From Individual Plans to Market Demand
A buyer’s demand schedule records the quantities that buyer plans to purchase at different prices, with other relevant conditions held fixed. A market demand schedule combines these plans for all buyers in the market. The essential rule is simple: at each price, add the quantities planned by the different buyers at that same price.
This is called horizontal addition because the quantities are combined across buyers at a common price. The price is not added or averaged. Since buyers may make different choices at the same price, the market total can be greater than any one buyer’s quantity. A buyer who chooses not to purchase contributes zero to that price row.
For this addition to be meaningful, the schedules must describe the same good, the same market, the same time period, and the same unit of measurement. For example, quantities planned per week cannot be added to quantities planned per month without first reconciling the time periods. The buyers’ choices must also be evaluated under the same price and the same background conditions.
The earlier material on individual demand and market demand distinguishes one buyer’s plan from the combined plan of all buyers. Here the task is to carry out that combination using schedules. The calculation is done price by price, not buyer by buyer across different prices.
A Reliable Row-by-Row Method
Begin with the set of prices appearing in the schedules. At each price, locate every buyer’s planned quantity, write zero for any buyer who does not purchase, and add across that row. Keep the price and the total’s units visible so that the result remains interpretable.
Use a common list of prices. Do not combine quantities recorded at different prices.
At each price, enter the buyer’s planned quantity. A buyer who does not purchase has quantity zero.
Sum the individual quantities to get the market quantity demanded at that price.
Re-add each row and confirm that the market total uses the same unit and time period as every individual quantity.
A zero is part of the schedule, not a blank to ignore. It says that a buyer plans no purchases at that price. Omitting that buyer from the addition gives the same arithmetic total, but writing the zero explicitly makes the data and the method clear. It also prevents a blank entry from being mistaken for missing information.
Worked Example: Adding Three Buyers at Each Price
Three households report how many reusable water filters they plan to buy in one month at the listed prices. All quantities are filters per month. Construct the market demand schedule.
| Price per filter | Household A | Household B | Household C | Market total |
|---|---|---|---|---|
| $10 | 0 | 4 | 2 | ? |
| $8 | 2 | 5 | 3 | ? |
| $6 | 4 | 6 | 4 | ? |
| $4 | 6 | 7 | 5 | ? |
Method. Add horizontally at each common price. The zero at $10 means Household A plans no purchases at that price.
At $10, the total is \(0+4+2=6\) filters per month. At $8, it is \(2+5+3=10\) filters per month. At $6, it is \(4+6+4=14\) filters per month. At $4, it is \(6+7+5=18\) filters per month.
| Price per filter | Market quantity demanded (filters per month) |
|---|---|
| $10 | 6 |
| $8 | 10 |
| $6 | 14 |
| $4 | 18 |
Check and common mistake avoided. Each total is the sum of exactly one row, and each is measured in filters per month. A tempting but incorrect operation would be to add Household A’s quantities across all prices and call the result the market quantity at $10. Those quantities describe different price situations; the market total at $10 is only \(0+4+2=6\).
Why Quantities Are Added at a Common Price
The rule follows from what the market total represents. Suppose there are \(n\) buyers, and buyer \(i\) plans to purchase \(q_i(P)\) units when the price is \(P\). The number of units all buyers together plan to purchase is the count of units bought by buyer 1, plus the count bought by buyer 2, continuing through buyer \(n\). Therefore:
The common price matters because each quantity in this sum must describe the same market situation. Adding \(q_1(P_1)\) to \(q_2(P_2)\) when \(P_1\ne P_2\) would combine plans made under different prices, so it would not give total quantity demanded at either one.
This result depends on the schedules measuring the same good in compatible units and over the same period. It also treats each buyer’s planned purchases as distinct units that can be counted together. It does not say that buyers have identical preferences or buy the same amount. A zero quantity is simply one valid value of \(q_i(P)\) in the sum.
Worked Example: Including Buyers Who Purchase Zero
A campus kiosk surveys three student groups about planned weekly purchases of fruit cups. The groups’ quantities at several common prices are shown below. Find the market schedule, and identify how the total changes as price falls.
| Price per cup | Group J (cups/week) | Group K (cups/week) | Group L (cups/week) |
|---|---|---|---|
| $15 | 0 | 5 | 0 |
| $12 | 1 | 5 | 2 |
| $9 | 2 | 4 | 3 |
| $6 | 3 | 2 | 4 |
| $3 | 4 | 3 | 4 |
Method. Add the three groups’ quantities separately at each price, retaining zeros for groups with no planned purchases.
At $15, \(0+5+0=5\) cups per week. At $12, \(1+5+2=8\). At $9, \(2+4+3=9\). At $6, \(3+2+4=9\). At $3, \(4+3+4=11\).
| Price per cup | Market quantity demanded (cups/week) |
|---|---|
| $15 | 5 |
| $12 | 8 |
| $9 | 9 |
| $6 | 9 |
| $3 | 11 |
As price falls from $15 to $3 through the listed prices, the market quantity goes from 5 to 8 to 9 to 9 to 11 cups per week. The total can stay the same between two listed prices, as it does between $9 and $6. At $15, two groups have zero purchases, but Group K’s 5 cups still make the market total 5, not zero.
Check and common mistake avoided. Recheck the $6 row: \(3+2+4=9\), not 10. Counting the number of groups that buy, or treating the two zero entries at $15 as missing quantities, would not produce the total number of cups demanded.
Reading the Combined Schedule Carefully
A market schedule is a list of price-and-quantity pairs. It does not require all buyers to participate at every price. Some buyers may purchase zero at a particular price while others purchase positive quantities. The market total is still obtained in exactly the same way: add every listed quantity for that row.
When the individual schedules show quantities that do not rise as price rises, the market totals will have the same property across those listed prices. For any two prices \(P_1\) and \(P_2\), if \(P_1>P_2\) and every buyer’s quantity at \(P_1\) is no greater than that buyer’s quantity at \(P_2\), then:
This is a direct consequence of adding the individual inequalities. It is a useful check on arithmetic when the schedules satisfy that pattern, but it does not replace row-by-row addition. In particular, a repeated market total at two prices can be correct even when some buyers’ quantities change, provided the changes offset in the total.
Worked Example: Combining Four Schedules and Checking the Result
A recreation center estimates the number of day passes four visitor groups plan to buy per weekend at each price. Construct the market schedule and find the change in total planned purchases from a price of $16 to a price of $8.
| Price per pass | Group A | Group B | Group C | Group D |
|---|---|---|---|---|
| $20 | 0 | 2 | 0 | 1 |
| $16 | 0 | 3 | 1 | 1 |
| $12 | 1 | 4 | 1 | 2 |
| $8 | 2 | 5 | 2 | 2 |
| $4 | 3 | 6 | 2 | 3 |
Method. First total each price row. Then compare the two requested market totals; do not compare only one group’s change.
At $20, \(0+2+0+1=3\) passes per weekend. At $16, \(0+3+1+1=5\). At $12, \(1+4+1+2=8\). At $8, \(2+5+2+2=11\). At $4, \(3+6+2+3=14\).
The market quantity rises from 5 passes per weekend at $16 to 11 passes per weekend at $8. The change is \(11-5=6\) additional passes per weekend. At $16, Group A’s zero is included; at $8, all four groups have positive quantities.
Check and common mistake avoided. The $16 total is 5, not 4, because Group C contributes one pass: \(0+3+1+1=5\). The $8 total is 11, so the requested difference is 6. Subtracting the $16 total from just one group’s $8 quantity would compare a group-level value with a market-level value.
Common Mistakes and Their Corrections
- Adding down a column instead of across a row. A column usually gives one buyer’s quantities at several prices. Those quantities describe different situations and are not the market total at one price. Choose a price and add across its row.
- Adding prices or averaging quantities. A market quantity is a total number of units planned at the common price, not an average buyer’s quantity. Use the sum of individual quantities.
- Dropping zero purchases as though they were missing data. Record zero for a buyer who does not purchase. A blank should be investigated; it is not automatically a zero.
- Mixing units or periods. Before adding, verify that every quantity refers to the same good and time period. Quantities per day and quantities per week cannot be combined as written.
- Assuming every buyer must buy something. Participation is not required for a buyer’s schedule to be included. A zero contributes zero to the total and does not change the addition rule.
Check Your Understanding
For each problem, use only quantities listed at the same price, and keep the stated time period and units.
- A market has three buyers. At a price of $7, their planned quantities are 2, 0, and 5 units per week. What is market quantity demanded at $7? (Answer: 7 units per week)
- At a price of $18, two neighborhood groups plan to buy 0 and 6 meal kits per month. At $12, they plan to buy 3 and 8 meal kits per month. Give the market quantity at each price and the difference between the totals. (Answer: 6 meal kits per month at $18; 11 at $12; the difference is 5 meal kits per month)
- Three buyers’ planned quantities of seedlings per season are shown here: at $9, 0, 3, and 2; at $6, 2, 4, and 3; at $3, 4, 5, and 4. Construct the market totals. (Answer: 5 seedlings per season at $9; 9 at $6; 13 at $3)
- At a common price, four buyers plan to purchase 1, 0, 4, and 2 transit passes per month. A student adds only the positive entries and reports 7. Is that total correct? Explain what the zero means. (Answer: Yes; the market total is 7 passes per month, and the zero means one buyer plans no purchases)
- Two buyers report planned quantities of 4 and 1 packages per week at $10, and 6 and 3 packages per week at $5. A calculation adds 4 and 3 to report market quantity at $10. Identify the error and give the correct market totals at both prices. (Answer: The calculation mixed prices; the correct totals are 5 packages per week at $10 and 9 packages per week at $5)