Why a Higher Price Can Make More Production Worthwhile
A producer deciding whether to make one more unit does not compare its price with zero. Producing it uses labor, materials, time, equipment, or other resources that could have been used in another way. The value of the best alternative forgone is its opportunity cost. When a producer expands output, it often has to use resources with increasingly valuable alternatives, so the cost of the next unit tends to rise.
The market price is the revenue received for each unit sold. When that price rises, additional units that were not worthwhile at the lower price may become worthwhile. This explains the usual positive relationship between price and quantity supplied. The relationship is a result of producers’ incentives under stated conditions, not a rule that every producer must always produce more whenever price rises.
The Unit-by-Unit Production Decision
First consider a price-taking producer: a producer that can sell additional units at the same given market price, rather than choosing the market price itself. Suppose output is measured in whole units, production is possible from zero up to some capacity, and the marginal costs of successive units are known. Hold technology, resource costs, and other relevant conditions fixed. Also suppose there is no separate start-up cost that changes the decision to produce at all. These assumptions let us focus on whether each additional unit adds to profit.
Let \(P\) be the price per unit and let \(MC_q\) be the marginal cost of the \(q\)th unit. If the producer makes \(q\) units, its revenue is \(Pq\). The change in economic profit from adding the \(q\)th unit is the revenue from that unit minus its marginal cost:
If \(P>MC_q\), that unit adds to profit. If \(P<MC_q\), it reduces profit. If \(P=MC_q\), producing it makes no difference to profit, so the producer is indifferent between producing it and stopping just before it, assuming there are no other relevant effects. When marginal costs rise with each successive unit, the profitable units come first and the producer stops before the first unit whose marginal cost exceeds price.
Why Marginal Costs Often Rise
A producer may have several ways to expand output, but those ways need not be equally costly. For example, early units might be made by workers and equipment already suited to the task. Additional units could require overtime, less suitable equipment, or workers reassigned from a more valuable task. The resources for those extra units have greater opportunity costs. If each successive unit requires resources whose next-best alternatives are more valuable, marginal cost rises.
The key point is not that every input becomes more expensive simply because the producer makes more. Rather, with some resources limited in the relevant period, expansion can involve progressively less suitable or more highly valued resources. The producer will use those resources only if the price received covers their marginal opportunity cost.
For a price-taking producer, treat the market price as the revenue received for each additional unit.
Include the economic value of resources used, including their best alternative uses.
Produce the unit if price exceeds marginal cost; do not produce it if marginal cost exceeds price.
With rising marginal costs, stop before the first unit whose marginal cost is above price. At equality, more than one output level can maximize profit.
Worked Example: A Higher Price Makes More Units Profitable
A small workshop can make four custom display stands. The marginal opportunity costs of the successive stands are $5, $8, $12, and $17. It sells each stand for the same market price. Compare its output at a price of $7 with output at a price of $13, assuming no start-up cost and no other changes.
Method. For each price, compare it with the cost of each successive stand. The gain from a unit is \(P-MC_q\).
At \(P=\$7\), the four per-unit gains are:
The first stand adds $2 to profit. The second would reduce profit by $1, and each later stand would reduce it further. The workshop therefore makes 1 stand. Its total gain relative to producing none is $2.
At \(P=\$13\), the per-unit gains are:
The first three stands add \(8+5+1=\$14\) in total. The fourth reduces profit by $4, so it is not worthwhile. The workshop makes 3 stands. The calculation checks: the higher price raises the number of profitable units from 1 to 3, while the unit with marginal cost $17 still costs more than the $13 price.
Common mistake avoided: Do not stop merely because the second unit is unprofitable at $7 and assume output must remain fixed. At $13, the second and third units have to be tested again; both now add to profit.
Why the Usual Relationship Is Upward
The decision rule also gives a short justification for why supply usually rises with price. Suppose a producer has a sequence of units with nondecreasing marginal costs: \(MC_1\le MC_2\le\cdots\). At a given price \(P\), the producer finds each unit with marginal cost below \(P\) worthwhile. If price rises to \(P'\), where \(P'>P\), every unit that was profitable before remains profitable, because \(P'>P>MC_q\). Some additional units may now satisfy \(MC_q<P'\). Thus the chosen output cannot be lower; it can rise or stay the same. It stays the same if the price increase still does not cover the cost of the next unit.
This argument relies on the marginal costs and production conditions being held fixed while price changes. A price change changes the producer’s incentive to choose an output; a change in the costs of resources or in production possibilities can change the underlying marginal costs. Those are different economic changes and should not be mixed together when applying the argument.
Worked Example: Correcting the Output Decision at Two Prices
A print service’s first three jobs have marginal opportunity costs of $8, $11, and $15. The market price rises from $10 to $12, with all other conditions unchanged. Determine output at each price and explain the change.
Method. Compare each job’s price with its own marginal cost, rather than treating all jobs as if they had the cost of the first job.
At \(P=\$10\), the gains from the three jobs are:
The first job adds $2 to profit. The second job costs $11, which is $1 more than its $10 price, and the third costs $15, which is $5 more than its price. Output is therefore 1 job, not 2.
At \(P=\$12\), the gains are:
The first two jobs add \(4+1=\$5\) in total; the third would reduce profit by $3. Output is therefore 2 jobs. The result checks against the costs: the second job’s cost is above the old price but below the new price, while the third job’s cost is above both prices.
Common mistake avoided: Saying output is 2 jobs at $10 incorrectly treats the $11 second-job cost as no greater than $10. Each unit must pass the price-versus-marginal-cost test at the price actually offered.
Worked Example: Comparing Total Gains as a Check
A food producer can prepare four batches for a local buyer. The marginal opportunity costs, in order, are $18, $23, $29, and $38 per batch. Compare the best output at prices of $25 and $32. Assume the buyer pays the same price for every batch and there are no start-up costs.
Method. First apply the marginal decision rule, then add the per-batch gains to check that the chosen output gives the greatest total gain.
At \(P=\$25\), the per-batch gains are:
The first two batches add \(7+2=\$9\). The third and fourth would reduce that total, so the best output is 2 batches. Checking nearby choices: one batch yields $7; two yield $9; three yield \(7+2-4=\$5\); and four yield \(5-13=-\$8\). Two batches give the greatest gain.
At \(P=\$32\), the gains are:
The first three batches add \(14+9+3=\$26\); the fourth reduces the total to \(26-6=\$20\). The best output is 3 batches. As a check, the gains for one, two, three, and four batches are $14, $23, $26, and $20. The higher price makes the third batch worthwhile, but not the fourth.
Common mistake avoided: The price increase does not make every available batch profitable. The fourth batch still has a $38 opportunity cost, greater than the $32 price.
When the Usual Result Needs Qualification
An upward-sloping supply relationship is usual when marginal costs rise as output expands, but the logic has limits. If marginal costs are constant over a range, a price increase may leave the chosen output unchanged over that range. If a producer has a maximum quantity it can make, output cannot rise beyond that limit. If marginal costs fall as production expands, the simple rising-cost explanation does not apply, and a producer’s output response may be less straightforward. A separate start-up cost can also affect whether the producer operates at all; the unit-by-unit rule alone does not settle that decision.
These qualifications do not change the central comparison. For an additional unit, price is the benefit to a price-taking producer and marginal opportunity cost is the cost. The usual upward relationship comes from the fact that expanding production tends to require units with higher marginal costs, not from a claim that every price increase automatically creates extra output.
Common Mistakes
- Confusing price with marginal cost. Price is what the producer receives for a unit; marginal cost is the opportunity cost of the resources used for that unit. A unit is worthwhile when price exceeds marginal cost.
- Using the first unit’s cost for every unit. If costs rise with output, each additional unit needs its own comparison.
- Assuming that any price increase must raise output. Output may stay the same if the higher price still does not cover the next unit’s marginal cost.
- Ignoring equality. When price equals marginal cost, the producer is indifferent about producing that unit under the stated assumptions; a unique output need not result.
- Forgetting the conditions. The usual comparison holds price, technology, and other cost conditions fixed. When those conditions change, marginal costs may change too.
Check Your Understanding
For each problem, use the marginal price-versus-cost rule and note any case where the producer is indifferent.
- A repair shop can take four additional contracts with marginal opportunity costs of $6, $9, $13, and $18. How many does it accept at a contract price of $11 and at a price of $14, assuming no start-up cost? (Answer: 2 contracts at $11; 3 contracts at $14.)
- A grower’s next three crates have marginal costs of $12, $12, and $18. At a price of $12 per crate, which output levels maximize the gain relative to producing none? (Answer: Any output from 0 through 2 crates.)
- A producer has successive marginal costs of $8, $13, and $20. What output is optimal at a price of $19, and what output choices are optimal if the price rises to $20? (Answer: 2 units at $19; any output of 2 or 3 units at $20.)
- A maker can produce three units at marginal costs of $7, $15, and $24. The price is $18. Calculate the gain for each unit, determine output, and verify the total gain at the chosen output. (Answer: Unit gains are $11, $3, and -$6; produce 2 units for a total gain of $14.)
- Explain why a rise in price from $10 to $12 need not change output if a producer’s next unit has a marginal cost of $14. State what would have to happen for that unit to become worthwhile. (Answer: Output need not change because $12 is still below the $14 marginal cost; the price must exceed $14 for that unit to add to profit, while equality makes the producer indifferent.)