Compare pricing rules without confusing revenue and welfare
Can a pricing change alter distribution even when quantity stays fixed?
Your task: Build two buyer-level price/value/surplus tables. Compare quantity, seller profit, consumer surplus and total surplus, then critique the information assumptions.
Read counts with their units. A percentage divides a part by its named whole and multiplies by 100. A model assumption is not an observed fact.
Price discrimination
Pricing differences across buyers or units not fully attributable to differences in cost.
Assumption
A condition accepted for a model or argument; it needs justification before applying the result elsewhere.
01 · TRY
Can a pricing change alter distribution even when quantity stays fixed?
Build two buyer-level price/value/surplus tables. Compare quantity, seller profit, consumer surplus and total surplus, then critique the information assumptions.
Build two buyer-level price/value/surplus tables. Compare quantity, seller profit, consumer surplus and total surplus, then critique the information assumptions. Use the supplied records and show one intermediate step.
Make a provisional claim
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Inspect evidence and test an explanation
The investigation controls appear when your local evidence is ready.
04 · UNDERSTAND
Connect evidence and mechanism
Compare pricing rules without confusing revenue and welfare
Question and record
Can a pricing change alter distribution even when quantity stays fixed?
Three fictional buyers value one unit at 10, 8 and 6. Marginal cost is 2 with no fixed cost. A seller can either charge one price or, in a separate idealized scenario, charge each buyer their exact willingness to pay. Resale is impossible only in the second scenario.
The quantities and graphs are teaching assumptions, not observed policy outcomes.
Mechanism and worked calculation
Price discrimination charges different prices for reasons not fully explained by costs. Perfect first-degree discrimination can transfer buyer surplus to the seller and expand trades relative to a restrictive single-price outcome. Group and quantity pricing require their own constraints. Total surplus and its distribution must be reported separately.
At uniform price 6, three units sell: revenue18, cost6, profit12, consumer surplus6. Exact-value prices yield revenue24, cost6, profit18 and consumer surplus0. Both examples trade three units and total surplus remains18.
Challenge the interpretation
Knowing every buyer value and preventing resale are strong assumptions. A real seller’s observed different prices can also reflect different costs, product versions or access policies. The example does not establish a general claim about fairness.
Your evidence task
Build two buyer-level price/value/surplus tables. Compare quantity, seller profit, consumer surplus and total surplus, then critique the information assumptions.
Revise your answer to “Can a pricing change alter distribution even when quantity stays fixed?” using both source IDs. Separate the checked calculation from a judgment, and identify evidence that could reverse your judgment.
Vocabulary
Price discrimination: Pricing differences across buyers or units not fully attributable to differences in cost.
Assumption: A condition accepted for a model or argument; it needs justification before applying the result elsewhere.
Independent extension
Independently extend the investigation “Compare pricing rules without confusing revenue and welfare” with a documented real dataset or scholarly source. Preserve definitions, recreate one calculation or evidence table, compare a rival explanation and report why the teaching example cannot establish the real-world conclusion.
Separate transferred surplus from new trades
This original fictional case has four buyers, each wanting at most one identical unit, with values 12, 9, 6 and 4 credits. A seller with market power has constant marginal cost, no fixed cost and enough capacity. Buyers purchase when value equals price; the ideal seller includes zero-margin trades. There are no externalities or administration costs. These conventions describe a model, not actual buyer behavior.
Predict: find the most profitable uniform price before comparing exact-value prices. Which buyers are excluded? Which extra trades add resource gains rather than merely transfer a payment?
Buyer values and cost use one fixed 0–12 credit scale. Bar heights are values, not payments; text/table report payments.
Enumerate uniform-price choices
For any unchanged set of purchasers, raising price to its lowest buyer value weakly raises profit. Therefore checking these value thresholds and no sale covers the profit maximum for this finite demand. Below-cost options are displayed but need not be chosen. All optimal ties are retained; if tied, the summary selects the largest quantity.
No sale: Q=0, revenue=0, cost=0, profit=0, consumer surplus=0, total surplus=0.
Price 12: Q=1, revenue=12, cost=3, profit=9, consumer surplus=0, total surplus=9.
Price 9: Q=2, revenue=18, cost=6, profit=12, consumer surplus=3, total surplus=15.
Price 6: Q=3, revenue=18, cost=9, profit=9, consumer surplus=9, total surplus=18.
Price 4: Q=4, revenue=16, cost=12, profit=4, consumer surplus=15, total surplus=19.
Exact-value Q=4; revenue=31, cost=12, profit=19, consumer surplus=0, total=19. Compared with uniform pricing, new resource gains are 4; buyer-surplus reduction is 3. Seller-profit increase equals their sum: 7.
Each row: value; trades; payment; consumer surplus; seller margin; total resource gain
Buyer/value
Uniform (trade; pay; CS; margin; total)
Exact-value (trade; pay; CS; margin; total)
1 / 12
yes; 9; 3; 6; 9
yes; 12; 0; 9; 9
2 / 9
yes; 9; 0; 6; 6
yes; 9; 0; 6; 6
3 / 6
no; 0; 0; 0; 0
yes; 6; 0; 3; 3
4 / 4
no; 0; 0; 0; 0
yes; 4; 0; 1; 1
Total surplus = sum of traded buyer values minus resource cost = seller profit + consumer surplus. Payments cancel as transfers. The maximum available resource surplus is 19; the uniform-price gap is 4. There are 4 strictly beneficial trades and 0 zero-gain trades. No consumer gains from the ideal exact-value rule here, even when aggregate resource surplus rises.
Transfer and challenge
Change cost to 6. Explain why reported quantity can rise without increasing total surplus: the third buyer is indifferent, and omitting that zero-gain trade also maximizes seller profit and total surplus. Withdraw one ideal premise and explain why you must withhold the exact-value prediction. Name evidence needed to distinguish value-based pricing from different costs or product versions; do not collect personal willingness-to-pay data.
Reasoning guide
At cost 3, uniform price 9 sells two units: profit 12, buyer surplus 3 and total 15. Exact-value pricing sells four: profit 19, buyer surplus zero and total 19. The profit increase 7 consists of transferred buyer surplus 3 and new gains 3+1=4. At cost 6, uniform prices 12 (one unit) and 9 (two units) tie at profit 6. The largest-quantity convention displays price 9, with total surplus 9; price 12 instead has total surplus 6. Exact-value pricing includes a third unit with value=cost=6: profit and total 9. Including or excluding it is immaterial to resource surplus. Higher quantity alone does not prove a welfare improvement or fairness.
Method source and model scope
Oregon State Intermediate Microeconomics, Module 16 supplies context for ideal first-degree discrimination and its information/resale assumptions. These numbers, diagrams and prose are original. The model does not establish feasible real-world targeting, legal permission, group-price effects or fairness. The earlier three-buyer lesson remains a separate equal-quantity comparison.
Copy the pricing comparison report
Writing and known feedback exposure are temporary. Reset clears writing and restores cost 3 with both premises, retaining exposure in this mount; reload clears it. Calculations are visible practice, not independent assessment.
Worked example
At uniform price 6, three units sell: revenue18, cost6, profit12, consumer surplus6. Exact-value prices yield revenue24, cost6, profit18 and consumer surplus0. Both examples trade three units and total surplus remains18.
