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The law of supply and demand
Two relations, a single price — and the distinction almost everyone misses: sliding along a curve, or shifting it.
Qd(P*) = Qs(P*) → the pair (P*, Q*)Problem / motivation
At a strawberry market, nobody decides the price — and yet one comes out, roughly the same for everyone. How? And above all: why do half the mistakes made on this chapter come from a single confusion, which this course will clear up?
First point, the one that changes everything: supply and demand are not QUANTITIES, they are RELATIONS. “The demand for strawberries” is not 20 kg: it says, for every possible price, how much buyers would want to buy at that price — 60 kg at €5, 20 kg at €10, 4 kg at €12. The same on the sellers' side for supply. A complete table, then, not a number.
From that comes the confusion to be cleared up. If the PRICE changes, you simply read another line of the same table: nothing else has moved. But if something else changes — a frost that destroys the harvest, a fashion that makes strawberries irresistible — then the WHOLE TABLE is replaced, and everything has to be recomputed. Sliding along the curve, or shifting the curve: two movements the narrative separates, and that the solving step puts in figures all the way.
Assumptions
In your view, which assumptions are needed for this model to hold? Jot down your ideas — no lead is wrong, this is your worksheet.
Your worksheet is still empty. Go for it: propose at least one idea.
0 idea(s) proposedFormalization
Let's build the strawberry market of one stall, in kilos per day. On the SELLERS' side: below €5/kg, the price does not cover costs, and nobody brings out their crates — supply is nil. Above it, each extra euro makes selling profitable for more producers and brings out 4 more kg. So we write down exactly what we have just said: 4 kg per euro ABOVE €5, that is Qs = 4 × (P − 5). Expanding gives the form usually met, Qs = 4·P − 20 — the “−20” means nothing on its own, it is only the 4 × 5 of the threshold. On the BUYERS' side: if strawberries were free, 100 kg would go in a day; each euro of price puts 8 kg off. Hence Qd = 100 − 8·P, which falls to 0 at €12.5/kg — beyond that, not a single buyer. These four numbers are invented for the example, but each has a meaning: two thresholds (€5 and €12.5) and two sensitivities (4 and 8 kg per euro). One word finally about the usual presentation, in case you meet this market elsewhere as a graph: the convention is to put quantity on the horizontal axis and price on the vertical one — demand slopes down from left to right, supply slopes up, and equilibrium is where they cross. It is disconcerting, since it is the price that commands quantities, but the usage is firmly established.
One single price makes the quantity demanded equal the quantity supplied. Set the equality: 100 − 8·P = 4·P − 20. Add 8·P to both sides: 100 = 12·P − 20. Add 20 to both sides: 120 = 12·P. So P* = €10/kg. That leaves HOW MUCH changes hands at that price: Qd = 100 − 80 = 20 kg, and Qs = 40 − 20 = 20 kg — the two coincide, a good sign. So a market's outcome is not a number but a PAIR: (P* = €10/kg; Q* = 20 kg). They are called the equilibrium price and the equilibrium quantity.
Here is the heart of the chapter. If the price goes from €10 to €11, the two relations have not changed one jot: you are simply reading another of their lines. That is SLIDING ALONG the curves. But if the frost destroys half the harvest, then at EVERY price there are half as many strawberries to sell: the supply relation itself is replaced, the curve SHIFTS, and the equilibrium has to be recomputed. That is how the apparent contradiction of the poll unravels: the frost lowers supply (a shift) while the rule “higher price ⇒ larger quantity supplied” goes on holding on the new curve (a slide). What shifts the curves? Never the price of the good itself — everything else: incomes, tastes, the price of other fruit, the weather, costs, taxes, the number of buyers or sellers (interpretation, point 2).
That leaves WHY the price would settle at €10. Try €8: buyers want 100 − 64 = 36 kg, and sellers offer only 32 − 20 = 12 kg. 24 kg are missing: that is a SHORTAGE, and disappointed buyers agree to pay more rather than go home empty-handed. Try €12: buyers want only 4 kg while sellers offer 28. 24 kg are left on the stall: that is a SURPLUS, and the seller cuts the price at the end of the market rather than throw them away. In both cases, the pressure pushes towards €10. One caveat, though: this convergence is a plausible mechanism, not a guaranteed law — the third card in the limits shows a worked case where the price never settles. Click each term:
Solving / calculation
Let's run the strawberry market from end to end: the equilibrium, the march towards it, then the poll's shock — the frost — finally in figures. It is the last stage that proves why the two movements had to be told apart.
- The two relations, and their domain of validity
Qd = 100 − 8·P (nil at €12.5); Qs = 4·P − 20 (nil at €5)the model only makes sense for P between €5 and €12.5/kg - Set the equilibrium and isolate P (two operations, shown)
100 − 8·P = 4·P − 20 → (+8P) 100 = 12·P − 20 → (+20) 120 = 12·PP* = €10/kg - The quantity traded at that price — the second member of the pair
Qd = 100 − 8×10 = 20; Qs = 4×10 − 20 = 20Q* = 20 kg a day: the pair is (€10/kg; 20 kg) - Too low: the shortage in figures
at €8: Qd = 36 kg, Qs = 12 kg24 kg missing → buyers outbid each other, the price rises - Too high: the surplus in figures
at €12: Qd = 4 kg, Qs = 28 kg24 kg unsold → the seller cuts the price, the price falls - THE FROST (the poll): at every price, half as many strawberries to sell
Qs becomes (4·P − 20) / 2 = 2·P − 10 — the supply curve SHIFTSthis is not a slide: the computation has to be redone - The new equilibrium
100 − 8·P = 2·P − 10 → 110 = 10·PP* = €11/kg and Q* = 100 − 88 = 12 kg - The proof that the distinction matters
at €11/kg: on the OLD supply, Qs = 24 kg against Qd = 12 kg; on the NEW one, Qs = 12 kg = Qdsame price, 12 kg unsold in one case, perfect equilibrium in the other
Keep the three takeaways. A market delivers not a price but a PAIR: here (€10/kg; 20 kg). The frost moves it to (€11/kg; 12 kg) — the price gains only 10% while the quantity traded loses 40%: a supply shock is paid for mostly in quantities. And above all, the last stage settles the poll's question: at €11/kg, the old market was drowning in 12 kg of unsold stock while the new one is exactly at equilibrium. Same price, opposite states — the only thing that changed is the relation itself. That is why “the price went up” and “supply fell” are not two ways of saying the same thing.
Qd = (100 − 8·P) × (buyers / 100); Qs = 4·(P − 5) × (1 − harvest lost / 100)Two things to do, in this order. One: move the PRICE alone and watch the shortage or the surplus appear — the curves do not move, you are sliding along them, and the equilibrium price displayed does not shift by a cent. Two: move the HARVEST LOST or the NUMBER OF BUYERS — there, a curve shifts and the equilibrium price changes before your eyes. Set the harvest lost to 50% to recover the course's frost.
Economic interpretation
Three readings: what a price is for, what shifts the curves, and a logical oddity worth having seen.
A high price tells sellers “produce more” and buyers “economise, take something else”: it coordinates thousands of decisions without anyone having to collect them. But who changes it, in practice? Nobody but the participants themselves: the grower whose stall empties before midday puts 50 cents more on it the next day; the one with full crates at 1 pm cuts the price. The “market” price is the average of those thousands of individual adjustments, not a central decision.
The DEMAND curve shifts when these change: buyers' income, their tastes and fashion, the price of competing products (Spanish strawberries) or complementary ones (whipped cream), the number of buyers, or what they expect future prices to be. The SUPPLY curve shifts when these change: costs of production, technology, the weather and harvests, taxes, the number of sellers. And one single thing NEVER shifts these curves: the price of the good itself — it makes you slide along them. Hence the test to apply in every exercise: “what changed, the price, or something else?”
Look carefully at the two halves of the course. In the two laws, it is the PRICE that commands quantities: you give yourself a price and read off the quantities that follow. In the march towards equilibrium, it is the reverse: it is the GAP in quantities (the 24 missing kg) that commands the price. Both arrows are true, but they do not act at the same moment — the relations describe intentions at a given price, the adjustment describes what happens when those intentions do not match. Many confusions arise from not having noticed that turnaround.
Limits / critiques
Exercises
On another market, Qd = 90 − 5·P and Qs = 3·P − 6. What is the equilibrium price (in €)?
On the course's strawberry market (Qd = 100 − 8·P, Qs = 4·P − 20), the price is frozen at €8/kg. How many kilos are missing?
Which of these events makes you SLIDE along the demand curve, rather than shifting it?
A fashion makes buyers want 20% more strawberries AT EVERY PRICE, with the harvest intact. What happens to the price and the quantity traded?
On that same market (Qd = 90 − 5·P, Qs = 3·P − 6), what quantity is traded at equilibrium?
Still on the strawberry market, a frost destroys half the harvest: at every price, supply is halved (Qs = 2·P − 10). What is the new equilibrium price (in €/kg)?
True or false: “the price of strawberries went up, so the demand for strawberries fell” is correctly worded.
For a fine wine, a very high price can attract more buyers. What is the best explanation?