From Schedules to a Market-Clearing Pair
A supply schedule and a demand schedule report quantities associated with prices. To find equilibrium from these tables, compare the two quantities at the same price. A price that appears in only one schedule cannot be checked on its own: both buyers’ planned purchases and sellers’ planned sales must be available for comparison.
The method is direct, but careful reading matters. Prices can be listed in different orders, schedules can use different price lists, and quantities can be reported in units, hundreds, or thousands. The equilibrium price is the price where the scheduled quantities match; the equilibrium quantity is their shared quantity, reported in the units used by the schedule.
This is the schedule-based application of market-clearing equilibrium. It does not require a graph or a supply-and-demand equation: the relevant evidence is in the table entries. Unless a problem supplies a rule for estimating values between listed prices, use the listed values rather than inventing quantities for unlisted prices.
Why the Matching-Quantity Test Works
The test follows from what the two schedules measure. At price \(p\), buyers plan to acquire \(Q_D(p)\) units, while sellers plan to provide \(Q_S(p)\) units. For the plans to match in the market-clearing sense, the planned amount buyers take must be the planned amount sellers provide. Thus the condition is equality, not merely that both quantities are positive or that the numbers are close.
When the equality holds, either schedule gives the equilibrium quantity. When it does not, that price is not a listed market-clearing price in the schedule. This reasoning identifies the equilibrium represented by the data; it does not by itself explain how prices change or what happens away from equilibrium.
Worked Example: Finding an Exact Match in a Shared Price List
A market’s weekly schedules are shown below. Quantities are individual units, and every price is in dollars per unit. Find the listed equilibrium.
| Price ($) | Quantity demanded | Quantity supplied |
|---|---|---|
| 2 | 100 | 20 |
| 4 | 80 | 40 |
| 6 | 60 | 60 |
| 8 | 40 | 80 |
Method. Compare the two quantity entries in each row, because each row holds the price fixed.
At $2, demand is 100 and supply is 20, so \(100\ne20\). At $4, demand is 80 and supply is 40, so \(80\ne40\). At $6, demand and supply are both 60, so \(60=60\). At $8, demand is 40 and supply is 80, so \(40\ne80\).
Answer and check. The listed equilibrium is price $6 per unit and quantity 60 units per week. Substitution into the schedule gives \(Q_D(6)=60\) and \(Q_S(6)=60\), confirming the match. The common mistake to avoid is selecting a price merely because its quantities are closest; only equality satisfies the stated condition.
When the Schedules Use Different Price Lists
A demand table and a supply table need not show identical rows. First identify prices that occur in both schedules, then compare quantities at those common prices. A row for a price appearing in only one table does not supply the missing quantity from the other table.
Note whether quantities are units, hundreds, or thousands, and retain that scale throughout.
Keep only prices for which both demand and supply entries are given.
Test whether the two quantities are exactly equal.
State the matching price and the shared quantity with its units.
Worked Example: Matching Schedules With Different Price Rows
A hypothetical market reports quantities in units per day. The demand schedule lists prices $4, $8, $12, and $16. The supply schedule lists prices $2, $4, $8, $12, and $16. Demand is 90, 75, 60, and 45 units at its listed prices, respectively. Supply is 15, 30, 45, 60, and 75 units at its listed prices, respectively. Find the listed equilibrium.
Method. Align the schedules by price. The supply entry at $2 has no corresponding demand entry, so it cannot be used in the comparison. The common prices are $4, $8, $12, and $16.
| Common price ($) | Quantity demanded (units/day) | Quantity supplied (units/day) | Match? |
|---|---|---|---|
| 4 | 90 | 30 | No |
| 8 | 75 | 45 | No |
| 12 | 60 | 60 | Yes |
| 16 | 45 | 75 | No |
At $4, \(90\ne30\). At $8, \(75\ne45\). At $12, \(60=60\). At $16, \(45\ne75\). Therefore the listed equilibrium is $12 per unit and 60 units per day. The final check is \(Q_D(12)=60=Q_S(12)\).
Common mistake avoided: Comparing demand at $12 with supply at $16 would compare different prices and could not establish equilibrium. The price must match as well as the quantities.
Exact Matches, Unlisted Prices, and Multiple Matches
A table gives information only at the prices it lists. If no common listed price has equal quantities, the correct conclusion is that no listed price clears the market in the given schedules. It does not follow that there can be no equilibrium at any price. But finding an unlisted equilibrium requires additional information, such as a specified functional form or a permitted interpolation method. Do not silently assume one.
Likewise, do not assume that a discrete table must have exactly one matching row. If quantities remain unchanged across more than one listed price, the equality condition may hold at multiple prices. Report every matching price and its common quantity, rather than choosing one arbitrarily. The data may indicate multiple listed market-clearing pairs even if a different model or additional information would be needed to characterize prices between those rows.
Worked Example: Checking Whether a Listed Match Exists
A local market schedule gives the following quantities in hundreds of units per week. Find the listed equilibrium, if one is shown.
| Price ($) | Quantity demanded (hundreds/week) | Quantity supplied (hundreds/week) |
|---|---|---|
| 3 | 24 | 12 |
| 6 | 21 | 15 |
| 9 | 18 | 17 |
| 12 | 15 | 20 |
Method. Compare demand and supply row by row, without rounding or filling gaps between prices.
At $3, \(24\ne12\). At $6, \(21\ne15\). At $9, \(18\ne17\). At $12, \(15\ne20\). No listed price has equal quantities, so the table shows no listed equilibrium.
The fact that the entries at $9 are numerically close does not make $9 an equilibrium: 18 hundreds is 1 hundred more than 17 hundreds, and equality is required. Nor can a price between $9 and $12 be declared an equilibrium from these rows alone. The correct conclusion is limited to the information provided: there is no matching listed price.
Check. Each of the four candidate prices was tested, and none produced equality. The common mistake avoided is treating the closest pair as a match or reporting an unsupported value between rows.
Worked Example: More Than One Listed Equilibrium
A schedule for a hypothetical product gives weekly quantities in units:
| Price ($) | Quantity demanded | Quantity supplied |
|---|---|---|
| 4 | 70 | 50 |
| 6 | 60 | 60 |
| 8 | 60 | 60 |
At $4, \(70\ne50\), so that row does not clear the market. At $6, \(60=60\), giving a listed equilibrium pair of price $6 and quantity 60 units per week. At $8, \(60=60\) as well, giving another listed equilibrium pair: price $8 and quantity 60 units per week.
Answer and check. Both listed prices, $6 and $8, satisfy the condition, and both have a common quantity of 60 units per week. Check each separately: \(Q_D(6)=Q_S(6)=60\), and \(Q_D(8)=Q_S(8)=60\). The repeated quantity does not justify discarding one matching price.
Common Errors and a Reliable Final Check
A correct answer includes both the price and the quantity, with units. State the price from the matching row and the shared quantity from that same row. Before finalizing, check that no price was mismatched, no quantity scale was lost, and every candidate price was handled consistently.
- Comparing different prices: Equality of quantities from separate price rows is not a market-clearing match. Compare only quantities associated with the same price.
- Accepting “close enough”: A near match is not equality. Unless the question explicitly asks for an approximation, use the exact schedule entries.
- Dropping a scale: If quantities are in hundreds, a listed quantity of 60 means 6,000 units, not 60 units. Preserve the stated unit or convert it explicitly.
- Assuming the schedules guarantee one answer: Check every common listed price. There may be no listed match or more than one.
- Inventing values between rows: Do not interpolate or extrapolate unless the problem provides a rule that supports it.
Check Your Understanding
For each problem, test the stated candidate prices only unless the question explicitly gives another rule.
- A snack market has demand and supply, respectively, of 140 and 60 packs at $1; 110 and 90 packs at $2; and 80 and 80 packs at $3. State the listed equilibrium price and quantity. (Answer: $3 per pack; 80 packs.)
- Demand is 36, 30, and 24 crates at prices $5, $10, and $15. Supply is 12, 24, 30, and 36 crates at prices $0, $5, $10, and $15. Find the equilibrium from the common listed prices. (Answer: $10 per crate; 30 crates.)
- A schedule reports quantities in hundreds of units. At $7, demand is 42 and supply is 39; at $9, demand is 36 and supply is 36; at $11, demand is 30 and supply is 33. Give the equilibrium in actual units. (Answer: $9 per unit; 3,600 units.)
- At candidate prices $2, $4, and $6, quantities demanded are 90, 75, and 60 units, while quantities supplied are 50, 70, and 65 units. Is there a listed equilibrium? (Answer: No listed price has equal quantities.)
- At $12 and $14, a schedule shows demand of 25 units and supply of 25 units at each price. At $10, demand is 30 and supply is 20. Report all listed equilibrium pairs. (Answer: $12 and 25 units; $14 and 25 units.)