When a small sale is worth making · Dr Craig Steven Wright

ECON-101 · Case 1 · 2–3 hours · Independent study

A sale can bring money into an account and still leave its seller worse off. A cheaper transaction fee can belong to the more expensive service. A price increase can improve the return on each order while reducing the return on the whole month. This case asks you to identify the decision in each of those statements, calculate what changes, and explain the limits of your conclusion.

You will advise Leila, a fictional maker of downloadable walking maps. All people, services, prices and business figures in the case are hypothetical. They are teaching assumptions, not current market quotations or business, investment, tax or legal advice. No purchase or external account is needed to complete the case.

Before you begin

You need percentages, multiplication, division and the ability to rearrange a simple equation. A calculator, paper or a spreadsheet is sufficient; calculus is not required. Keep intermediate values to at least four decimal places and round monetary answers to two decimal places only at the end. Write down units beside quantities: pounds per order, orders per month, or hours per month.

By the end, you should be able to calculate weighted revenue; distinguish cash outlays from opportunity costs; separate a marginal decision from a decision to operate; test how much demand can fall after a price increase; and compare services over a stated time horizon without allowing sunk expenditure to dictate the choice.

Allow 15 minutes for the situation and definitions, 30 minutes for the first two tasks, 30 minutes for demand and switching, 15 minutes for checking, and 30–60 minutes for the decision brief and optional reading. Work through the questions before opening the feedback. The worked solutions are intentionally public for self-study; opening them is not an assessment submission or evidence of mastery.

The decision: one month of a small map business

Leila has made a collection of neighbourhood walking maps. Customers buy either one map for £2.00 or a three-map bundle for £5.00. A bundle is one order and one payment, regardless of how many files it contains. Her planning assumption is that 75% of orders are single maps and 25% are bundles. The starting forecast is 120 orders next month: 90 singles and 30 bundles.

She has at most 20 hours available next month for the map business and freelance editing together. Editing work is available in divisible hours, up to all 20 hours, and pays £18 per hour after its own incremental expenses. Leila is indifferent between the two activities apart from their financial return for this exercise. Every hour spent on maps therefore displaces £18 of available editing income. There is no additional value assigned to reputation, enjoyment or future learning in the numerical model.

Service A is already configured. Leila can use it next month or stop selling without a cancellation charge. Its monthly operating charge is paid only if she operates. Service B offers a smaller fixed fee per transaction but a higher percentage fee and monthly charge. Switching requires both a cash payment and additional time.

Planning data: all amounts in pounds sterling (GBP)
Input	Service A	Service B
Fixed fee per order	£0.20	£0.05
Percentage fee on the order price	3%	5%
Avoidable monthly operating charge	£40	£55
Delivery and storage expense per order	£0.10	£0.10
Expected service time per order	3 minutes	3 minutes
Monthly maintenance and administration	4 hours	4 hours
Additional cost to switch from A	None	£36 cash and 2 hours, once

For this model, fees are calculated exactly and aggregated before rounding. There are no minimum charges, refunds, failed payments, taxes, advertising expenses or other costs. Delivery expense and service time apply once per order, including a bundle. Both services have identical reliability, customer experience and demand. Treat these as assumptions to challenge later, not facts about actual providers.

Last month Leila paid £240 for illustrations and spent six hours making the maps. Neither money nor time can be recovered, and the finished work can be used under either service. Her existing laptop will be kept for editing whether or not she sells maps; an accounting allocation of £12 of its monthly cost would not change her cash spending or its alternative use. No new equipment is needed. These details matter because a decision should include the consequences it can still change.

A small vocabulary for a precise answer

Scarcity: Available resources cannot satisfy every competing use. Here, the 20-hour limit makes time a constraint even though a digital file can be copied cheaply.
Opportunity cost: The value of the best alternative given up. Leila gives up available editing earnings when she uses an hour on maps. Do not add every possible alternative together.
Marginal change: The difference caused by a particular additional action. The cost of one more order differs from the cost of opening the business for an entire month.
Fixed and variable costs: A fixed cost does not change with order count within the relevant period and capacity. A variable cost changes with orders. Fixed does not mean unavoidable: next month's operating charge can be avoided by stopping.
Sunk cost: A past commitment that cannot now be recovered. The illustration payment and completed design hours are sunk for this decision. A future switching payment is not sunk before Leila chooses to incur it.
Economic contribution per order: Order revenue less the cash and opportunity costs that vary with that order. In this case it is the amount available to cover monthly fixed economic costs.

We will call revenue less the stated cash outlays the cash surplus. Subtract the value of displaced editing time as well to obtain the economic surplus relative to editing. These are defined measures for this case, not a complete set of accounting statements. Be explicit about the comparison whenever you use the word “profit”.

Task 1: follow the money through one order

Start with Service A. Calculate its transaction fee for a £2 single and a £5 bundle. Then calculate the weighted average order price and fee. Explain why simply averaging £2 and £5 would misrepresent the assumed sales mix. Check your average by multiplying it by 120 and comparing it with revenue from 90 singles and 30 bundles.

Convert three minutes of service time into hours, and value that time at £18 per hour. For each product, subtract the transaction fee, delivery expense and time cost from its price. Finally, calculate the weighted economic contribution. Keep the £40 monthly charge and four maintenance hours separate for now.

Suppose the shop is already operating this month and has spare capacity. A customer requests one additional single map at the posted £2 price, without changing other sales. Should Leila accept? Now derive the lowest price that makes this additional order worthwhile under the same assumptions. Explain why that price would not necessarily sustain the business if charged for every order.

Public worked feedback: orders, fees and contribution

Service A charges £0.20 + 0.03 × £2 = £0.26 on a single and £0.20 + 0.03 × £5 = £0.35 on a bundle. Weighted revenue is 0.75 × £2 + 0.25 × £5 = £2.75 per order. Weighted fees are 0.75 × £0.26 + 0.25 × £0.35 = £0.2825. The unweighted mean of £3.50 would incorrectly assume equal numbers of the two order types.

Total revenue is 120 × £2.75 = £330, which also equals 90 × £2 + 30 × £5. Three minutes is 0.05 hours, so time costs £0.90 per order. A single contributes £2 − £0.26 − £0.10 − £0.90 = £0.74. A bundle contributes £5 − £0.35 − £0.10 − £0.90 = £3.65. The weighted contribution is £1.4675 per order.

The additional £2 order is worthwhile because it adds £0.74 relative to using those three minutes for editing. At an arbitrary price p, contribution is 0.97p − £1.20. Setting this equal to zero gives p = £1.20 ÷ 0.97, approximately £1.2371. With penny prices, £1.24 is the lowest price with a positive contribution under this fee convention. That calculation assumes no effect on other sales and available capacity; it does not cover monthly fixed costs.

Task 2: should the shop operate next month?

Build two separate calculations for 120 orders. First show revenue, transaction fees, delivery expense and the operating charge to find cash surplus. Then calculate all map-business hours and subtract their opportunity cost. Reconcile your economic result to “orders × contribution − monthly fixed economic costs”.

Compare operating with using the available hours for editing. You can either compare the two complete allocations of the 20-hour budget or calculate the incremental difference directly. Do both once to check that they agree. Do not deduct editing income twice.

Find the expected monthly order count at which Service A's economic surplus becomes zero, holding the 75:25 mix constant. Distinguish that threshold from the price threshold in Task 1. Classify the illustration payment, past design hours, laptop allocation, next month's operating charge and next month's maintenance hours. Which can still affect the operating decision?

Public worked feedback: the month and the alternative

At 120 orders, transaction fees total £33.90 and delivery costs £12. Cash surplus is £330 − £33.90 − £12 − £40 = £244.10. Orders require six hours, and maintenance takes four, giving ten hours valued at £180. Economic surplus is therefore £64.10. The contribution method gives the same answer: 120 × £1.4675 − (£40 + 4 × £18) = £64.10.

If Leila operates, the other ten hours earn £180 from editing, giving combined cash receipts after the specified business outlays of £424.10. If she only edits, 20 hours earn £360. The difference is again £64.10. The £180 time cost belongs in the incremental economic calculation; subtracting it from the complete-allocation comparison as well would count it twice.

The operating threshold is £112 ÷ £1.4675, approximately 76.3203 expected orders. At an integer expected volume, 77 is above that threshold. The constant mix is an expectation: exactly 77 realised orders cannot have exactly a 75:25 split. If you require that exact realised mix, compare multiples of four; 80 is the first such volume above the threshold. Actual product counts should replace averages when known.

The £240 and six completed hours are sunk. The laptop allocation changes neither resource use nor expenditure between these options, so it is not incremental here. The £40 and four future maintenance hours are avoidable fixed costs and belong in the monthly decision. A business can rationally accept an extra order while operating, yet rationally decide not to reopen next month.

Task 3: a higher price, but how many customers?

Leila considers raising both prices by 10%, to £2.20 and £5.50. Keep Service A, the same mix and every other assumption. Calculate the new weighted price, transaction fee and contribution. Then examine two demand scenarios: a 15% decline from 120 to 102 expected orders, and a 20% decline to 96.

Find the exact expected order count at the new prices that produces the old £64.10 economic surplus. Convert the difference from 120 into a percentage. This is a decision boundary: the maximum demand reduction compatible with matching the starting result. It is not a forecast of how buyers will respond.

For expected-volume calculations, fractional numbers of singles and bundles are permitted; they represent an average across uncertain outcomes. Realised monthly sales will be whole numbers. Consider how your recommendation changes if the bundle share falls after the price change, service requests become longer, or some customers postpone rather than abandon purchases.

Before calling the increase successful, specify what you would measure and for how long. A useful comparison needs comparable exposure to customers and some account of seasonality. A busy holiday month followed by a quiet month does not isolate the effect of price. No demand curve has been supplied, so do not claim to have found the revenue-maximising or profit-maximising price.

Public worked feedback: a demand boundary

The new weighted price is £3.025 and the average fee is £0.29075. Contribution becomes £3.025 − £0.29075 − £0.10 − £0.90 = £1.73425. At 102 expected orders, economic surplus is 102 × £1.73425 − £112 = £64.8935, or £64.89. That is only about £0.79 better than the starting case. At 96 orders it is £54.488, or £54.49, about £9.61 worse.

To match the old surplus, solve N × £1.73425 − £112 = £64.10. This gives approximately 101.5425 expected orders, a maximum decline of about 15.3813%. With integer expected volumes and the assumed mix, 102 clears the boundary. A small error in the demand estimate could reverse the recommendation because the 15% scenario has so little headroom.

The boundary holds only while mix, per-order time, other costs and the relevant alternative remain unchanged. Record orders by product, net receipts, support minutes and comparable customer exposure. A changed mix requires a new weighted contribution. These scenarios do not establish an elasticity estimate or a causal effect of the price rise.

Task 4: a cheaper fee is not the whole comparison

Return to the original £2 and £5 prices. Calculate Service B's weighted transaction fee, contribution and recurring monthly economic surplus at 120 orders. Compare like with like: first ignore the one-off switch, then include it. What is the recurring difference between B and A as a function of order count N?

Find the recurring order threshold at which B becomes preferable, and the first-month threshold after including £36 and two hours of switching. Check both thresholds against the 20-hour time budget. An algebraic answer outside feasible capacity is not an available business plan.

Finally, suppose Leila expects 240 orders each month for the next ten months. This is a separate scenario, not new evidence about actual demand. Assume the original mix, prices, editing opportunity, service quality and costs remain constant, with no discounting. Calculate the cumulative advantage of switching after three months and after ten. Explain what you would need to believe before relying on the longer horizon.

Public worked feedback: switching and the time horizon

Service B's weighted fee is £0.05 + 0.05 × £2.75 = £0.1875. Contribution is £1.5625 per order, and fixed monthly economic costs are £55 + £72 = £127. At 120 orders, recurring economic surplus is £60.50, compared with A's £64.10. B saves £0.095 per order, but costs £15 more each month. Its recurring advantage is therefore £0.095N − £15.

The recurring threshold is approximately 157.8947 expected orders; 158 is the first integer expected volume above it. Switching adds £36 cash plus two hours worth £36, a total economic cost of £72. First-month advantage becomes £0.095N − £87, which is positive only above approximately 915.7895 orders.

That first-month threshold is infeasible. With A, four fixed hours leave 16 hours for orders, a maximum of 320 at three minutes each. With B in the switching month, six fixed hours leave 14 hours, allowing only 280 orders. Beyond these limits, the linear model would need another staffing or service-time assumption.

At 240 orders, B's recurring advantage is £7.80 per month. Three months recover only £23.40 of the £72 switch, leaving a £48.60 disadvantage. Ten months recover £78, leaving a £6 advantage. The simple payback is about 9.23 months, so ten full months are needed to get ahead. Both allocations fit the time budget at 240 orders. A £6 margin over ten months is fragile evidence for a switch if demand, reliability or workload might change.

Task 5: test the limits of the recommendation

Pick two assumptions that could plausibly change the result. For each, identify the direction of change, the relevant calculation and the information Leila would need. Prefer a specific test, such as timing support requests by product, over a general instruction to “do more research”.

For example, an additional minute of work on every order costs £0.30 at the stated alternative wage. Across 120 orders it reduces the monthly economic surplus by £36. An extra £1 of unavoidable accounting allocation does not have that same effect. Conversely, if the editing work disappears, £18 ceases to be a demonstrated opportunity cost. Time may still be valuable, but you must identify the next-best feasible use rather than assume it is either worthless or worth the old wage.

Also distinguish private return from social value. The model measures Leila's choice under stated prices and opportunities. It does not measure every benefit to walkers, every burden on a neighbourhood or the fairness of access. Those are separate questions requiring additional evidence and clearly stated objectives.

Optional reading on the providers' own sites

The case is self-contained. These links offer further study; no external readings, diagrams or exercises are reproduced here. External material remains subject to its provider's terms and attribution requirements. If a provider requires registration or enrolment for any resource or activity, create and use your own account on that provider's site. A learning account here does not enrol you elsewhere, grant paid access or transfer course credit.

OpenStax, Principles of Economics 3e, section 2.1: a foundation for budget constraints, marginal choices and sunk costs. Read after Task 2 and compare its treatment of opportunity cost with your explanation.
CORE Econ, The Economy 1.0, Unit 3: Scarcity, work, and choice: a broader treatment of time allocation and constrained choice. This is the explicitly identified 1.0 edition; use the opening sections to extend the case's time-budget reasoning.
MIT OpenCourseWare, 14.01 Principles of Microeconomics, Fall 2023 syllabus: an optional path to a fuller undergraduate course. The syllabus says some single-variable calculus at the level of MIT 18.01 is used, with no other prerequisites. Its separately linked MITx course requires sign-up. Those requirements belong to the MIT resources; this case requires no calculus.

Provider links and the MIT prerequisite statement were checked against the official sources on 10 October 2026. Provider access arrangements can change.

Your deliverable: a 400–600 word decision brief

Write to Leila as the decision-maker. Recommend whether she should operate next month on the starting forecast, whether the 10% price increase is justified by the information available, and whether she should switch services. Distinguish the starting month from the separate ten-month, 240-order scenario. A cautious conditional recommendation can be stronger than an unsupported definite answer.

Open with your recommendation and its scope: the relevant prices, volume, service and time horizon.
Support it with weighted revenue, cash surplus and economic surplus. Explain the role of the editing alternative in ordinary language.
Give the demand boundary for the proposed price change and explain what evidence is still missing.
Evaluate switching with both its ongoing savings and its one-off cash and time costs. Address feasibility and the fragility of the longer-horizon result.
Identify two material assumptions and a practical way to check each. Close with what would cause you to revise your recommendation.

Attach a short calculation sheet outside the word count. Label assumptions, show intermediate calculations and distinguish exact values from rounded display amounts. You may consult the public feedback, but write the recommendation in your own words. Completion records, where available, are study records rather than externally accredited marks.

Self-assessment rubric: 20 points

Economic framing, 4 points: identifies the best alternative, the period and feasible options; correctly treats past costs and avoidable future commitments.
Numerical accuracy, 6 points: calculates weighted revenue and fees, time costs, monthly surplus, demand boundary and switching comparison correctly, with clear units and appropriate rounding.
Uncertainty and boundaries, 4 points: treats demand scenarios as assumptions, checks capacity and sales mix, and explains when the result would cease to apply.
Decision quality, 4 points: gives a supported, conditional recommendation and two specific evidence-gathering steps rather than a list of unexplained numbers.
Communication, 2 points: provides a coherent 400–600 word brief and an auditable calculation sheet without overstating precision or certainty.

A score is useful only if it tells you what to improve. For each category, note one sentence or calculation that earns credit and one change that would make the reasoning clearer.

Public worked feedback: what a defensible recommendation must establish

Operating with A at the starting forecast improves Leila's position by £64.10 relative to available editing. The £244.10 cash surplus alone is insufficient to establish that result because ten hours have an alternative use. Past illustration and design expenditure should not force continued operation.

The proposed price increase is preferable only if its demand and mix effects preserve enough contribution. With the assumed unchanged mix, about 101.5425 expected orders match the original result. The 102-order scenario clears the boundary by less than £1, so it supports caution and measurement rather than a confident prediction.

At 120 orders, A has the better recurring result and avoids switching expenditure. At 240 orders for ten stable months, B is ahead by only £6 after the £72 switch. A defensible brief can decline that switch because the forecast is fragile, provided it acknowledges the positive conditional arithmetic. It can also recommend it conditionally with a clear justification for trusting the assumptions. Neither conclusion should hide the unfavourable three-month comparison or claim first-month payback is feasible.

There is room for judgment about uncertainty and the value of gathering information. There is less room for ambiguous cost definitions or missing alternatives. Revisit the calculation where your conclusion differs, state the changed assumption, and explain how it changes the choice.