Each person's demand curve comes from her own choices, as in Price Changes and the Demand Curve. A market is many buyers facing the same price. To get market demand, add up what all of them want at each price, which produces a piecewise function with kinks.
🔑 Key idea
Market demand is the horizontal sum of individual demands: $$Q(P) = q_1(P) + q_2(P) + \cdots,$$ where each $q_i(P) = 0$ above that buyer's choke price. Each time the price falls past another buyer's choke price, the market curve gets a kink and becomes flatter.
💡 Why it works
At a given price every buyer decides alone how much to buy, and the market quantity is the total. So we add quantities at the same price, moving horizontally across the graph. We never add prices: two buyers who each would pay \$5 for a first unit don't make a buyer who would pay \$10. A buyer whose choke price is below the current price buys nothing, not a negative amount, which is why the formula switches when the price crosses a choke price.
Buyer 1: $q_1 = 30 - 2P$ (choke price 15). Buyer 2: $q_2 = 24 - 3P$ (choke price 8). Above \$8 only buyer 1 buys, so market demand follows $D_1$; below \$8 it is $Q = 54 - 5P$. The kink is at $P = 8$, $Q = 14$.
✏️ Worked example: Quantity at two prices
With $q_1 = 30 - 2P$ and $q_2 = 24 - 3P$ (each zero when negative), find the market quantity at $P = 10$ and $P = 4$.
At $P = 10$: $q_1 = 10$; $q_2 = 24 - 30 < 0$, so $q_2 = 0$. Market: 10.
At $P = 4$: $q_1 = 22$ and $q_2 = 12$. Market: 34.
Answer: 10 and 34.
✏️ Worked example: The whole curve
Write market demand for the two buyers as a piecewise function.
For $P \ge 15$: nobody buys, $Q = 0$.
For $8 \le P < 15$: only buyer 1, $Q = 30 - 2P$.
For $0 \le P < 8$: both, $Q = 54 - 5P$.
Check continuity at the kink: $30 - 16 = 14$ and $54 - 40 = 14$.
Answer: $Q = 0$, then $30 - 2P$, then $54 - 5P$, with the kink at $P = 8$.
⚠️ Common mistake
Adding prices instead of quantities, or using $54 - 5P$ at every price. Adding the inverse demands $P = 15 - q/2$ and $P = 8 - q/3$ gives nonsense, because it treats one unit as if both people paid for it. And at $P = 10$ the formula $54 - 5P = 4$ is wrong: it counts buyer 2's "$-6$" units. Check: at any price, find each buyer's quantity first, replace negatives with 0, then add.
Kinks matter beyond the picture. Right at the kink the market's elasticity jumps: just above \$8 only buyer 1 responds to a price change, and just below it both do, so the curve is flatter and more elastic below the kink. A seller who cuts the price past a choke price suddenly reaches a whole new group of buyers.
Public goods are the exception: everyone consumes the same units, so there we add willingness to pay vertically. See Providing Public Goods Efficiently.
Practice
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