The model in brief
The demand curve shows how much of a good buyers want at each price, holding everything else constant. It slopes downward because a higher price reduces quantity demanded. The supply curve shows how much sellers want to sell at each price, and it slopes upward because a higher price makes production more profitable. The market is in equilibrium where the two curves meet, at the price where quantity demanded equals quantity supplied.
Always keep the idea of ceteris paribus, which means all other things equal, in mind. A change in the good's own price causes a movement along the curve. A change in anything else shifts the whole curve.
Movements versus shifts, and what shifts each curve
| Curve | Shifts right (increase) if | Shifts left (decrease) if |
|---|---|---|
| Demand | Income rises (normal good), price of a substitute rises, price of a complement falls, tastes favor the good, more buyers, expected future price rises | The opposite of each |
| Supply | Input costs fall, technology improves, more sellers, subsidies, favorable weather, expected future price falls | The opposite of each |
When you describe a shift, follow a standard chain: state which curve shifts and why, the direction of the shift, the new equilibrium and the change in price and quantity. For example, a rise in the price of coffee shifts the demand for tea right, which raises the equilibrium price and quantity of tea.
| Change | Equilibrium price | Equilibrium quantity |
|---|---|---|
| Demand increases, supply constant | Rises | Rises |
| Demand decreases, supply constant | Falls | Falls |
| Supply increases, demand constant | Falls | Rises |
| Supply decreases, demand constant | Rises | Falls |
| Both increase | Unclear (depends on sizes) | Rises |
| Demand increases, supply decreases | Rises | Unclear (depends on sizes) |
Solving for equilibrium with equations
Exam problems often give linear equations. Set quantity demanded equal to quantity supplied and solve.
Equilibrium (hypothetical market)
Demand: Qd = 120 - 2P. Supply: Qs = 3P.
Set Qd = Qs: 120 - 2P = 3P, so 120 = 5P and P = 24. Substitute to find quantity: Q = 3 x 24 = 72.
To draw the diagram, find the intercepts. Demand reaches zero quantity at P = 60 (since 120 - 2P = 0) and zero price at Q = 120. Supply passes through the origin. Label the axes (price on the vertical axis, quantity on the horizontal), both curves, the equilibrium point and its coordinates.
Many courses present demand in inverse form, with price as a function of quantity. Here P = 60 - 0.5Q for demand and P = Q/3 for supply. Be ready to move between forms, because surplus triangles use the inverse form.
Price ceilings and floors
A price ceiling is a legal maximum price. If it is set below equilibrium, it binds and creates a shortage. A price floor is a legal minimum. If it is above equilibrium, it binds and creates a surplus. If a control is set on the wrong side of equilibrium, it has no effect.
| Policy | Level | Quantity demanded | Quantity supplied | Result |
|---|---|---|---|---|
| Price ceiling | $18 | 120 - 36 = 84 | 3 x 18 = 54 | Shortage of 30 units |
| Price floor | $30 | 120 - 60 = 60 | 3 x 30 = 90 | Surplus of 30 units |
With a binding ceiling, the quantity actually traded is the smaller one, which is 54, so the market also loses transactions. Mention the usual side effects in a discussion: queues, black markets and falling quality under ceilings, and storage or waste costs under floors.
Taxes, incidence and deadweight loss
A tax per unit shifts the supply curve up (if levied on sellers) by the amount of the tax. The result is a higher price for buyers, a lower price received by sellers and fewer units traded. Who legally pays the tax does not determine who bears it. Incidence depends on elasticity.
A $5 tax on sellers (continuing the example)
New supply is Qs = 3(P - 5) = 3P - 15. Set equal to demand: 120 - 2P = 3P - 15, so 135 = 5P and P = 27, with Q = 66.
- Buyers now pay 27, up 3 from 24. Sellers receive 27 - 5 = 22, down 2 from 24. Buyers bear 3 of the 5 tax and sellers bear 2.
- Tax revenue is 5 x 66 = $330.
- The deadweight loss is the triangle of lost trades: 0.5 x 5 x (72 - 66) = $15.
Whichever side is less elastic bears more of the tax. Here demand is less elastic than supply at the equilibrium, so buyers bear the larger share.
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Get an instant quoteConsumer and producer surplus
Consumer surplus is the difference between what buyers are willing to pay and what they pay. Producer surplus is the difference between the price sellers receive and the lowest price they would accept. Both are areas on the diagram, usually triangles, and total surplus measures the market's gains from trade.
| Before tax | After the $5 tax | |
|---|---|---|
| Consumer surplus | 0.5 x (60 - 24) x 72 = 1,296 | 0.5 x (60 - 27) x 66 = 1,089 |
| Producer surplus | 0.5 x 24 x 72 = 864 | 0.5 x 22 x 66 = 726 |
| Tax revenue | 0 | 330 |
| Total | 2,160 | 2,145 |
| Deadweight loss | 15 |
Check: the total before the tax (2,160) minus the total after (2,145) equals the deadweight loss of 15, which matches the triangle calculation above. This reconciliation is a good habit for catching mistakes.
Elasticity
Elasticity measures how responsive quantity is to a change in something else. The price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price. For analysis, ignore the minus sign unless asked, and describe size.
| Value of absolute elasticity | Description | Effect of a price rise on total revenue |
|---|---|---|
| Greater than 1 | Elastic | Revenue falls |
| Equal to 1 | Unit elastic | Revenue unchanged |
| Less than 1 | Inelastic | Revenue rises |
Midpoint method
Price rises from $10 to $12 and quantity falls from 100 to 80. Using midpoints, the change in quantity is -20 / 90 = -22.2 percent, and the change in price is 2 / 11 = 18.2 percent. Elasticity = -22.2 / 18.2 = -1.22, so demand is elastic. Check with revenue: 10 x 100 = 1,000 before and 12 x 80 = 960 after, so revenue fell, which is what elastic demand predicts.
Point elasticity on a linear demand curve
With Qd = 120 - 2P at P = 24, Q = 72. The slope in terms of quantity is -2, so elasticity = -2 x (24 / 72) = -0.67, inelastic. On a straight line, elasticity differs at each point, and is unit elastic at the midpoint, which is P = 30 here.
| Other elasticity | Formula | Interpretation |
|---|---|---|
| Income elasticity of demand | Percentage change in quantity divided by percentage change in income | Positive for normal goods, above 1 for luxuries, negative for inferior goods |
| Cross-price elasticity | Percentage change in quantity of A divided by percentage change in price of B | Positive for substitutes, negative for complements |
| Price elasticity of supply | Percentage change in quantity supplied divided by percentage change in price | Higher when production can adjust quickly |
Determinants of price elasticity of demand: availability of substitutes, whether the good is a necessity or luxury, share of income spent on it, and the time horizon. Demand is generally more elastic over longer periods.
Practice problem with solution
Demand is Qd = 200 - 4P and supply is Qs = 6P - 20. (a) Find the equilibrium. (b) What happens with a price floor of $26? (c) What if demand rises to Qd = 240 - 4P? (d) Compute the elasticity of demand at the original equilibrium. (e) Find the effects of a $5 tax on sellers.
Solution
- (a) 200 - 4P = 6P - 20, so 220 = 10P and P = 22, Q = 6 x 22 - 20 = 112.
- (b) At 26: Qd = 200 - 104 = 96 and Qs = 156 - 20 = 136. There is a surplus of 40, and only 96 units are sold.
- (c) 240 - 4P = 6P - 20, so 260 = 10P, giving P = 26 and Q = 136. Price and quantity both rise.
- (d) Elasticity = -4 x (22 / 112) = -0.79, so demand is inelastic at that point.
- (e) New supply is Qs = 6(P - 5) - 20 = 6P - 50. Set equal to demand: 200 - 4P = 6P - 50, so P = 25 and Q = 100. Buyers pay 3 more (25 versus 22) and sellers keep 20, which is 2 less. Tax revenue is 5 x 100 = $500. Deadweight loss is 0.5 x 5 x (112 - 100) = $30. Because demand is inelastic, buyers bear the larger share (3 of the 5).
Writing economics answers well
- Draw a clear diagram Label both axes, every curve and the equilibrium. Use a ruler or drawing tool and show the shift with an arrow and a new label.
- Explain in a chain Cause, shift, new equilibrium, effect on price and quantity, in that order.
- Use the right terms Distinguish between a change in quantity demanded (movement) and a change in demand (shift).
- Show your algebra Set up the equation, solve step by step and state the units.
- Evaluate when asked Consider elasticity, time frame, and real-world limits.
- Use a real example Link the model to a recent market, but keep the model central.
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