Economia
Supply and Demand: Summary, Market Equilibrium and Solved Exercises
Supply and demand explained: the two curves, equilibrium price, shifts versus movements along the curve, surplus and shortage, price elasticity, with 5 solved exercises and 3 FAQs.
Recommended for: Grade 11 · Grade 12
Demand tells you how much buyers want to purchase at each price, supply how much producers want to sell. The equilibrium price is the one price at which the two quantities are equal: you find it by setting Qd = Qs. Above equilibrium goods go unsold; below equilibrium there are not enough of them.
The two curves
The demand curve slopes downward: the higher the price, the less people buy. That is why the price appears with a minus sign in formulas such as Qd = 100 − 2P.
The supply curve slopes upward: the higher the price, the more it pays to produce and sell. Here the price appears with a plus sign, as in Qs = 20 + 2P.
Watch out for a convention that trips people up: in economics the price goes on the vertical axis and the quantity on the horizontal one, the opposite of what you would do in a maths class.
Market equilibrium
Equilibrium is where the two curves cross. Three steps get you there:
- set Qd = Qs;
- solve the equation for the equilibrium price P;
- substitute P into either formula to get the quantity Q, then check it with the other formula.
That final check is not a formality: if the two quantities disagree, you made an arithmetic mistake.
Movement along the curve or shift of the curve
This is where most exam mistakes happen.
If the price of the good itself changes, the curve does not move: you simply end up on a different point of the same curve.
If anything else changes, the entire curve moves. Demand shifts because of income, tastes and trends, the price of substitutes or complements, the number of buyers, expectations. Supply shifts because of input costs, technology, taxes and subsidies, the number of firms.
| what changes | effect |
|---|---|
| price of the good | movement along the curve |
| income, tastes, price of substitutes | shift of demand |
| costs, technology, taxes | shift of supply |
Who moves, what follows
Four cases worth memorising, all of which you can rebuild by sketching two lines:
- demand shifts right (increases): price ↑, quantity ↑;
- demand shifts left (decreases): price ↓, quantity ↓;
- supply shifts right (increases): price ↓, quantity ↑;
- supply shifts left (decreases): price ↑, quantity ↓.
Surplus and shortage
When the price is not the equilibrium price, the market does not clear.
If the price is above equilibrium, producers bring more to market than buyers want: that is a surplus, unsold stock. The pressure pushes prices down.
If the price is below equilibrium, goods sell out and there are not enough: that is a shortage. The pressure pushes prices up.
Elasticity in two lines
Price elasticity of demand measures how strongly quantity reacts to a price change:
elasticity = % change in quantity / % change in price
If the absolute value is greater than 1, demand is elastic: quantity reacts a lot, and raising the price lowers total revenue. If it is less than 1, demand is inelastic: quantity barely reacts, and raising the price raises revenue. Necessities tend to be inelastic; luxuries and goods with many substitutes tend to be elastic.
The exercises below start with computing equilibrium, move on to identifying shifts and to surpluses and shortages, and end with elasticity and its effect on total revenue.
Solved exercises
1. In a market, demand is Qd = 100 − 2P and supply is Qs = 20 + 2P, where P is the price in dollars and Q the quantity in thousands of units. Find the equilibrium price and quantity. base
Show solution
- At equilibrium the quantity demanded equals the quantity supplied, so I set Qd = Qs.
- 100 − 2P = 20 + 2P.
- Move the unknowns to one side and the numbers to the other: 100 − 20 = 2P + 2P, so 80 = 4P.
- P = 80 / 4 = 20 dollars.
- Substitute into demand: Qd = 100 − 2·20 = 60.
- Check with supply: Qs = 20 + 2·20 = 60. Both quantities match, so the answer is correct.
Answer: Equilibrium price P = 20 dollars ; equilibrium quantity Q = 60 thousand units
2. For each situation, state which curve shifts and in which direction, and what happens to equilibrium price and quantity: (a) a heat wave in the ice cream market; (b) the price of cocoa doubles in the chocolate market; (c) the price of gasoline rises sharply in the bicycle market. base
Show solution
- Always ask first: does the cause act on buyers (demand) or on producers (supply)?
- (a) Heat makes more people want ice cream: consumer tastes change, so demand shifts right. Both equilibrium price and quantity rise.
- (b) Cocoa is an input for chocolate: producers' costs rise, so supply shifts left. Price rises and quantity falls.
- (c) Gasoline is used by cars, and cars are a substitute for bicycles: if driving costs more, demand for bicycles shifts right. Price and quantity both rise.
Answer: (a) demand shifts right: P↑ Q↑ ; (b) supply shifts left: P↑ Q↓ ; (c) demand shifts right: P↑ Q↑
3. Using the same curves as exercise 1 (Qd = 100 − 2P, Qs = 20 + 2P), the government fixes the price by law at 30 dollars. What happens to the market? And if it fixed the price at 10 dollars? intermedio
Show solution
- At P = 30: Qd = 100 − 2·30 = 40 and Qs = 20 + 2·30 = 80.
- Supply exceeds demand by 80 − 40 = 40 thousand units: there is a surplus, that is, unsold stock in warehouses.
- At P = 10: Qd = 100 − 2·10 = 80 and Qs = 20 + 2·10 = 40.
- Demand exceeds supply by 80 − 40 = 40 thousand units: there is a shortage, with queues and waiting lists.
- Notice that 30 is above the equilibrium price (20) and 10 is below it: a price forced above equilibrium creates a surplus, a price forced below equilibrium creates a shortage.
Answer: At P = 30 a surplus of 40 thousand units (unsold stock) ; at P = 10 a shortage of 40 thousand units
4. In the market of exercise 1, energy costs rise and producers cut the quantity supplied by 40 thousand units at every price, so the new supply is Qs' = 2P − 20. Demand stays Qd = 100 − 2P. Find the new equilibrium and compare it with the original one. intermedio
Show solution
- Set Qd = Qs' again: 100 − 2P = 2P − 20.
- 100 + 20 = 2P + 2P, so 120 = 4P.
- P = 120 / 4 = 30 dollars.
- Quantity: Qd = 100 − 2·30 = 40. Check: Qs' = 2·30 − 20 = 40. They match.
- Compare with the original equilibrium (P = 20, Q = 60): price rises by 10 dollars, quantity falls by 20 thousand units.
- This is the typical result of a leftward shift in supply: less is sold, at a higher price.
Answer: New equilibrium P = 30 dollars and Q = 40 thousand units ; price rises from 20 to 30 and quantity falls from 60 to 40
5. Still with Qd = 100 − 2P, a firm that controls the market considers raising the price from 20 to 25 dollars. Compute the price elasticity of demand over that range, say whether demand is elastic or inelastic, and determine whether total revenue rises or falls. avanzato
Show solution
- Find the two quantities: at P = 20, Qd = 100 − 40 = 60 ; at P = 25, Qd = 100 − 50 = 50.
- Percentage change in quantity: (50 − 60) / 60 = −10/60 ≈ −16.7%.
- Percentage change in price: (25 − 20) / 20 = 5/20 = +25%.
- Elasticity = % change in quantity / % change in price = −16.7 / 25 ≈ −0.67.
- The absolute value 0.67 is less than 1, so demand is inelastic: quantity reacts less than proportionally to price.
- Total revenue before: 20 · 60 = 1200. Total revenue after: 25 · 50 = 1250.
- Revenue rises by 50, which matches the theory: when demand is inelastic, raising the price increases total revenue.
Answer: Elasticity ≈ −0.67 (absolute value 0.67 < 1), so demand is inelastic ; total revenue rises from 1200 to 1250
FAQ
What is the difference between a shift of the curve and a movement along the curve?
If the price of the good itself changes, you move along the curve: the curve stays put and only the quantity demanded or supplied changes. If anything else changes (income, tastes, the price of substitutes, production costs, technology), the whole curve shifts left or right. Rule of thumb: the price of the good moves the point, everything else moves the curve.
Why does the demand curve slope downward?
Two effects work together. First, the substitution effect: if a good gets more expensive, many buyers switch to a similar good that is now relatively cheaper. Second, the income effect: with the same wage, a higher price means you can afford less overall. On top of that there is diminishing marginal utility, meaning each extra unit of the same good gives you less satisfaction, so you are willing to pay less for it.
What happens if a government sets a price ceiling below equilibrium?
A shortage appears: at that price buyers want more than producers are willing to sell. The result is not that everyone buys cheaply, but that many people cannot find the good at all. Queues, waiting lists, rationing and often a black market at prices above equilibrium follow. That is why price ceilings usually work only as a temporary measure.