Why Build a Demand Schedule?
A buyer may be asked how many units of a good they plan to purchase at several possible prices. Recording each answer in a consistent table makes the plans easier to compare and use. The key task is not to explain why the buyer chose those quantities; it is to represent the stated plans accurately, with each quantity matched to its price and to the conditions under which the buyer made the plan.
A schedule needs more detail than a list of prices and numbers. The good must be identified, the unit of sale must remain the same, and the time period must be stated. The buyer and other relevant circumstances must also be held fixed. For example, “four” could mean four packages per week or four packages per month. Without the period, the quantity is incomplete.
The phrase “plans and is able to purchase” matters: a stated wish to own a good is not, by itself, a purchase plan. The schedule records a buyer’s planned quantity at each price, not necessarily the quantity ultimately purchased. Sales, purchases, and plans can differ; for instance, a product may be unavailable, or a buyer’s circumstances may change after stating a plan.
Make the Conditions Explicit
Before putting numbers into a schedule, pin down what counts as the good and what one unit means. “Coffee” could mean a particular size and type of package, not any coffee product. If one row concerns a 250-gram package and another concerns a 500-gram package, the quantities do not describe the same unit of the same good. In that case, the rows should not be combined as if they were directly comparable.
Also specify the time period over which the buyer plans to purchase. A schedule might describe units per day, per week, or per month. When the original answers use different periods, convert them only if the information supports a valid conversion. If a conversion requires an assumption about how purchases are distributed over time, state that assumption.
Finally, the buyer’s other relevant circumstances must be fixed for the comparison. These can include the buyer’s resources, preferences, and expectations. In this context, “held fixed” means that the schedule compares plans made under one specified set of circumstances; it does not claim those circumstances never change. This condition helps keep each row interpretable as part of the same buyer’s set of plans.
This notation simply lists the price–quantity pairs. It does not say that the buyer’s plans must follow any particular numerical pattern. The schedule reports the stated pair for each price; its first job is accurate recording.
A Reliable Construction Method
Use the following sequence when a problem gives purchase plans in sentences, notes, or a mixed-format table. It keeps the recorded quantity attached to the correct price and exposes missing or inconsistent information before the schedule is presented.
Write down exactly what is being purchased and what one unit means, such as one standard 250-gram package.
State whose plans are recorded and whether quantities refer to a day, week, month, or another period.
Keep every stated price with the quantity the buyer associates with that price. Do not average or add quantities merely because they appear in the same set of notes.
Set aside entries that concern a different good, unit, buyer, period, or set of relevant circumstances unless a valid adjustment is specified.
Use clear headings, consistent units, and an orderly price listing. Recheck every row against the original plans.
Worked Examples
Worked Example: Tabulating One Buyer’s Weekly Plans
A household buyer states how many standard boxes of a particular breakfast cereal they plan to purchase each week at different prices. The box size, buyer, weekly period, and all other relevant circumstances are the same in each statement. The plans are: at $3 per box, 14 boxes; at $5, 11 boxes; at $7, 7 boxes; and at $9, 4 boxes. Construct the schedule and check it against the statements.
Method. Record each price with the quantity stated for that price. The unit is one standard box, and the quantity unit is boxes per week. No conversion or adjustment is needed.
| Price per standard box | Planned quantity (boxes per week) |
|---|---|
| $3 | 14 |
| $5 | 11 |
| $7 | 7 |
| $9 | 4 |
Check. The four rows reproduce all four stated plans: $3 is paired with 14, $5 with 11, $7 with 7, and $9 with 4. The price column is dollars per box, while the quantity column is boxes per week. The schedule therefore identifies both the good’s unit and the purchase period.
A common mistake would be to record 14, 11, 7, and 4 without a quantity heading. Those numbers would not tell a reader whether they refer to boxes per week, boxes per month, or something else. The correction is to label the quantity column with its unit and period.
Worked Example: Converting Daily Plans to a Weekly Schedule
A buyer plans purchases of the same single-serve snack package over a regular seven-day week. The stated plans are 3 packages per day at $1.50 per package, 15 packages per week at $2.00, 2 packages per day at $2.50, and 7 packages per week at $3.00. Construct a weekly schedule. Assume that each daily plan applies on all seven days.
Method. Use packages per week for every row. Multiply each daily quantity by 7; leave each weekly quantity unchanged.
At $1.50, the stated daily plan is 3 packages. Thus \(3\times7=21\) packages per week.
At $2.00, the plan is already 15 packages per week, so it remains 15.
At $2.50, the stated daily plan is 2 packages. Thus \(2\times7=14\) packages per week.
At $3.00, the plan is already 7 packages per week, so it remains 7.
| Price per package | Stated plan | Planned quantity (packages per week) |
|---|---|---|
| $1.50 | 3 packages per day | 21 |
| $2.00 | 15 packages per week | 15 |
| $2.50 | 2 packages per day | 14 |
| $3.00 | 7 packages per week | 7 |
Check. The two daily plans were multiplied by seven, and the two weekly plans were not changed. The final quantity column uses one unit throughout: packages per week.
Common mistake and correction. Copying the raw quantities into a weekly table would give 3, 15, 2, and 7 packages per week. That calculation wrongly treats “per day” and “per week” as identical units. Convert the daily entries first: \(3\times7=21\) and \(2\times7=14\). The conversion depends on the stated assumption that each daily plan applies on all seven days.
Worked Example: Keeping Different Products Out of One Schedule
A buyer gives several plans for coffee over one week. For a specified roast sold in a standard 250-gram bag, the buyer plans 8 bags at $4 per bag, 6 bags at $5, 4 bags at $6, and 3 bags at $7. The buyer also says that at $5 they would plan to buy 4 bags of a 500-gram family size. Construct a schedule for the specified 250-gram bag and explain how to treat the additional statement.
Method. Include only plans that match the named product, package size, buyer, and weekly period. The first four statements satisfy those conditions, so they form the schedule:
| Price per 250-gram bag | Planned quantity (250-gram bags per week) |
|---|---|
| $4 | 8 |
| $5 | 6 |
| $6 | 4 |
| $7 | 3 |
The additional plan is 4 bags per week at $5, but those are 500-gram bags. It is not an entry in the schedule for the specified 250-gram bag. The product unit differs, and the price is stated per bag rather than as a price for an equivalent quantity of coffee. Even though both entries use dollars and bags, adding the quantities would combine different goods.
Check. The schedule contains four valid plans for the same package, each expressed in bags per week. It does not include the family-size statement. A common mistake is to enter 10 bags at $5 by adding 6 and 4. That would report a quantity for two package sizes together, not the buyer’s plan for the standard 250-gram bag.
Why Fixed Conditions Matter
A schedule is a set of comparisons that makes sense only when each row describes the same buyer choosing among prices for the same good under the same stated conditions. This can be expressed by treating planned quantity as a function of price and other conditions:
Here \(p\) is the good’s price, \(q^d\) is the buyer’s planned quantity, and \(z\) represents the other relevant conditions. In a schedule, \(z\) is held fixed while the recorded price varies.
The reason is straightforward. Suppose one entry is made with conditions \(z_1\), and another with different conditions \(z_2\). Their difference can be written as:
Because both price and conditions may differ, this comparison alone cannot identify which change is associated with the different planned quantity. If instead the conditions are fixed, the comparison is:
Now the entries refer to one buyer, one good, and one set of conditions. This is why a schedule must describe its assumptions, rather than merely list numbers. It also explains why plans from separate circumstances should not be pooled automatically.
Common Construction Errors
- Leaving out the period. “Quantity 8” is incomplete. Write “8 units per week” or state the relevant period explicitly.
- Mixing units of sale. A quantity of large packages cannot be silently combined with a quantity of small packages. Identify the unit before tabulating.
- Pairing a quantity with the wrong price. Read each statement carefully and preserve its price–quantity match when rearranging the information into a table.
- Combining different buyers’ plans. A schedule for one buyer is not made by adding the plans of several buyers. The resulting object would describe something different.
- Treating planned purchases as observed sales. A schedule records what the buyer plans to purchase under stated conditions. It does not guarantee that those purchases occur.
- Converting a period without an assumption. Multiplication by seven is valid for a daily plan only when the plan is meant to apply on each of seven days. State the conversion basis instead of silently changing the unit.
Careful construction is useful well beyond an exercise in table-making. A schedule lets a reader see exactly what the buyer planned at each listed price and whether the observations are comparable. For an actuarial professional, the discipline is familiar: define the unit, establish the observation period, and distinguish a stated plan from an observed outcome. These habits are aligned with the SOA VEE Economics (Validation by Educational Experience) syllabus.
Check Your Understanding
For each problem, identify the valid price–quantity pairs and keep the good, buyer, unit, and time period clear.
- A buyer plans to purchase 5 identical water filters per month at $8 each, 3 per month at $10 each, and 1 per month at $12 each. State the schedule’s goods unit and period, then list the pairs. (Answer: identical water filters; filters per month; \(($8,5),($10,3),($12,1)\).)
- A buyer plans 2 identical cartons of juice per day at $2 per carton and 9 cartons per week at $3. Convert both plans to cartons per week and state the assumption needed for the conversion. (Answer: 14 cartons per week at $2, and 9 cartons per week at $3; assume the daily plan applies on all seven days.)
- For the same buyer and week, a store records 7 standard notebooks at $4 each and 3 premium notebooks at $6 each. Can these entries form one schedule for standard notebooks? Explain. (Answer: No. The premium notebooks are a different product; only the standard-notebook plan is a valid entry for that schedule: \(($4,7)\).)
- A buyer’s plans for the same refill cartridge and the same month are 6 cartridges at $5, 4 at $7, and 2 at $9. A second buyer plans 3 cartridges at $7 under the same product and period. Construct the first buyer’s individual schedule and explain whether the second buyer’s plan belongs in it. (Answer: \(($5,6),($7,4),($9,2)\), with quantities in cartridges per month; the second buyer’s plan does not belong in the first buyer’s individual schedule.)
- A buyer states a plan of 4 packages per day at $1.25 per package and 20 packages per week at $1.50. If the daily plan applies on all seven days, give both weekly quantities and the difference between them. (Answer: 28 packages per week at $1.25 and 20 packages per week at $1.50; the first weekly quantity exceeds the second by 8 packages.)