Market equilibrium and shocks
Learning goals
After this page, you can:
- Predict the direction of price and quantity after a shock to one curve.
- Solve two straight lines for the equilibrium price and quantity (spreadsheet level).
- Explain why a price ceiling below equilibrium creates a shortage, and a price floor above it creates a surplus.
The idea
A concert sells out in minutes at $80. The same afternoon, tickets resell for $300. Nobody broke a rule. The posted price was simply below the point where the two curves cross.
Where price settles. Put the demand curve and the supply curve on one picture. They cross once. At that price, the amount buyers want equals the amount sellers offer. This is the equilibrium. A manager might call it “the price that clears the market.”
Why does the market go there? Suppose the price is below the crossing point. Buyers want more than sellers offer. This is a shortage. Some buyers offer to pay more. Sellers raise price and output. The gap closes. Now suppose the price is above the crossing point. Sellers offer more than buyers want. This is a surplus. Inventory piles up, sellers discount, and the gap closes from the other side. Nobody is in charge of this.
A quick test for any news story: if the price is not moving toward the crossing point, something is stopping it. Usually it is a rule, a contract, or a posted price that is costly to change.
Reading a shock. A shock is anything that shifts one curve. Use three steps every time:
- Which curve? Ask who is hit directly. Weather, input costs, technology and rules on producers hit supply. Income, tastes, rivals’ prices and the number of buyers hit demand.
- Which way? More at every price = right. Less = left.
- Read the new crossing point.
| Shock | Price | Quantity |
|---|---|---|
| Demand shifts right | up | up |
| Demand shifts left | down | down |
| Supply shifts right | down | up |
| Supply shifts left | up | down |
The pattern: when demand moves, price and quantity move together. When supply moves, they move apart. Use this to read real data. Price up and sales up? Demand shifted. Price up and sales down? Supply shifted.
Solving it with straight lines. Write demand as Q = a + b·P (b is negative). Write supply as Q = s·P + c. At equilibrium the two quantities are equal. One line of algebra gives the answer in the box below. In the Excel lab, a, b, s and c sit in four cells and P* is one formula.
Price controls. A price ceiling is a legal maximum. If it sits above the equilibrium, it does nothing (it is “non-binding”). If it sits below the equilibrium — rent control in a hot city, a gasoline price cap after a storm — buyers want more than sellers offer. The shortage never clears. You see lines, waiting lists, and resale markets.
A price floor is a legal minimum. Above the equilibrium — a minimum wage above the market wage, a farm support price — sellers offer more than buyers take. The surplus shows up as unsold stock or unemployed workers.
The sold-out concert is the same picture without a law. The promoter set a price below the crossing point. The resale market is the price finding its way to equilibrium.
Demand Q = a + b·P, supply Q = s·P + c
\[ P^* = \frac{a - c}{s - b} \qquad Q^* = s \cdot P^* + c \]
Shortage at a ceiling Pc = Qd(Pc) − Qs(Pc)
Try it
The chart shows lunches from campus food trucks. Try these:
- Make price rise and quantity fall with one slider. Which curve did you move, and which way?
- Make price and quantity both rise with one slider.
- Choose “price ceiling” and set it 50 cents below P*. Read the shortage. Now shift demand right by 100. Does the shortage grow or shrink?
Worked example
Problem. Campus food-truck lunches. Demand is Q = 1,110 − 220·P. Supply is Q = 170·P − 50. Find the equilibrium. Then a new dorm opens and demand rises by 100 lunches at every price. Then student government caps the price at $2.50.
Step 1. Set the two quantities equal. 1,110 − 220P = 170P − 50, so 1,160 = 390P and P* = $2.97.
Step 2. Find the quantity. Q* = 170 × 2.97 − 50 ≈ 456 lunches. Check with the demand line: 1,110 − 220 × 2.97 ≈ 456. Same number.
Step 3. The dorm opens. a becomes 1,210. P* = (1,210 + 50) ÷ 390 = $3.23, and Q* ≈ 499. Demand shifted right: price up, quantity up — the first row of the table.
Step 4. The $2.50 cap (in the original market, before the dorm). Buyers want 1,110 − 220 × 2.50 = 560. Sellers offer 170 × 2.50 − 50 = 375. The shortage is 185 lunches a day. (After the dorm opens, buyers want 660 at $2.50, so the shortage grows to 285.)
Check with Excel. Put a, b, s, c in cells B1:B4. Then =(B1-B4)/(B3-B2) gives P*.
Check yourself
Used-car prices rose sharply in 2021 while the number of used cars sold also rose. Which single shift explains both facts?
P and Q together → demand moved; P and Q apart → supply moved.
Demand is Q = 800 − 100P and supply is Q = 100P − 200. The equilibrium price is:
P* = (a − c)/(s − b) = (800 + 200)/(100 + 100) = 5.
A city caps rents at $900 when the market rent is $1,300. The predictable result is:
Ceiling below equilibrium → shortage.
A concert sells out in minutes at $80 and tickets resell at $300. Which statement is FALSE?
Resale premium is evidence of a shortage; without a shortage there is no premium.
The minimum wage is raised above the market wage for entry-level restaurant jobs. In that labor market we expect:
Floor above equilibrium → surplus.
Video
Video coming soon.