From Producer Information to Supply Schedules
A supply problem often gives information about what individual sellers will offer at several possible prices. The task is to put those offers into a consistent schedule, combine the sellers when asked for market supply, and decide whether a change is a movement along a curve or a shift of the curve. The key discipline is to compare quantities at the same price and to keep the other conditions that affect supply visible.
A schedule can be presented as a table, a graph, or an equation. A discrete schedule lists quantities at selected prices; it does not necessarily specify what sellers would supply at every price between them. In all formats, identify the product, market, time period, units, and conditions being held fixed. A quantity per week cannot be added directly to a quantity per month, for example, without converting the time units.
For sellers \(1,2,\ldots,n\), let \(q_j(P)\) be seller \(j\)'s quantity supplied at price \(P\), with the relevant nonprice conditions held fixed. Market quantity at that price is the sum of the individual quantities:
This addition is called horizontal summation: quantities are added across sellers at a common price. The calculation assumes the sellers offer the same or suitably comparable product in the same market and time period, and that each seller's quantity is counted once. It does not add prices or combine quantities reported at different prices.
A Reliable Schedule-Solving Method
Use the following sequence when a problem asks for a market schedule or a classification of a supply change.
Record the product, time period, prices, quantity units, and which nonprice determinants are unchanged.
Keep individual schedules separate until the corresponding price row is identified.
Check that every market total equals the sum of that row's individual quantities.
A change in the good's own price, with other conditions fixed, changes quantity supplied along the same curve. A change in a nonprice determinant changes the supply schedule itself.
Worked Supply Problems
Worked Example: Aggregating Three Weekly Schedules
Three hypothetical bakeries sell the same type of packaged bread in one local market. Their weekly quantities, in hundreds of packages, are shown below. Treat each schedule as unchanged except for the listed price. Construct market supply at each price, then classify the change when price rises from $4 to $6 per package.
| Price per package | Bakery A | Bakery B | Bakery C |
|---|---|---|---|
| $4 | 0 | 2 | 1 |
| $6 | 3 | 2 | 4 |
| $8 | 5 | 4 | 4 |
Method. Add the bakeries' quantities horizontally, row by row. At $4, market supply is \(0+2+1=3\) hundred packages per week. At $6, it is \(3+2+4=9\) hundred per week. At $8, it is \(5+4+4=13\) hundred per week.
| Price per package | Market quantity (hundreds per week) |
|---|---|
| $4 | 3 |
| $6 | 9 |
| $8 | 13 |
Classification. The quantity rises from 3 to 9 hundred per week as the bread's own price rises from $4 to $6, and no other condition has changed. That is a movement along the existing market supply schedule, not a shift. Check: at $6, the market total of 9 is exactly \(3+2+4\), the three bakeries' quantities at $6.
Common mistake avoided. Calling the rise from 3 to 9 a rightward shift confuses a change in price with a change in a nonprice determinant. Both quantities come from the same fixed schedule; the price change selects a different row.
Worked Example: An Input-Cost Increase
Two hypothetical workshops supply replacement brackets, measured in hundreds per month. A rise in the price of a metal input reduces Workshop A's quantity at each listed bracket price; Workshop B is unaffected. Construct the old and new market schedules and identify the direction of the change. Assume product quality, the market, and the time period stay fixed.
| Price per bracket | A before cost increase | A after cost increase | B, both schedules |
|---|---|---|---|
| $5 | 1 | 0 | 0 |
| $10 | 4 | 3 | 3 |
| $15 | 7 | 6 | 6 |
Before the increase: at $5, total supply is \(1+0=1\) hundred per month; at $10, it is \(4+3=7\); at $15, it is \(7+6=13\).
After the increase: at $5, total supply is \(0+0=0\) hundred per month; at $10, it is \(3+3=6\); at $15, it is \(6+6=12\).
| Price per bracket | Market supply before | Market supply after | Change |
|---|---|---|---|
| $5 | 1 | 0 | -1 |
| $10 | 7 | 6 | -1 |
| $15 | 13 | 12 | -1 |
At every listed price, the new market quantity is one hundred brackets per month lower. The input-cost increase is a nonprice change in production conditions, so the market supply schedule shifts left. This example's schedule makes the reduction uniform at the listed prices; a shift need not be the same size at every price in other problems.
Check: at $10 after the increase, \(3+3=6\), which matches the new market total. Do not apply the input-cost change to Workshop B: the problem states that it is unaffected.
Worked Example: Combining a Technology Change and Seller Entry
A hypothetical market for reusable storage crates has two existing suppliers, X and Y. A technology improvement raises X's offered quantities, and a new supplier, Z, enters. Quantities are in tens of crates per day. The prices and conditions other than technology and entry are held fixed. Compare the old and new market schedules, then distinguish the schedule shift from a price change along the new schedule.
| Price per crate | X old | X new | Y, both | Z before entry | Z after entry |
|---|---|---|---|---|---|
| $10 | 0 | 1 | 1 | — | 0 |
| $20 | 2 | 4 | 3 | — | 2 |
| $30 | 4 | 7 | 5 | — | 3 |
The dash means Z was not in the market before entry. Before either change, totals are \(0+1=1\) ten crates per day at $10, \(2+3=5\) at $20, and \(4+5=9\) at $30. After both changes, the totals are \(1+1+0=2\) at $10, \(4+3+2=9\) at $20, and \(7+5+3=15\) at $30.
| Price per crate | Old market quantity | New market quantity | Increase |
|---|---|---|---|
| $10 | 1 | 2 | 1 |
| $20 | 5 | 9 | 4 |
| $30 | 9 | 15 | 6 |
At each listed price, the new market quantity exceeds the old one, so the market supply schedule shifts right. This conclusion follows from the technology improvement and entry, not from a change in crate price. For comparison, on the new schedule, a price increase from $20 to $30 corresponds to a quantity increase from 9 to 15 tens of crates per day; that comparison is a movement along the new schedule.
Check: the new total at $30 is \(7+5+3=15\). The increase from the old total is \(15-9=6\), equal to the technology-related increase for X, \(7-4=3\), plus Z's new offer of 3.
Why Horizontal Summation Works
At a given price, each seller's schedule answers the same question: how much will this seller offer under the stated conditions? If seller 1 offers \(q_1(P)\), seller 2 offers \(q_2(P)\), and so on, the amount available from all of them is the total of those offers. Therefore:
The price must be common to the terms in this sum because the market schedule asks for aggregate quantity at one particular price. Adding quantities from different price rows would answer no consistent market-supply question. The result is a market schedule; it does not by itself establish an equilibrium price or quantity. Determining market-clearing equilibrium requires comparing supply with demand.
Classifying Changes Without Confusing Them
A useful test is to ask what changed between the two observations. If only the good's own price changed and the schedule's other conditions remained fixed, quantity supplied changed along the same curve. If a condition affecting producers changed—such as input availability or cost, production technology, expectations, capacity, or the number of sellers—then the supply schedule shifted. These are different comparisons: a movement compares points on one schedule, while a shift compares schedules under different conditions.
A frequent schedule error is to add vertically or to compare mismatched rows. For example, in Worked Example 1, an incorrect calculation might add the market totals at $4 and $6, \(3+9=12\), and report 12 as supply at one of those prices. That number is not market supply at either price: 3 belongs to $4 and 9 belongs to $6. The correction is to select one price first and sum only the sellers' quantities in that row, such as \(3+2+4=9\) hundred packages per week at $6.
In exam-style problems, show the row-by-row arithmetic rather than only giving the final market schedule. This makes unit errors and omitted sellers easier to detect. For a claimed shift, compare old and new quantities at matching prices. A direction of change can be identified from those comparisons; the schedules need not be parallel, and the shift need not be a constant quantity at each price.
Check Your Understanding
For each problem, keep the price, time period, and quantity units aligned before calculating.
- Two hypothetical food carts supply lunches per day. At prices of $8 and $12, Cart A supplies 3 and 5 lunches, and Cart B supplies 2 and 4. Construct market supply at both prices and classify the change from $8 to $12 if all other conditions are fixed. (Answer: 5 lunches per day at $8 and 9 at $12; a movement along the same market supply schedule.)
- Three farms supply crates per week at a common price of $6: Farm A offers 12 crates, Farm B offers 7, and Farm C offers 5. A new packing method raises A's offer by 4 crates at every price, while B and C are unchanged. Find the old and new market quantities at $6 and classify the change. (Answer: 24 crates per week before, 28 after; a rightward shift.)
- At a price of $15, two hypothetical repair shops supply 6 and 9 service appointments per week. At $20, they supply 8 and 10. No other determinant changes. Find market supply at both prices and explain why this is not evidence of a shift. (Answer: 15 appointments per week at $15 and 18 at $20; the price change produces a movement along the same schedule.)
- A market has three sellers. At $10, their quantities are 0, 4, and 2 units per day; at $20, they are 3, 5, and 4. A nonprice change raises the first seller's quantity by 2 units at each listed price, with the other sellers unaffected. Give old and new market quantities at each price and classify the change. (Answer: old totals are 6 at $10 and 12 at $20; new totals are 8 and 14 units per day; supply shifts right.)
- At $25, a market schedule shows 11 units per week. A later observation shows 14 units per week at $30, and a technology improvement occurred between observations. Can the entire quantity increase be assigned to the technology change? State what can and cannot be concluded from the information. (Answer: No. The observations differ in both price and technology, so they combine a movement along supply and a possible shift; the technology effect cannot be isolated without quantities at a common price or further information.)