Understand markups, entry barriers, network effects, and the limits of concentration measures.
By the end: Explain how a firm can restrict output and why a high price alone does not prove market power.
A price-setter faces a tradeoff
A price-taking firm treats the market price as given. A firm facing downward-sloping demand for its own product must usually lower its price to sell more. With one uniform price, expanding sales can reduce revenue on units it would otherwise have sold at the higher price. Marginal revenue can therefore lie below price. A profit-maximizing seller compares marginal revenue with marginal cost, not simply price with marginal cost.
Consider demand price 100 minus quantity and constant marginal cost 20, with no fixed cost. Competitive pricing at 20 would support 80 units. A single-price monopolist chooses 40 units at price 60: its profit is 1,600. Profit can be rewritten as 1,600 minus the square of the difference between quantity and 40. A square cannot be negative, so profit is largest when that square is zero, at quantity 40. The restriction leaves trades unmade whose buyers would have paid more than their production cost.
Why extra sales bring less than the posted price
Start with the seller's decision rather than the word monopoly. Quantity means units sold during one period. Price means currency units paid for each unit. The demand schedule tells this seller the uniform price at which buyers collectively purchase each quantity, with incomes, alternatives, and product quality held fixed. It does not give the seller independent control over both price and quantity. Choosing a higher quantity requires accepting the lower price on that schedule. Assume every unit produced is sold, the seller knows demand, and buyers cannot obtain an identical product elsewhere at a fixed competitive price.
Use a paper comparison away from the optimum. At quantity 20, the stated demand gives a price of 80. Multiplying 20 units by 80 currency units per unit gives revenue of 1,600 per period. Producing them costs 400 because each costs 20. Profit is therefore 1,200. At quantity 30, price is 70, revenue is 2,100, and cost is 600. Profit rises to 1,500. Selling ten additional units increases profit by 300, so average extra profit across those ten units is 30 per unit. That average is neither the new price nor the total profit margin.
To explain the revenue increase, separate new customers from existing sales. The ten additional units bring in 700 at the new price of 70. But the original twenty units now each sell for 10 less, reducing receipts by 200. The net revenue increase is 500, not 700. Additional production costs 200, leaving the 300 profit increase. Marginal revenue describes the revenue gained at the margin, after this effect on other sales. The 200 of forgone receipts on existing sales is not a bill paid to someone else. Subtracting that sacrifice from the 700 received on new sales leaves the 500 increase in total revenue over this ten-unit expansion.
Why ten extra sales add only 300 to profit
In this invented uniform-price expansion from 20 to 30 units, new sales bring 700, but repricing existing sales sacrifices 200 and extra production costs another 200. The resulting profit gain is 300; the final bar summarizes, rather than adds to, the preceding components. A price-taking seller would avoid the repricing loss. Demand and costs are assumed known.
A price-taking firm faces a different calculation. If it can sell either twenty or thirty units at an unchanged market price of 70, revenue rises by the full 700 when sales expand. With the same additional cost of 200, profit rises by 500. That comparison holds the market price fixed for this individual firm. It does not imply that every firm could expand indefinitely without changing the market price. The contrast is between the demand perceived by one small seller and the demand faced by a seller large enough to affect its own price.
The benchmark's constant cost also matters. Doubling production doubles variable cost, and there is no fixed cost to recover. Actual entry, capacity limits, quality choices, or costs that rise with output would require a different calculation. This example isolates a pricing mechanism. The multiplication and subtraction are accounting calculations conditional on the chosen quantity. The claim that the seller chooses the highest-profit quantity adds a behavioral assumption. Whether an actual seller knows its demand or follows that rule requires evidence beyond the arithmetic.
Which cost changes would alter the pricing calculation?
Cost assumptions and output choice
Cost condition
Expansion test
Profit boundary
Constant unit cost
Same cost per extra unit
No fixed cost recovery
Rising unit cost
Reprice extra production
Optimum may change
Fixed outlay
Check if avoidable
Must finance operation
Capacity limit
Exclude excess output
Best feasible quantity
The invented benchmark isolates uniform pricing with constant unit cost and no fixed outlay. These alternatives identify which part of the calculation would change, rather than predicting a new optimum. Rising marginal costs alter the expansion test; a fixed outlay changes total profitability. Actual capacity and entry costs require evidence before applying either alternative.
Why do rivals not immediately enter?
Entry may require large sunk investments, access to infrastructure, patents, data, distribution, or customer attention. Network effects mean a service can become more useful as more people use it. Switching costs can make an incumbent's customers difficult to attract. Scale economies can make duplication expensive. Some barriers reflect real technical costs; others arise from exclusionary conduct or legal privilege.
Economic rent is a return above the minimum needed to keep a resource or participant in its current use. It can arise from scarcity, legal rights, bargaining power, or innovation. A temporary innovation rent may reward experimentation, while durable exclusion can protect inefficient producers. Ordinary rent paid for a building and economic rent are related words but not identical concepts.
Entry requires a recoverable business case
A high operating margin can attract a rival without making entry feasible. Separate a cost already incurred by an incumbent from a cost a newcomer must still pay. A sunk investment cannot be recovered after exit. A fixed investment does not vary with current output, but may still be avoidable before the investment decision. An incumbent that already owns specialized equipment may rationally keep producing even when expected receipts would not justify buying the equipment again. The newcomer must compare future receipts with the full avoidable entry cost.
Consider a separate paper project lasting two years. Ignore discounting, taxes, uncertainty, and resale value to isolate entry costs. A newcomer must pay 900 before operating. After paying all other operating costs, it expects receipts of 400 in each year. The two years generate 800, which is 100 less than entry costs. Entry has a negative net payoff even though each operating year would show a positive contribution. An incumbent whose identical installation is already paid for could receive the same 800 by continuing rather than closing. This does not prove that its original investment was wise.
If the newcomer instead expects 500 in each year, the total becomes 1,000 and the net payoff becomes 100. But expected sales after entry must allow for customer switching and incumbent responses. A forecast that assumes the newcomer receives the incumbent's current sales without affecting prices is not an entry model. A rival may offer lower prices yet fail to cover the cost of reaching customers. Conversely, a new production method could reduce the initial investment enough to make entry viable. Which case applies is an empirical question about alternatives and costs.
Positive operations need not justify entry
Both invented forecasts subtract the same avoidable entry outlay of 900. Two annual operating contributions of 400 leave a net loss of 100; contributions of 500 leave a net gain of 100. An incumbent with the installation already paid for faces a different decision. Discounting, resale value, and uncertainty are omitted; actual post-entry sales could invalidate either forecast.
Network effects and scale economies describe different mechanisms. A scale economy lowers cost per user as a system expands. A network effect raises a user's benefit when other relevant users join. In a paper messaging example, a service with a fee of 2 gives a user benefit of 12 when their contacts participate, leaving a net benefit of 10. A free rival gives benefit of only 4 while those contacts remain elsewhere. Free access does not induce switching in that comparison. If coordinated adoption raises the rival's benefit to 12, the comparison reverses. These assumed benefits are money equivalents, not measured satisfaction.
Compatibility rules, access contracts, patents, and customer ownership of data can change the rival's feasible options. Describing those rules identifies a mechanism without deciding whether a particular restriction is justified. A patent might finance an uncertain discovery while also preventing a cheaper current supplier from entering. An open access obligation might reduce exclusion while requiring someone to finance shared infrastructure. Evaluating either arrangement requires the investment counterfactual and the incidence of its costs. Economic rent concerns the return above the relevant alternative, so its measurement also depends on which alternative is genuinely available and over what horizon.
Work through the mechanism
1. Revenue less variable cost
Q is output and price is 100 minus Q. Marginal cost is 20, with no fixed cost. This is a uniform-price seller, not a price taker.
2. Expand the revenue and cost terms
Multiplying Q by each term in the demand price gives 100Q minus Q squared. Subtracting the cost 20Q leaves 80Q minus Q squared.
3. Check the square
Multiply Q minus 40 by itself. The two cross terms each subtract 40Q, while negative 40 times negative 40 adds 1,600.
4. Rewrite to reveal the maximum
The square is nonnegative, so subtracting it cannot raise profit above 1,600. Equality occurs at Q = 40; demand then gives price 60.
Uniform-price benchmark
Quantity
Price
Variable cost
Profit
Competitive price equals cost
80
20
1,600
0
Monopoly choice
40
60
800
1,600
Demand is price = 100 − quantity. Marginal cost is 20, with no fixed cost, externalities, quality changes, or entry in this benchmark.
Separate a transfer from a lost trade
The displayed monopoly benchmark is a static calculation and table, not a slider experiment. Read the competitive row as a counterfactual with the same demand and marginal cost. It does not show an actual industry moving through time. The monopoly row sells fewer units at a higher price, which changes both the distribution of gains on completed trades and the number of trades. Those are separate effects. This paper extension uses the areas under the same straight demand line to measure them, with willingness to pay treated as a money measure of buyer benefit.
At price 20 and quantity 80, the first units have willingness to pay near 100 and the last units near 20. Buyer surplus is the triangular area between demand and price. The triangle has width 80 units and height 80 currency units per unit. Half of 80 times 80 is 3,200 currency units per period. Seller receipts cover the constant production cost, so seller surplus and profit are zero here. This zero profit follows from the deliberately omitted fixed costs and opportunity costs beyond the stated marginal cost, not a general prediction about business accounts.
At the monopoly price of 60, buyers purchase 40 units. Their surplus triangle now has width 40 and height 40, giving 800. Each completed unit sells for 40 above its production cost. Across 40 units this gives seller profit of 1,600. Total buyer surplus plus profit is therefore 2,400, compared with 3,200 in the competitive counterfactual. The difference is 800. Buyers lose 2,400 in surplus, but only 800 of that loss is a reduction in this model's total gains. The remaining 1,600 becomes the seller's profit.
Transfer and missing gains are different losses
Each row accounts for the benchmark's 3,200 potential gains, not actual receipts. Monopoly reallocates 1,600 to the seller and leaves 800 unrealized; only buyer and seller portions count as realized surplus. Competitive pricing realizes all 3,200 for buyers here. This invented comparison holds demand and constant cost fixed, excluding fixed costs, external effects, and distributional weights.
The missing 800 comes from the forty units between quantities 40 and 80. Their buyers would pay more than production cost, but less than the monopoly price needed to expand uniform-price sales. The gap between willingness to pay and cost falls from 40 to zero across that interval. A triangle with width 40 and height 40 has area 800. This is the deadweight loss in the benchmark. It excludes external effects, administrative costs, changes in innovation, and differences in the ethical importance of a currency unit to different people. Those omissions delimit what the number measures.
A transfer of profit back to buyers could change who receives the 2,400 without restoring the missing trades. Conversely, requiring price 20 would expand output here, but could fail to finance a different technology with substantial fixed costs. One cannot copy this result into that different cost model without checking its budget. A policy assessment must specify the feasible production and financing arrangement. Maximizing the sum of money surpluses is an efficiency criterion under stated assumptions. Choosing distributional weights, rights, or acceptable concentration of authority adds normative premises that the area calculation cannot supply.
Returning profit does not restore missing trades
Policy mechanisms in the benchmark
Alternative
Completed trades
Financing check
Return existing profit
Same missing trades
Redistribute residual
Require price at cost
Missing trades restored
Covers variable costs
Fixed-cost technology
Depends on pricing
Recover fixed outlay
In the invented static benchmark, reallocating existing profit and expanding output solve different problems. The transfer row holds price and quantity unchanged; requiring the competitive price instead changes which trades occur. Neither comparison establishes a feasible remedy for a technology with fixed costs. Financing and demand must be checked again before carrying the output result into that alternative.
Assess conduct and counterfactuals
Concentration measures summarize market shares within a defined market. They do not by themselves establish a markup, harm, or efficiency. A highly productive firm may gain share by lowering costs; a local market with many nominal sellers may still have limited effective choice. Market definition, entry conditions, switching, and buyer power affect the interpretation.
Competition policy can address mergers, collusion, or exclusion, while regulation may be needed for bottleneck infrastructure. Remedies have tradeoffs and implementation limits. Price discrimination can change both distribution and total output relative to one uniform price. The simple monopoly calculation is a benchmark, not a description of every large company or a proof that breaking up any large firm would improve outcomes.
Test the market boundary and the proposed remedy
A market share has a denominator. A shop can supply half the bread sold on its street, a small share of bread in its city, and none of the meals prepared at home. The economically useful boundary depends on what customers would substitute if terms worsened. Geography matters when delivery, travel time, or spoilage prevents distant sellers from constraining local prices. Product quality and contract duration matter when a superficially similar alternative does not meet the same need. Counting firms before defining these options gives a precise number for an uncertain concept.
Take a paper market with annual sales of 100, split among four firms selling 40, 30, 20, and 10. The largest seller has a 40% share. A common concentration index adds squared percentage shares. Squaring and adding gives 1,600 plus 900 plus 400 plus 100, totaling 3,000. If the two smallest firms merge and combined sales remain 30, the shares become 40, 30, and 30. The index becomes 1,600 plus 900 plus 900, or 3,400. The increase is 400 index points. No price or cost appears in this calculation.
A merger changes concentration, not a price formula
In the invented market, shares of 40, 30, 20, and 10 yield 3,000 squared-share points. Combining the two smallest sellers gives shares of 40, 30, and 30 and an index of 3,400. The 400-point increase holds total sales and the market boundary fixed. Broader substitution could change that boundary; neither bar estimates a markup or welfare loss.
Consequently, that increase does not calculate a price increase or a welfare loss. Suppose instead that customers can readily buy an equivalent product from suppliers omitted from the initial boundary. The original denominator understates their alternatives. Or suppose the smaller sellers all depend on the largest firm's distribution facility. Their separate names may overstate independence. Evidence on substitution, access terms, contracts, and entry helps distinguish these cases. A credible market-power argument connects the concentration statistic to a mechanism that limits alternatives; it does not ask the statistic to substitute for that mechanism.
Compare two possible remedies in another paper case. A network costs 600 per period to maintain and 2 per connection to operate. At 100 connections, total cost is 800 and average cost is 8. Splitting it into two separate networks, each with maintenance cost 600 and fifty connections, raises combined cost to 1,400. Average cost becomes 14. This assumption gives duplication a real opportunity cost of 600 per period. It does not establish that one private owner should be unconstrained. Shared access, public ownership, regulated prices, or competition over operation would each assign finance and decision rights differently.
Pricing every connection at marginal cost 2 in the single-network case raises only 200, leaving the maintenance budget short by 600. A proposed subsidy or access charge must identify who supplies that amount and how behavior might change. Charging an average price of 8 balances this particular budget only if all hundred connections remain purchased. Demand could invalidate that assumption. This is why a remedy needs its own model. Evidence that a seller has market power does not by itself identify the cheapest feasible remedy, and a real cost advantage does not establish that its distribution of gains is fair.
Exercises
Check the monopoly calculation
For the stated demand and cost, compare profit at quantities 39, 40, and 41. Why does selling one more unit not add the full posted price to revenue?
Hint
The uniform price changes on all units.
Worked answer
Quantity
Price
Revenue
Cost
Profit
39
61
2,379
780
1,599
40
60
2,400
800
1,600
41
59
2,419
820
1,599
This is uniform pricing: all customers pay the same price in each scenario.
Profits are 1,599, 1,600, and 1,599. Moving from 40 to 41 lowers price from 60 to 59, so total revenue rises only from 2,400 to 2,419. The extra unit brings 59 but the original 40 units each lose 1 of revenue.
Do high prices prove monopoly?
Two towns have different bread prices. One has higher energy and transport costs. Is the price difference sufficient evidence of monopoly power?
Hint
Separate costs from the markup over a relevant cost measure.
Worked answer
Possible explanation
Useful evidence
Higher costs
Input prices and logistics
Market power
Markups, entry barriers, substitution, conduct
Different product
Quality and service differences
A price comparison without these distinctions does not identify the cause.
No. Higher costs can explain a higher competitive price. Evidence on costs, demand, substitution, entry, and conduct is needed to distinguish that explanation from market power. A market-power claim should specify a credible competitive counterfactual.
Sources and further reading
The lessons and answers stand alone. These optional references identify underlying models, evidence, and perspectives. All numerical examples here are invented unless explicitly attributed; none is a forecast or a personal investment recommendation.
Competitive schedules, surplus, taxation, and limits of equilibrium reasoning. All numerical curves in these lessons are separately constructed teaching examples.