Class 11: Supply, Demand, and the Consumer
Textbook reading: Kreps, Chapter 13, all of it (it is short), including the GM case in 13.5 and Problem 13.1. Then skim Chapter 10: read 10.1, 10.2, and 10.5 properly, and read 10.3 and 10.4 only for the idea of bang for the buck and money left over. Every derivative in Chapter 10 becomes a table of incremental values in this course, exactly as in Lab 5, so skip the algebra on pages 227 to 234 entirely.
Key Ideas
The most famous picture in economics
- In unit 2, one firm chose a price. Unit 3: markets where no one chooses the price, because every seller is small
- Market demand curve: the horizontal sum of every buyer’s demand at each price
- Supply curve: how much sellers bring to market at each price they take as given. Horizontal sum of individual supplies, exactly as for demand
- Two extremes
- Perfectly elastic supply: sellers have an equally good outlet elsewhere, so they supply any amount at that outside price and nothing below it
- Perfectly inelastic supply: the quantity is already fixed and comes to market at any price above the fallback
Equilibrium
- Equilibrium: the price where supply equals demand
- Above it, goods sit unsold and sellers undercut; below it, shelves empty and buyers bid up
- The picture needs many buyers, many sellers, a commodity good, and buyers who shop the cheapest seller first
- Nothing in the picture requires the price to be positive. When supply far exceeds demand at every price, the equilibrium price is zero, whatever the good is worth to the person holding it
- A tax collected from sellers shifts the supply curve up by the tax. Who ends up paying depends on the shape of the curves, not on who writes the cheque
Where a demand curve comes from
- A consumer with a table of incremental values and a price list, as in Lab 5
- Two cases that look alike and are not
- Money left over. Cash spent here is cash not spent elsewhere, so treat money left over as a good worth one unit of utility per dollar. Buy every unit whose incremental value is at least its price. Her demand curve for a good is her column of incremental values
- A fixed budget that can only be spent here. The money has no outside use, so no single unit is judged against its price. Instead she lists the affordable bundles, the combinations of goods the budget covers, and chooses the one whose total value to her is highest. Her demand for one good now depends on the price of the other, because that price changes which bundles she can afford
GM’s truck coupons
- 1993: GM settles a class action by giving 4.7 million truck owners a coupon worth $1,000 off a new GM truck ($500 if transferred once)
- The Wall Street Journal called it a $4.7 billion settlement; the judge called it nearly worthless
- Both are right: supply equals demand in the coupon market
Problems of the Day
Q31: Who Pays the Dollar
The city adds a $1 tax on every unit sold at the Saturday market, collected from the stallholder. Rosa, who speaks for the growers, says every price tag will simply go up $1. Councillor Tom says shoppers won’t pay a cent more; the growers will have to eat the cost of the tax.
There are three stalls:
Honey. The beekeeper sells jars at $8. Whatever doesn’t sell at the market goes to a grocer, who also pays $8 a jar. After the farmer’s market tax, will the beekeeper keep the farmer’s market price at $8 and take home $7, or raise the price?
Peaches. Thirty growers each picked ten boxes this morning and have to sell them today. Shoppers at the market want 400 boxes at $5, 300 at $6, and 200 at $7, and will buy peaches from the stands that price the lowest first. Whatever doesn’t sell at the market goes to a cannery, which pays $4.90 a box. What price did a box of peaches fetch before the tax, and what price do they go for now?
What’s the difference between the honey example and the peach example?
What this teaches. Who bears a tax depends on the elasticity of supply. Honey supply is perfectly elastic (the grocer gives beekeepers an equally good outlet, so they will not accept a cent less) and the tax falls on shoppers; today’s peach supply is perfectly inelastic (the boxes are picked and the cannery is a poor fallback) and the tax falls on growers.
Q32: The Third Cup
Jonah runs the campus café: coffee $2, donut holes $1. Two regulars, Emily and Oscar, happen to value each cup and each donut hole identically:
| 1st | 2nd | 3rd | 4th | 5th | |
|---|---|---|---|---|---|
| Coffee | $6.00 | $3.00 | $1.60 | $1.00 | |
| donut hole | $4.00 | $2.50 | $1.50 | $1.20 | $0.80 |
Oscar pays cash. Emily pays with $7 of dining dollars that work only at the café, for coffee or donut holes, and expire tonight; she never tops them up with cash. Each buys the combination worth most to them. Today each buys two coffees.
Jonah wants to cut coffee to $1.50. “Each of them buys a third cup,” he says. Sam, the barista, says Emily can’t: “She has $7 whatever the price.” How many extra coffees does the cut sell?
What this teaches. Where an individual demand curve comes from. A cash buyer with money left over buys every unit worth at least its price, so his table of incremental values read sideways is his demand curve; a buyer with a fixed budget chooses among the bundles she can afford the one worth most to her in total, so her demand for coffee depends on the price of donut holes too, and a price cut can be absorbed entirely by buying more of the other good.
Q33: The Voucher Settlement
A gym loses a lawsuit brought by 2,000 former members. Nadia, their lawyer, negotiates the settlement: each gets a voucher for $100 off a year’s membership, usable this year. A voucher may be sold once; in a buyer’s hands it is worth $50 off. “A $200,000 settlement,” Nadia tells the paper, “far better than the $8 a head the gym offered in cash.”
Hal, a former member who moved away, objects that his voucher is worthless. The gym sells 500 memberships a year at $600; 150 of those are former members coming back.
Which offer is worth more to the 2,000, and by how much?
What this teaches. Supply and demand in a market nobody designed. Vouchers are in perfectly inelastic supply (1,850 of them) against a demand of 350 buyers, so the equilibrium price is zero no matter how much a voucher saves its holder; the face value of a settlement and its market value are different things when supply dwarfs demand.
Answers
Q31. Honey. Beekeepers will not keep less than $8, so the market price rises to $9. Shoppers pay the whole dollar; Rosa is right here. Peaches. Today 300 boxes sell at $6. After the tax a $6 price leaves growers $5, still above the cannery’s $4.90, so all 300 boxes still come to market and the price stays $6. Growers pay the whole dollar; Tom is right here.
Q32. Oscar. With cash, he buys a cup while it is worth at least its price. At $2: two cups (the third is worth $1.60). At $1.50: three cups, the third just clearing. Jonah is right about Oscar. Emily at $2. Dining dollars buy nothing else, so she compares whole bundles that $7 covers and takes the one worth most to her: three coffees and one donut hole, $10.60 + $4 = $14.60; two coffees and three donut holes, $9 + $8 = $17; one coffee and five donut holes, $6 + $10 = $16. She buys two coffees and three donut holes. Emily at $1.50. The affordable bundles change: four coffees and one donut hole, $11.60 + $4 = $15.60; three coffees and two donut holes ($6.50 spent), $10.60 + $6.50 = $17.10; two coffees and four donut holes, $9 + $9.20 = $18.20; one coffee and five donut holes, $16. The best bundle is still two coffees, now with four donut holes. Sam is right about Emily. The cut sells one extra coffee, Oscar’s third. For Oscar a cheaper cup only has to beat its own price; for Emily the bundle holding a third cup has to beat the bundle holding a fourth donut hole instead, and $17.10 loses to $18.20.
Q33. Members who come back. 150 would have joined anyway and each saves $100: $15,000. Nadia is right about them. Vouchers for sale. The other 1,850 can only sell. The buyers are the 350 joiners who are not former members, each willing to pay up to $50. Draw it: buyers take 350 vouchers at any price up to $50 and none above; sellers offer 1,850 at any price above zero. With 1,850 sellers chasing 350 buyers, any seller asking more than nothing is undercut, and the price falls to zero. Hal is right about his. The cash. 2,000 × $8 = $16,000. Verdict. The cash offer is worth $1,000 more than the vouchers. A voucher is worth only what someone will pay for it, and with more than five vouchers for every possible use nobody has to pay anything.