MBA Pricing Concept Card Template

Pricing Concept Card: [Product, market or course]

A concept card on pricing with market power for the MBA managerial economics core: the profit-maximising price and the markup rule (Lerner index), price discrimination of the first, second and third degree, versioning, bundling, two-part tariffs, value-based pricing and dynamic pricing with capacity limits. It is for MBA students preparing for class, problem sets and exams, and for managers who set or review prices. It gives the idea in plain language, the formulas with a notation table, fully solved examples with Excel formulas, one half-solved example, one exercise, a chart, a decision diagram, common mistakes and a self-test with an answer key. Source basis: Cournot (1838), Pigou (1920), Lerner (1934), Oi (1971), Littlewood (1972), Adams and Yellen (1976), Mussa and Rosen (1978), written up in original words with fictional examples. Replace every [bracketed] value and every row marked Example. Competition and consumer law limits on pricing are named as dated facts only; this card is a learning aid, not legal advice.

Document control

Contents

• When to use it
• The idea in plain language
• Formulas and notation
• Assumptions, limits and legal checks
• How managers use it
• Decision diagram
• Worked example A (fully solved): from one price to many
• Value-based and dynamic pricing
• Worked example B (half solved): versioning
• Exercise C (unsolved)
• Connections to other cards
• Common mistakes and misconceptions
• Self-test questions
• My notes and next steps
• Sources and further reading
• Answer key
• Revision history

When to use it

Use this card when your firm sets its price rather than taking it from the market: the product is differentiated, there are few rivals, switching costs are high, or the product is new. Typical decisions: launch price, price change, list price and discount policy, price by segment or channel, plan or version design, bundles, subscriptions with a fee plus usage charge, and prices that change with demand and remaining capacity.

The idea in plain language

One price. A price setter faces a downward-sloping demand curve: to sell one more unit it must lower the price on every unit. It should keep expanding output while the extra revenue from the last unit (marginal revenue) exceeds its extra cost (marginal cost), and stop where the two are equal (Cournot 1838). Lerner (1934) turned this into a rule of thumb: the percentage margin over price equals one over the absolute elasticity. Elastic demand means thin margins; inelastic demand at the firm level means the price is too low.

Many prices. A single price leaves money on the table in two ways: some buyers would have paid more (consumer surplus) and some buyers who value the product above its cost do not buy (deadweight loss). Pigou (1920) classified the ways to charge different buyers different prices:

• First degree (perfect): each buyer pays their full willingness to pay. Rarely achievable, but individual negotiation, auctions and some personalised prices move toward it.
• Second degree (self-selection): the seller offers a menu (versions, quantity tiers, plans) and buyers choose; the menu must make each type prefer the option designed for it (Mussa and Rosen 1978 on quality menus).
• Third degree (segments): different prices for observable groups (students, regions, business size, channel), with a lower price for the more elastic group.

Bundling sells products together. When buyers' values for two products are negatively correlated, a bundle evens out willingness to pay and captures more surplus; mixed bundling, which offers the bundle and the separate items, usually does best when marginal costs are material (Adams and Yellen 1976). Versioning offers degraded or enhanced versions of one product to make buyers sort themselves. A two-part tariff charges an access fee plus a usage price; with identical buyers, setting the usage price at marginal cost and capturing consumer surplus in the fee is optimal (Oi 1971).

Value-based pricing starts from the buyer, not from cost: what is the product worth compared with the next best alternative? Dynamic pricing changes prices over time as demand information arrives and capacity is used up; revenue management in airlines and hotels started with a simple rule for protecting seats for late, high-paying customers (Littlewood 1972).

Formulas and notation

Single price. Maximise $\pi = P(Q)\,Q - C(Q)$; the condition is $MR = MC$, with $MR = P\left(1 + 1/\varepsilon\right)$. Rearranged, the markup rule:

$L = \frac{P - MC}{P} = -\frac{1}{\varepsilon}, \qquad P^* = MC \cdot \frac{\varepsilon}{1 + \varepsilon} \quad (\varepsilon < -1)$

For linear inverse demand $P = \alpha - \beta Q$: $MR = \alpha - 2\beta Q$.

Third-degree discrimination. Set output in each segment so that $MR_1 = MR_2 = MC$. Combined with the markup rule:

$\frac{P_1}{P_2} = \frac{1 + 1/\varepsilon_2}{1 + 1/\varepsilon_1}$

so the segment with the more elastic demand gets the lower price.

Two-part tariff with identical buyers (Oi 1971): $p = MC$ and $F = CS(p)$. For individual demand $q = a - bp$, $CS(p) = \tfrac{1}{2}\,(a - bp)\,(a/b - p)$.

Bundling. A buyer of type $j$ buys the bundle at price $P_B$ if $r_j + m_j \geq P_B$ and the bundle gives more surplus than any separate purchase. Profit is computed type by type; with a handful of types, enumerate the candidate prices (each type's value for each item and for the bundle) and pick the best.

Economic value to the customer:

$EVC = \text{reference value} + \text{positive differentiation value} - \text{negative differentiation value}$

The price should sit between your cost and the EVC; where in that range depends on competition and on how credibly the value can be proven.

Littlewood's rule (two fare classes, low fare books first): protect $y$ units for high-fare demand, where

$P(D_H > y) = \frac{p_L}{p_H}, \qquad y = F^{-1}_{D_H}\!\left(1 - \frac{p_L}{p_H}\right)$

and the booking limit for the low fare is capacity minus $y$.

Assumptions, limits and legal checks

Other jurisdictions have their own rules on price discrimination, price display and surge pricing. Ask counsel for each market before using segment, personalised or dynamic prices.

How managers use it

1. Sanity check on a list price. Compare the current margin $(P - MC)/P$ with $1/|\varepsilon|$. A large gap is a signal to investigate, not an instruction.
2. Segment pricing. Student, region, channel and company-size prices are third-degree discrimination; the question is always whether the segments differ in elasticity and whether arbitrage can be blocked.
3. Plan design (good, better, best). Software and service plans are second-degree discrimination; the entry plan is often deliberately limited so that high-value buyers do not take it.
4. Bundles and suites. Bundles reduce the spread of willingness to pay; mixed bundles also serve buyers who want only one item.
5. Subscriptions and memberships. A fee plus usage pricing captures surplus while keeping usage high.
6. B2B pricing. Quantify the customer's savings (value-based pricing) and share them; arm the sales team with the value calculation, not only the price list.
7. Capacity businesses. Airlines, hotels, events, rentals and logistics use booking limits and dynamic prices to fill capacity with the best mix of customers.
8. Algorithmic pricing. Software that sets prices automatically still needs the economics here, a legal review and limits on how far and how fast prices can move.

Decision diagram

The diagram routes a pricing problem to the right tool. Several boxes can apply to one product; for example, a software firm may use plans (second degree), a student discount (third degree) and a suite bundle at the same time.

Worked example A (fully solved): from one price to many

Corvane Robotics (fictional) sells autonomous picking robots to warehouses, plus software modules and a robot service plan. All numbers are invented.

A1. Single price with the markup rule

The firm-level own-price elasticity for the picking robot is estimated at -2.5, and the marginal cost is USD 12k per robot.

How the price responds to elasticity, at the same cost:

Excel: =12*A2/(1+A2) with the elasticity in column A. As demand becomes more elastic (more substitutes), the price approaches marginal cost: the competitive limit.

A2. Third-degree price discrimination

Corvane sells to two segments it can tell apart by contract: large third-party logistics operators (segment L) with annual demand $Q_L = 120 - 2P$, and small e-commerce warehouses (segment S) with $Q_S = 80 - 2.5P$ (P in USD k). Robots are installed and registered to a site, so resale is impractical. Marginal cost is USD 12k.

Total profit with discrimination: USD 1,402k on 73 robots. Uniform price for comparison: total demand $Q = 200 - 4.5P$ while both segments buy ($P \leq 32$), profit $(P - 12)(200 - 4.5P)$, maximised at $P = 254/9 = 28.22$ (=(200+4.5*12)/(2*4.5)), selling 63.56 to L and 9.44 to S, also 73 robots in total, for a profit of USD 1,184.2k (=(254/9-12)*(200-4.5*254/9)). Discrimination raises profit by USD 217.8k (18.4%). With linear demands and both segments served, total output is the same in both regimes; what changes is who gets the robots and at what price. Consumer surplus falls from USD 1,027.7k to USD 701k.

The chart shows profit at each uniform price. There are two peaks: USD 28.22k (serve both segments) and USD 36k (serve only segment L, profit USD 1,152k). When segments are very different, a uniform price may drop the low segment entirely; discrimination lets the firm serve both.

A3. Bundling (Adams and Yellen 1976)

Corvane sells two software modules for its robots, RouteOpt and PredictMaint, on monthly subscriptions per site. Each module costs USD 20 a month per site to support (marginal cost). Four customer types, one site each, have these monthly values (USD):

Excel: separate =2*(75-20)*2; pure bundle =4*(105-40); mixed =(95-20)+2*(115-40)+(95-20). The prices were found by enumerating every candidate price (each type's value for each item and for the bundle) and keeping the best combination.

Values are negatively correlated, so the bundle narrows the spread (105 to 115) and the pure bundle beats separate selling. Mixed bundling does better still: it does not force W1 and W4 to take a module they value below its USD 20 cost (W1 values PredictMaint at 10), and it captures the full efficient surplus of USD 300 (every value above cost: 75 + 0 + 55 + 20 + 20 + 55 + 0 + 75). In practice set prices one dollar below each threshold (94, 94, 114) so that indifferent buyers clearly buy: profit USD 296.

A4. Two-part tariff (Oi 1971)

Corvane offers robot-as-a-service: a monthly access fee per warehouse plus a charge per thousand picks. Each warehouse's monthly demand is $q = 500 - 20p$ (thousand picks, $p$ in USD per thousand picks); marginal cost is USD 5 per thousand picks. All warehouses are alike.

The two-part tariff doubles profit and doubles usage. The single price leaves USD 1,000 of consumer surplus and a deadweight loss of USD 1,000 (=0.5*(400-200)*(15-5)); the two-part tariff captures both. With different buyer types, the fee must be low enough for the smallest buyer you want to serve, and the usage price is then usually set above marginal cost.

Value-based and dynamic pricing

Economic value to the customer

A warehouse operator's next best alternative to the Corvane robot is a rival robot at USD 60,000 (Example). The Corvane robot saves an extra USD 8,000 a year in labour for five years (discount rate 10%), but needs USD 6,000 of extra integration work.

With a marginal cost of USD 12,000 (A1), the price range is USD 12,000 to about USD 84,300. A price of USD 72,000 (Example) leaves the buyer about USD 12,300 better off than with the rival, which a sales team can show in a proposal. Value-based pricing needs evidence the buyer believes: pilots, references and guarantees. The A1 markup price (USD 20,000) and the EVC price are different questions: the markup rule summarises how the whole market responds, while EVC is the ceiling for one well-informed buyer; use EVC to segment and to negotiate.

Dynamic pricing with fixed capacity (Littlewood 1972)

Northfield Outdoor Co. (fictional) runs a 60-place guided mountain course. Early-bird places sell at USD 250 and book first; full-price places at USD 400 are bought later, by customers who decide close to the date. Full-price demand is uncertain, roughly normal with mean 25 and standard deviation 8.

So Northfield should protect 22 places and cap early-bird sales at 38. The logic: hold back one more place only if the chance of selling it at USD 400 is worth more than a certain USD 250. Modern dynamic pricing extends this with many fare classes, demand forecasts updated daily and prices instead of fixed classes (Talluri and van Ryzin 2004). Two cautions: customers who learn that prices fall late may wait (strategic buyers), and surge prices on essentials attract regulatory and reputational risk.

Worked example B (half solved): versioning

Corvane sells its fleet-dashboard software in two versions. Standard limits reporting to daily data; Pro adds real-time alerts. There are 40 high-type customers (large sites) and 60 low-type customers (small sites). Monthly values and costs per customer (USD):

Tasks:

1. Price Standard so that low types buy it: $P_S =$ [ ].
2. The high type must prefer Pro to Standard: $50 - P_{Pro} \geq 30 - P_S$, so the highest Pro price is $P_{Pro} = 50 - (30 - P_S) =$ [ ].
3. Profit with both versions: $60 \times (P_S - 2) + 40 \times (P_{Pro} - 5) =$ [ ] (=60*(20-2)+40*(40-5)).
4. Compare with three single-product alternatives: Pro only at 50 to high types: [ ]; Standard only at 20 to all: [ ]; Pro only at 25 to all: [ ].
5. The high type earns a surplus of [ ] even though the firm knows its value. Why can the firm not take it?
6. The firm considers making Standard even weaker, so that high types value it at 26 instead of 30 (low types still at 20). New Pro price: [ ]. New profit: [ ].

Exercise C (unsolved)

Northfield's indoor climbing wall sells day passes to two groups it can identify by ID card: students with daily demand $Q_S = 300 - 10P$ and other adults with $Q_A = 200 - 4P$ (P in USD). Marginal cost is USD 6 per visit.

1. Find the profit-maximising price and quantity for each group, and total profit.
2. Compute the elasticity at each price and verify the Lerner condition.
3. Find the best uniform price (check that both groups still buy), quantity and profit.
4. By how much does discrimination raise profit? Which group pays more, and why?
5. Name two ways the wall could stop adults from using student passes, and one fairness risk.

Connections to other cards

• Demand elasticity (mba/mba-demand-elasticity-card): every tool here needs an elasticity or a demand curve.
• Market structure (mba/mba-market-structure-card): the amount of market power sets how far price can exceed marginal cost.
• Game theory (mba/mba-game-theory-card): price wars, matching, price leadership and signalling.
• Marketing mix and segmentation (mba/mba-marketing-mix-card, mba/mba-stp-positioning-card): price as part of the offer; segments as the basis for third-degree pricing.
• Customer lifetime value (mba/mba-customer-lifetime-value-card): subscription and two-part pricing affect retention and lifetime value.
• Break-even (mba/mba-cvp-breakeven-card): the volume needed to justify a price cut.
• Course guide (mba/mba-microeconomics-guide): the integrative Trailhead stove mini-case uses this card.

Common mistakes and misconceptions

1. Cost-plus by habit. A fixed markup on cost ignores demand; it is right only by accident.
2. Letting fixed costs set the price. Fixed costs decide whether to sell at all, not the profit-maximising price.
3. Using the market elasticity for one firm. A firm faces a more elastic demand than its industry.
4. Pricing in the inelastic range. If $|\varepsilon| < 1$ at your price, raising it increases profit.
5. Ignoring arbitrage. Segment prices fail if low-price buyers can resell or if high-value buyers can pretend to be in the low segment.
6. Forgetting self-selection in menus. Price each premium version so the high type still prefers it.
7. Assuming bundling always helps. Pure bundling can lose to separate sales when values are positively correlated or marginal costs are high; check mixed bundling.
8. Setting the usage price above cost in a two-part tariff with identical buyers. It shrinks the surplus the fee can capture.
9. Confusing EVC with price. EVC is a ceiling; leave the buyer a reason to switch.
10. Dynamic pricing without guardrails. Strategic waiting, fairness backlash and legal disclosure duties are real costs.

Self-test questions

1. Elasticity is -3 and MC is USD 45. What is the profit-maximising price and the Lerner index?
2. A product has a 75% margin over price. What firm-level elasticity is consistent with profit maximisation?
3. In third-degree discrimination, which segment gets the lower price, and why?
4. State the two conditions needed for third-degree discrimination to work.
5. What makes a menu of versions a second-degree, not third-degree, scheme?
6. Why does mixed bundling beat pure bundling in Worked example A3?
7. In a two-part tariff with identical buyers, why is the usage price set at marginal cost?
8. A rival product costs USD 900; yours saves the buyer an extra USD 300 in present value and needs USD 100 of extra training. What is the EVC?
9. With $p_L = 120$, $p_H = 200$ and high-fare demand normal with mean 40 and standard deviation 10, how many units should be protected? Give the Excel formula.
10. Give two reasons why algorithmic dynamic pricing needs limits.

My notes and next steps

Sources and further reading

• Cournot, A. A. (1838). Recherches sur les principes mathématiques de la théorie des richesses. Hachette.
• Pigou, A. C. (1920). The Economics of Welfare. Macmillan.
• Lerner, A. P. (1934). The concept of monopoly and the measurement of monopoly power. Review of Economic Studies, 1(3), 157–175.
• Oi, W. Y. (1971). A Disneyland dilemma: two-part tariffs for a Mickey Mouse monopoly. Quarterly Journal of Economics, 85(1), 77–96.
• Littlewood, K. (1972). Forecasting and control of passenger bookings. AGIFORS Symposium Proceedings, 12, 95–117. Reprinted (2005) in Journal of Revenue and Pricing Management, 4(2), 111–123.
• Adams, W. J., and Yellen, J. L. (1976). Commodity bundling and the burden of monopoly. Quarterly Journal of Economics, 90(3), 475–498.
• Mussa, M., and Rosen, S. (1978). Monopoly and product quality. Journal of Economic Theory, 18(2), 301–317.
• Talluri, K. T., and van Ryzin, G. J. (2004). The Theory and Practice of Revenue Management. Springer.
• US Federal Trade Commission, Price discrimination: Robinson-Patman violations (guidance page, checked 2026-10-28).
• Directive (EU) 2019/2161 of the European Parliament and of the Council of 27 November 2019, amending Directive 2011/83/EU among others, Official Journal of the European Union, L 328, 18 December 2019, https://data.europa.eu/eli/dir/2019/2161/oj (checked 2026-10-28).
• Treaty on the Functioning of the European Union, Article 102, https://data.europa.eu/eli/treaty/tfeu_2016/art_102/oj (checked 2026-10-28).
• Textbooks (further reading, by name only): Nagle and Müller, The Strategy and Tactics of Pricing; Shapiro and Varian, Information Rules; Besanko, Dranove, Shanley and Schaefer, Economics of Strategy; Pindyck and Rubinfeld, Microeconomics.
• Open resource: OpenStax, Principles of Economics (3rd edition), chapter on monopoly, CC BY-NC-SA 4.0, openstax.org.

Answer key

Worked example B.

1. $P_S = 20$.
2. $P_{Pro} = 50 - (30 - 20) = 40$.
3. $60 \times 18 + 40 \times 35 = 1{,}080 + 1{,}400 = 2{,}480$ USD a month.
4. Pro only to high types at 50: $40 \times 45 = 1{,}800$. Standard to all at 20: $100 \times 18 = 1{,}800$. Pro to all at 25: $100 \times 20 = 2{,}000$. Versioning (2,480) beats all three.
5. USD 10 (50 - 40): the information rent. If Pro cost more than 40, high types would switch to Standard, which gives them 30 - 20 = 10. The firm cannot tell types apart, so it must leave this rent to make them choose Pro. (At exactly 40 the high type is indifferent; in practice price Pro at 39, profit USD 2,440.)
6. Weakening Standard reduces its appeal to high types: $P_{Pro} = 50 - (26 - 20) = 44$, profit $60 \times 18 + 40 \times 39 = 2{,}640$ (=60*(20-2)+40*(44-5)). Deliberately degrading the basic version is called damaging the good; it raises profit as long as low types still value it at 20.

Exercise C.

1. Students: $P = 30 - Q/10$, $MR = 30 - Q/5 = 6$, $Q = 120$, $P = 18$, profit $12 \times 120 = 1{,}440$. Adults: $P = 50 - Q/4$, $MR = 50 - Q/2 = 6$, $Q = 88$, $P = 28$, profit $22 \times 88 = 1{,}936$. Total USD 3,376 a day.
2. Students $\varepsilon = -10 \times 18/120 = -1.5$, Lerner $12/18 = 0.667$. Adults $\varepsilon = -4 \times 28/88 = -1.273$, Lerner $22/28 = 0.786 = 1/1.273$.
3. Total demand $Q = 500 - 14P$ (both buy below USD 30); profit $(P - 6)(500 - 14P)$ peaks at $P = 584/28 = 20.86$ (=(500+14*6)/(2*14)), $Q = 208$, profit USD 3,090.29. Both groups buy, since 20.86 < 30.
4. By USD 285.71 a day (3,376 - 3,090.29), about 9.2%. Adults pay more because their demand is less elastic at the relevant prices.
5. Check student ID at entry; issue named, non-transferable passes. Fairness risk: adults on low incomes may see the gap as unfair; an off-peak price open to all can soften it.

Self-test.

1. $P = 45 \times 3/2 = 67.50$; $L = 22.5/67.5 = 0.333$.
2. $L = 0.75 = 1/|\varepsilon|$, so $\varepsilon = -1.33$.
3. The more elastic segment, because the markup rule gives it a smaller margin over marginal cost.
4. The firm can identify the segments (with different elasticities), and buyers cannot resell or switch segments (no arbitrage). Market power is assumed.
5. The buyer chooses the option; the seller does not observe the buyer's type and cannot assign prices by segment.
6. Pure bundling forces W1 and W4 to take a module they value at USD 10, below its USD 20 cost, and it caps what W2 and W3 pay at 105. Mixed bundling sells the single module to W1 and W4 at 95 and the bundle to W2 and W3 at 115.
7. Any usage price above cost reduces the quantity used and shrinks consumer surplus by more than the usage margin gains; with identical buyers the fee captures the whole surplus, so pricing usage at cost maximises the total.
8. $900 + 300 - 100 = 1{,}100$ USD.
9. $y =$ =NORM.INV(1-120/200,40,10) $= 40 + 10 \times (-0.2533) = 37.47$, so protect about 37 units.
10. Strategic customers learn to wait and erode prices; fairness and reputational backlash; legal duties such as disclosure of personalised prices; and pricing algorithms can amplify errors or move prices in ways that raise competition-law questions.

Revision history

Standard and licence note

Based on the standard treatment of pricing with market power in managerial economics (Cournot 1838, Pigou 1920, Lerner 1934, Oi 1971, Littlewood 1972, Adams and Yellen 1976, Mussa and Rosen 1978) and on the official FTC and EUR-Lex pages named in the text, checked in October 2026. The text, the examples and the questions are original; no textbook text is copied or paraphrased, and Corvane Robotics and Northfield Outdoor Co. are fictional. The template is independent and not affiliated with or endorsed by any business school, authority or software vendor. Check the current official versions of every dated fact and legal rule before you rely on them. Template licence: MIT.