Principles of Microeconomics / Unit 5 MIC 0426 review, 2 to 3 minutes
From Utils to a Demand Curve
The idea
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 consumer, a budget, two prices and a table of marginal utilities that fall as quantity rises. Spend the budget by the rule: compute marginal utility per dollar for the next unit of each good and buy the higher, until the money is gone and the two ratios match as nearly as whole units allow. That is the best bundle; on the indifference-curve diagram it is the tangency of the budget line with the highest reachable curve, the same choice in a second language. Now raise one good's price; the budget line rotates in around the other intercept, and two things happen at once. The good is relatively dearer, so the rule shifts purchases toward the other good: the substitution effect, which always cuts the dearer good's quantity. And the same income buys less, so the consumer is poorer in real terms: the income effect, which cuts quantity further if the good is normal. Record the new quantity at the new price; repeat at a third. The price and quantity pairs are points on this consumer's demand curve, which slopes down because substitution always pushes that way and the income effect usually does. Finally, add every consumer's quantity at each price, and the horizontal sum is the market demand curve that unit two took as given.
In practice
Worked example: a budget of twelve dollars, sandwiches with marginal utilities of forty, thirty-two, twenty and twelve, juices at two dollars with marginal utilities of sixteen, twelve, eight and four. At four dollars a sandwich the rule bought two sandwiches and two juices. Raise the sandwich price to six. Per dollar the first sandwich now gives about six point seven and the first juice eight: juice. Then the sandwich at six point seven against the second juice at six: sandwich, eight dollars spent. Then the second sandwich at five point three against the second juice at six: juice, ten dollars, and the last two dollars buy a third juice, since a sandwich is unaffordable. The new bundle is one sandwich and three juices, and two points on the sandwich demand curve are four dollars and two, six dollars and one. Part of the drop is substitution toward juice; part is a budget that now buys less of everything.
Where people slip
Three cautions. Compare marginal utility per dollar, never marginal utilities; the sandwich always had the larger marginal utility and was still the good to cut. The income effect is a purchasing-power effect: money income never changed, which is the situation exam questions describe. And the utils were a device: the bundle, the points and the downward slope would survive any ranking that keeps the same order.
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