundle of two goods that gives a consumer the same satisfaction. Higher curves are preferred; curves slope down and are steeper on the left than the right. Two books with a hundred snacks, or eleven with forty, sit on one curve. This route needs no utility numbers, only the ability to rank bundles, the theory's honest minimum.

The curve's slope.

MIC 0421 The Marginal Rate of Substitution

The marginal rate of substitution is how much of one good a consumer gives up for one more of the other at equal satisfaction: the curve's slope, which falls along it. With many snacks and few books, a book is worth many snacks. The falling rate is diminishing marginal utility again: the scarcer good is worth more at the margin.

Where the best bundle sits.

MIC 0422 The Tangency Rule

The best affordable bundle is where the budget line touches the highest reachable indifference curve, and at that tangency the marginal rate of substitution equals the price ratio. A curve crossing the budget line twice leaves a higher curve reachable between. Tangency and the equal-ratios rule are one condition in two languages: the last dollar buys the same satisfaction either way.

Separating the two effects with the diagram.

MIC 0423 Decomposing a Price Change on the Diagram

After a price rise, draw a line parallel to the new budget line and tangent to the old curve; it has the new prices and the old satisfaction. Along the old curve to that tangency is the substitution effect; from there to the new bundle is the income effect. The effects are separated for analysis only, since one price change causes both at once.

Two entries on where the model bends: attributed findings from behavioral economics, reported without a verdict.

Where the model bends.

MIC 0424 Loss Aversion and Framing

Behavioral economics finds, in one attributed study, that a loss weighs about twice an equal gain, and that people judge a saving as a share of the price rather than in dollars: a ten-dollar saving moves a clock buyer and not a phone buyer. These are attributed findings that refine the model rather than replace it, and the course reports both views and takes neither.

Money treated differently by its label.

MIC 0425 Mental Accounting and Commitment Devices

Mental accounting treats dollars differently by their source, though money is fungible; holding savings at two percent beside credit-card debt at fifteen costs money every month. Commitment devices bind a future self, such as automatic saving one must opt out of. Whether these are errors to correct or preferences to respect is the open question the course leaves open.

One capstone entry: the whole of consumer theory run end to end, from a table of utils to the market's demand curve.

The unit in one worked chain.

MIC 0426 From Utils to a Demand Curve

The whole of consumer theory is one chain, and running it end to end shows why the demand curve of unit two slopes down. Start with a budget, two prices and a table of marginal utilities that fall as quantity rises. Spend the budget by the rule, buying whichever good's next unit gives more per dollar, until the money is gone and the ratios match as nearly as whole units allow: the best bundle, which on the indifference diagram is the tangency. Now raise one good's price; the budget line rotates in, and two things happen at once. The good is relatively dearer, so purchases shift toward the other: the substitution effect, which always cuts the dearer good's quantity. And the same income buys less: the income effect, which cuts quantity further if the good is normal. Record the new quantity at the new price and repeat; the pairs are points on this consumer's demand curve, which slopes down. Add every consumer's quantity at each price, and the horizontal sum is the market demand unit two took as given. With twelve dollars, sandwiches with marginal utilities of forty, thirty-two, twenty and twelve, and juices at two dollars with sixteen, twelve, eight and four, the rule bought two sandwiches and two juices at four dollars a sandwich. At six dollars the first juice, at eight per dollar, beats the first sandwich at about six point seven; then the sandwich beats the second juice; then the second juice beats the second sandwich; and the last two dollars buy a third juice. The new bundle is one sandwich and three juices: two points on the sandwich demand curve, four dollars and two, six dollars and one. Compare marginal utility per dollar, never marginal utilities; the income effect is a purchasing-power effect with money income unchanged; and the utils were a device, since the bundle and the slope survive any ranking that keeps the order.

Look at what you can now do. You can say that for a normal good the income effect reinforces substitution and for an inferior good it pulls against it, and that an upward-sloping demand curve would need the income effect to win. You can derive points of a demand curve by rerunning the rule at each price with everything else held fixed. You can build market demand by adding quantities at each price, never averaging and never adding prices. You can state the tangency rule, the marginal rate of substitution equal to the price ratio, and split a price change on the diagram with a parallel line. And you can report loss aversion, framing and mental accounting as attributed refinements, and run the chain from a table of utils to the market's demand curve. Unit six turns to the firm and the costs behind the supply curve.