Why Market Supply Can Have Steps
Producers do not all need the same price to make output available. One producer may be willing to offer a small quantity at a relatively low price, while another may require a higher price before offering any output. A market made up of producers with different minimum acceptable prices can therefore have a supply curve that rises in distinct steps rather than smoothly. This is a useful way to represent discrete capacities and is aligned with the SOA VEE Economics (Validation by Educational Experience) syllabus.
The key is to distinguish a producer’s price threshold from the quantity the producer can supply at that threshold. As price reaches each threshold, the corresponding quantity becomes available. Market supply adds the quantities offered by all producers at that price; it does not average their thresholds.
This model treats an offer as a discrete block: it is unavailable below its threshold and available at its stated quantity at or above that threshold. A producer with more than one block can have several thresholds, so its own supply schedule may have steps. The market schedule combines all those blocks. This is a simplifying representation; it does not describe a producer that smoothly adjusts output at every small price change.
How Thresholds Create Jumps and Plateaus
List the distinct offer thresholds from lowest to highest. At each threshold, add the quantities of every block with that threshold to the total quantity already available. Between two successive thresholds, no additional block enters, so the market quantity stays constant. At a threshold, the quantity jumps. If several blocks share a threshold, their quantities create one combined jump.
Here, \(\mathbf{1}(p\ge r_{ij})\) equals 1 when the price has reached block \(j\)'s threshold and 0 otherwise. The expression formalizes the step schedule: each block contributes either its full stated quantity or zero. It assumes that blocks are available exactly at their listed thresholds, that quantities are measured on the same basis, and that other conditions affecting supply are held fixed.
The reason for the market total is straightforward. At a given price, each producer supplies the sum of its eligible blocks. Adding those producer quantities counts every available block once, which is exactly the market quantity. Grouping blocks with equal thresholds then shows where jumps occur and how large they are.
For each producer, note its quantity and the minimum price at which that quantity is offered.
Arrange distinct prices from low to high; combine quantities offered at the same price.
At each threshold, add its newly available quantity to all quantities already available.
Include a block when the price equals its threshold as well as when it exceeds it.
Worked Schedules
Worked Example: Three Producers with Separate Thresholds
Three hypothetical growers offer produce in the same market. Grower A offers 3 crates at a minimum price of $8 per crate. Grower B offers 2 crates at $10, and Grower C offers 4 crates at $12. Find market quantity supplied at prices of $9, $10, and $12, then write the step schedule.
Method. List the thresholds in ascending order and add the quantity that becomes available at each one. The common mistake to avoid is adding all growers' capacities at every price, even when some growers' thresholds have not been reached.
At $8, only A's threshold has been reached, so \(Q_s=3\) crates. At $9, no new block enters, so \(Q_s=3\) crates. At $10, B's 2 crates become available: \(3+2=5\) crates. At $12, C's 4 crates become available: \(5+4=9\) crates.
| Price range or threshold | New quantity available | Total market quantity supplied |
|---|---|---|
| Below $8 | 0 crates | 0 crates |
| $8 to below $10 | 3 crates at $8 | 3 crates |
| $10 to below $12 | 2 crates at $10 | 5 crates |
| $12 and above | 4 crates at $12 | 9 crates |
Thus the requested quantities are 3 crates at $9, 5 crates at $10, and 9 crates at $12. The boundary checks matter: at exactly $10, B is included; at exactly $12, C is included. The final total, \(3+2+4=9\), matches the total capacity offered by all three growers.
Worked Example: Several Blocks and a Shared Threshold
Three hypothetical workshops offer components. Workshop P offers 2 batches at $5 per batch and a further 3 batches at $9. Workshop Q offers 4 batches at $7. Workshop R offers 1 batch at $9 and 2 batches at $11. Construct the market supply schedule and find quantity supplied at $8 and $9.
Method. Treat each offer as a separate block, even when one workshop has multiple blocks. Then combine all blocks that share a price threshold. The mistake to avoid is counting only the first block of a multi-block producer or overlooking that two producers have offers at the same threshold.
At $5, P's first block adds 2 batches, giving a total of 2. At $7, Q adds 4, so the cumulative total is \(2+4=6\). At $9, P adds 3 and R adds 1; the combined jump is \(3+1=4\), giving \(6+4=10\). At $11, R adds its final 2, giving \(10+2=12\).
| Threshold reached | Blocks newly available | Cumulative market quantity |
|---|---|---|
| $5 | P: 2 batches | 2 batches |
| $7 | Q: 4 batches | 6 batches |
| $9 | P: 3 batches; R: 1 batch | 10 batches |
| $11 | R: 2 batches | 12 batches |
At $8, the $5 and $7 thresholds have been reached but the $9 threshold has not, so supply is 6 batches. At exactly $9, the two blocks at that threshold are included, so supply is 10 batches. As a check, the total capacity is P's \(2+3=5\), plus Q's 4, plus R's \(1+2=3\), for \(5+4+3=12\) batches. This equals the schedule's final total.
Worked Example: Reading a Market Jump in Thousands
Three hypothetical recyclers offer recovered material, with quantities measured in thousands of kilograms. Recycler J offers 5 thousand kilograms at $14 per kilogram. Recycler K offers 3 thousand kilograms at $11 and a further 2 thousand kilograms at $16. Recycler M offers 4 thousand kilograms at $14. Find the market supply just below $14, at exactly $14, and at $16. State the size of the jump at $14.
Method. Sort all blocks by threshold, keeping the unit “thousand kilograms” throughout. A frequent mistake is to treat “5 thousand” as 5 kilograms, or to exclude offers at a price exactly equal to their threshold.
At $11, K's first block contributes 3 thousand kilograms. There is no additional block between $11 and $14, so just below $14 supply is 3 thousand kilograms. At exactly $14, J adds 5 and M adds 4, so the jump is \(5+4=9\) thousand kilograms. Supply at $14 is \(3+9=12\) thousand kilograms. At $16, K's final block adds 2, so supply is \(12+2=14\) thousand kilograms.
The jump at $14 is 9 thousand kilograms, and the requested quantities are 3 thousand kilograms just below $14, 12 thousand kilograms at $14, and 14 thousand kilograms at $16. The capacity check is J's 5, plus K's \(3+2=5\), plus M's 4, totaling 14 thousand kilograms. The schedule reaches that full total at the highest listed threshold.
What Heterogeneity Tells You
A step-shaped market supply curve does not require all producers to have the same costs or capacities. Rather, differences in minimum acceptable prices determine the locations of the jumps, and the quantities offered at those prices determine their sizes. If many small offers have different thresholds, the jumps may be small and numerous. If several large offers share a threshold, the curve has a larger jump at that price.
In this model, a plateau means that no additional offer block becomes available over that price interval. It does not mean that producers have no capacity remaining; a producer may have additional capacity with a higher threshold. Likewise, a jump represents newly offered quantity at the listed price, not a continuous increase in each producer's output.
The thresholds can be interpreted as minimum acceptable prices that reflect production costs, opportunity costs, or other conditions specific to the producer and block. The schedule alone does not establish why a threshold has its value. It records the offers under the stated conditions; changing costs, capacity, or other determinants would require a different schedule.
Common Mistakes
- Excluding a block at its threshold. Under the stated convention, an offer at threshold \(r\) is available when \(p=r\), because the condition is \(p\ge r\).
- Adding producer capacities before their thresholds. A producer's block is not part of market quantity supplied below its minimum acceptable price.
- Forgetting tied offers. If two or more blocks have the same threshold, their quantities belong in the same market jump.
- Confusing a block's quantity with cumulative quantity. The jump is the newly available amount; the market quantity at that price also includes all earlier blocks.
- Mixing units. Keep units such as crates, batches, or thousands of kilograms consistent when adding quantities.
Check Your Understanding
For each problem, apply the threshold rule and check cumulative quantities against total offered capacity where possible.
- Producer A offers 2 units at $4. Producer B offers 5 units at $6, and Producer C offers 3 units at $6. Find market supply at $5 and at exactly $6. (Answer: 2 units at $5; 10 units at $6.)
- A mill offers 4 tons at $7 and another 2 tons at $10. A second mill offers 3 tons at $8. Find market supply at $7, $8, and $10, and give the jump at $10. (Answer: 4 tons, 7 tons, and 9 tons, respectively; the jump at $10 is 2 tons.)
- Three producers offer blocks as follows: A offers 1 batch at $3 and 4 batches at $9; B offers 2 batches at $6; C offers 3 batches at $9. Find market supply immediately below $9 and at exactly $9. (Answer: 3 batches immediately below $9; 10 batches at $9.)
- Suppliers U and V each offer 2 thousand units at $12. Supplier W offers 5 thousand units at $15. Find the market jump at $12, supply at $14, and supply at $15. (Answer: the jump at $12 is 4 thousand units; supply is 4 thousand units at $14 and 9 thousand units at $15.)
- A market has blocks of 3 units at $5, 2 units at $5, 4 units at $8, and 1 unit at $11. A student reports supply of 4 units at $8 by adding only the block with an $8 threshold. Correct the calculation and state the jump at $8. (Answer: supply at $8 is 9 units, because \(3+2+4=9\); the jump at $8 is 4 units.)