Chapter 1 established that scarcity forces choices and that the price system coordinates those choices. This chapter introduces the specific mechanism through which prices emerge: the interaction of supply and demand. The supply-and-demand model is the most widely used tool in economics. It explains how prices are determined in competitive markets, predicts how prices respond to changes in underlying conditions, and reveals the unintended consequences of price interventions.
The model rests on a simple premise: in a competitive market — one with many buyers, many sellers, and a homogeneous product — no single participant can dictate the price. Instead, the price emerges from the collective behavior of all participants. Our task is to formalize this process.
The phrase "willing and able" matters. Desire alone is not demand — a student who wants a Ferrari but cannot afford one does not contribute to the demand for Ferraris. Demand requires both the willingness to buy and the purchasing power to follow through. The phrase "holding all other factors constant" — sometimes written in Latin as ceteris paribus — is equally important. Demand describes the relationship between price and quantity when everything else stays the same. When other things change (income, tastes, the price of related goods), we are no longer moving along the same demand curve — we are shifting to a new one.
Why does demand slope downward? Two reinforcing mechanisms are at work:
Both effects push in the same direction: higher price, lower quantity demanded.
Consider a neighborhood's demand for cups of lemonade per day:
| Price ($/cup) | Quantity demanded (cups/day) |
|---|---|
| 0.50 | 90 |
| 1.00 | 80 |
| 1.50 | 70 |
| 2.00 | 60 |
| 2.50 | 50 |
| 3.00 | 40 |
| 3.50 | 30 |
| 4.00 | 20 |
| 4.50 | 10 |
| 5.00 | 0 |
Each row represents a price-quantity pair. Notice the inverse relationship: as price rises by \$1.50, quantity falls by 10 cups. This regular pattern can be captured by a linear demand function:
where $a$ is the quantity demanded when price is zero (the horizontal intercept) and $b$ is the absolute value of the slope. From the table: $a = 100$ and $b = 20$:
$$Q_d = 100 - 20P$$The inverse demand function — price as a function of quantity:
$$P = \frac{a}{b} - \frac{1}{b}Q = 5 - \frac{Q}{20}$$Figure 2.1. The demand curve shows the quantity demanded at each price, holding all other factors constant. It slopes downward by the law of demand. Hover over the curve or the schedule points for exact values.
A movement along the demand curve occurs when the good's own price changes — the consumer moves to a different point on the same curve. A shift of the demand curve occurs when any factor other than the good's own price changes. The entire curve moves left or right.
A critical rule of thumb: If you're analyzing the effect of a change in the good's own price, you move along the curve. If you're analyzing the effect of anything else, you shift the curve. Mixing these up leads to serious analytical errors.
There is a deeper reason why supply curves slope upward: increasing marginal cost. As a firm produces more, it eventually runs into capacity constraints. Each additional unit costs more to produce than the last. The firm produces that unit only if the price covers its rising marginal cost.
| Price ($/cup) | Quantity supplied (cups/day) |
|---|---|
| 0.50 | 0 |
| 1.00 | 10 |
| 1.50 | 20 |
| 2.00 | 30 |
| 2.50 | 40 |
| 3.00 | 50 |
| 3.50 | 60 |
| 4.00 | 70 |
From the table: $c = -10$, $d = 20$, so $Q_s = 20P - 10$. The inverse supply function: $P = 0.50 + Q/20$.
Figure 2.3. The supply curve shows the quantity supplied at each price. It slopes upward because higher prices make production more profitable. Hover for exact values.
Set $Q_d = Q_s$:
Solving:
Example 2.1
Using $Q_d = 100 - 20P$ and $Q_s = 20P - 10$:
\$100 - 20P = 20P - 10 \implies 110 = 40P \implies P^* = 2.75$
$Q^* = 100 - 20(2.75) = 45$ cups per day. Verification: $Q^* = 20(2.75) - 10 = 45$ ✓
Surplus (price too high). At $P = 3.50$: $Q_d = 30$ but $Q_s = 60$. Sellers have 30 unsold cups — a surplus. They cut prices until $P^* = 2.75$.
Shortage (price too low). At $P = 1.50$: $Q_d = 70$ but $Q_s = 20$. Frustrated buyers bid the price up to $P^*$.
The demand intercept $a$ represents "how much people want the good" — driven by income, tastes, expectations, or number of buyers. Slide it to simulate a demand shift and watch the equilibrium move along the supply curve.
Figure 2.5. Drag the slider to shift the demand curve. The green equilibrium point moves along the supply curve. Shaded areas show consumer surplus (blue) and producer surplus (red). The dashed line is the original demand curve for reference.
The supply intercept $c$ represents production costs. A frost in the lemon-growing region raises costs (shifting supply left, making $c$ more negative). A technology improvement lowers costs (shifting supply right, making $c$ less negative). Watch the equilibrium ride along the demand curve.
Figure 2.6. Drag the slider to shift the supply curve. The equilibrium rides along the demand curve. When supply shifts right (lower costs), price falls and quantity rises — the signature of a supply increase.
When both curves shift at the same time, one variable's direction is unambiguous (both shifts push it the same way), while the other is ambiguous (depends on magnitudes). Use both sliders to explore:
Figure 2.7. Drag both sliders. Watch how some combinations produce unambiguous outcomes (both shifts push price the same way) while quantity becomes ambiguous, or vice versa. The dashed curves show the original positions.
General principle for simultaneous shifts:
| Demand ↑ | Demand ↓ | |
|---|---|---|
| Supply ↑ | Q ↑ unambiguous; P ambiguous | P ↓ unambiguous; Q ambiguous |
| Supply ↓ | P ↑ unambiguous; Q ambiguous | Q ↓ unambiguous; P ambiguous |
A heat wave increases demand for lemonade. The demand intercept rises from $a = 100$ to $a = 120$: $Q_d = 120 - 20P$.
New equilibrium: \$120 - 20P = 20P - 10 \implies 130 = 40P \implies P^* = 3.25$, $Q^* = 120 - 20(3.25) = 55$.
Result: price rises from \$1.75 to \$1.25 (+\$1.50), quantity rises from 45 to 55 (+10 cups). Both increase when demand shifts right.
A frost destroys lemon groves, raising costs. Supply intercept shifts from $c = -10$ to $c = -30$: $Q_s = 20P - 30$.
New equilibrium: \$100 - 20P = 20P - 30 \implies 130 = 40P \implies P^* = 3.25$, $Q^* = 100 - 20(3.25) = 35$.
Result: price rises from \$1.75 to \$1.25 (+\$1.50), quantity falls from 45 to 35 (−10 cups). Price and quantity move in opposite directions when supply shifts left.
Heat wave ($a = 120$) and lemon frost ($c = -30$) hit simultaneously.
\$120 - 20P = 20P - 30 \implies 150 = 40P \implies P^* = 3.75$, $Q^* = 120 - 20(3.75) = 45$.
Price rises unambiguously (\$1.75 → \$1.75) because both shifts push price up. Quantity is unchanged (45 → 45) because the two shifts are equal in magnitude and push quantity in opposite directions. If the demand shift were larger, Q would rise; if the supply shift were larger, Q would fall.
Drag the price ceiling. When it's above equilibrium (\$1.75), it has no effect. As you drag it below equilibrium, a shortage appears and grows.
Figure 2.8. Drag the ceiling below \$1.75 to see the shortage appear. The gap between quantity demanded and quantity supplied is the shortage — allocated by queuing, rationing, or black markets instead of price.
The city imposes a price ceiling of \$1.00 per cup on lemonade ($Q_d = 100 - 20P$, $Q_s = 20P - 10$, $P^* = 2.75$).
At $P = 2.00$: $Q_d = 100 - 20(2) = 60$, $Q_s = 20(2) - 10 = 30$.
Shortage = $Q_d - Q_s = 60 - 30 = 30$ cups. The ceiling is binding (below $P^*$), creating a shortage of 30 cups per day. Some willing buyers cannot purchase lemonade at the controlled price.
Real-world application: Rent control. The most prominent price ceiling is rent control. When the cap is below the market-clearing rent: shortage of apartments, deterioration of quality (landlords underinvest), misallocation (apartments go to those who found them first, not those who value them most), reduced construction, and black-market side payments.
Figure 2.9. Drag the floor above \$1.75 to see the surplus appear. The gap between quantity supplied and quantity demanded is the surplus — unsold output (or, in labor markets, unemployment).
The city imposes a price floor of \$1.50 per cup on lemonade.
At $P = 3.50$: $Q_d = 100 - 20(3.50) = 30$, $Q_s = 20(3.50) - 10 = 60$.
Surplus = $Q_s - Q_d = 60 - 30 = 30$ cups. The floor is binding (above $P^*$), creating a surplus of 30 cups per day. Sellers cannot find enough buyers at the mandated price.
Real-world application: The minimum wage. The most prominent price floor is the minimum wage. If set above the equilibrium wage, the simple model predicts a surplus of labor — unemployment. However, Card and Krueger's famous 1994 study found no significant employment effect of a minimum wage increase in New Jersey, illustrating why theoretical predictions must always be tested against data. If firms have monopsony power, a minimum wage can actually increase employment.
When a country opens to international trade, the market operates at the world price $P_W$. If $P_W < P^*_{domestic}$, the country imports (domestic demand exceeds domestic supply at the world price). If $P_W > P^*_{domestic}$, the country exports.
The world price of lemonade is $P_W = 2.00$, below the domestic equilibrium of $P^* = 2.75$.
At $P_W = 2.00$: $Q_d = 100 - 20(2) = 60$, $Q_s = 20(2) - 10 = 30$.
Imports = $Q_d - Q_s = 60 - 30 = 30$ cups per day. Domestic consumers gain from cheaper lemonade; domestic producers lose as they produce less at the lower price.
A tariff of $t = 0.50$ per cup is imposed on imported lemonade. Domestic price rises to $P_W + t = 2.50$.
At $P = 2.50$: $Q_d = 100 - 20(2.50) = 50$, $Q_s = 20(2.50) - 10 = 40$.
Imports fall from 30 to 10 cups. Tariff revenue = \$1.50 \times 10 = \\$1.00$. Two DWL triangles appear: (1) production DWL from inefficient domestic production replacing cheaper imports ($\frac{1}{2}(0.50)(40 - 30) = 2.50$), (2) consumption DWL from lost consumer purchases ($\frac{1}{2}(0.50)(60 - 50) = 2.50$). Total DWL = \$1.00.
Figure 2.10. Adjust the world price to see imports (when $P_W$ is below autarky equilibrium) or exports (when above). Add a tariff to see imports shrink, domestic production rise, and deadweight loss appear. The yellow triangles are DWL from the tariff.
Maya has set up her lemonade stand. She surveys her neighborhood and estimates daily demand: $Q_d = 100 - 20P$. Her supply function, based on costs: $Q_s = 20P - 10$.
Setting demand equal to supply: \$100 - 20P = 20P - 10 \implies P^* = 2.75$, $Q^* = 45$.
Maya will sell 45 cups per day at \$1.75 each, earning revenue of \$123.75/day. Her opportunity cost is \$120/day (the bookstore job from Chapter 1). She's making at most \$1.75 per day above her opportunity cost — precarious. Any shock (a tax, a competitor, a rise in lemon prices) could push her into negative territory.
| Label | Equation | Description |
|---|---|---|
| Eq. 2.1 | $Q_d = a - bP$ | Linear demand function |
| Eq. 2.2 | $Q_s = c + dP$ | Linear supply function |
| Eq. 2.3 | $a - bP^* = c + dP^*$ | Equilibrium condition |
| Eq. 2.4 | $P^* = (a - c)/(b + d)$ | Equilibrium price |
| Eq. 2.5 | $Q^* = a - bP^*$ | Equilibrium quantity |