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Learn through experiments

Price a fictional pop-up shop

Does the price with highest revenue also give highest profit?

Entering midway? Revisit Trace a loan balance for the preceding worked example, or start here and use the explanation below.

1 · Try

Start with a concrete question

An original synthetic market buys 100 − 5 × price units, floored at zero. All money uses fictional credits. Change price and costs to inspect a business model, not a real investment.

Try the initial inputs, then write a prediction before changing one setting. All calculations run locally on your CPU.

Go directly to the experiment · Review basic mathematics

2 · Predict

What do you expect?

Predict how a higher cost per unit changes your preferred price.

3 · Experiment

Change one thing. Inspect what happens.

  1. Compare prices 8, 10, 12 and 14 at unit cost 4 and fixed cost 80.
  2. Find the highest revenue and highest profit among those choices. Explain the difference.
  3. Raise fixed costs. Check whether the best price changes in this model, and whether operating remains profitable.
Experiment inputs
Inputs
Your settingsMechanism
Calculation belowEvidence
Compare outcomes
Units demanded50
Revenue500 credits
Profit220 credits

Compare the current results

Every bar starts at zero and uses the same numeric scale in this chart. The upper bound automatically adjusts to the largest current value (at least 1), so compare the numbers when changing inputs. Units and quantities come from each label; different kinds of quantity are not interchangeable. Displayed values are rounded to at most six significant digits.
0500
  • Revenue (credits)500
    Revenue (credits): 500Horizontal bar from zero to 500, on the shared zero to 500 numeric axis.
  • Variable costs (credits)200
    Variable costs (credits): 200Horizontal bar from zero to 200, on the shared zero to 500 numeric axis.
  • Fixed costs (credits)80
    Fixed costs (credits): 80Horizontal bar from zero to 80, on the shared zero to 500 numeric axis.

Follow the calculation

  1. Synthetic demand assumption: units = max(0, 100 − 5 × 10) = 50.
  2. Revenue = price × units = 10 × 50 = 500.
  3. Variable cost = 4 × 50 = 200. Fixed cost = 80.
  4. Profit = 500 − 200 − 80 = 220 credits.

Higher prices increase revenue per sale but reduce sales in this assumed market. Revenue is not profit.

Captures keep your inputs, prediction and observation. Results are recalculated from those inputs. Resetting inputs keeps your captures and challenge history.

4 · Understand

Explain the mechanism

Price a fictional pop-up shop

An original synthetic market buys 100 − 5 × price units, floored at zero. All money uses fictional credits. Change price and costs to inspect a business model, not a real investment.

Before you change anything

Predict how a higher cost per unit changes your preferred price.

Follow the mechanism

Revenue is money from sales. Profit subtracts both costs that vary with sales and costs paid regardless of volume.

At price 10, demand is 50. Revenue is 500, variable cost is 200 and fixed cost is 80, leaving profit 220.

At price 12, demand is 40: revenue falls to 480 but profit rises to 240 because fewer costly units are sold.

Calculate it yourself

Demand = max(0, 100 − 5 × price); profit = (price − unit cost) × demand − fixed cost.

Try a counterexample

  1. Compare prices 8, 10, 12 and 14 at unit cost 4 and fixed cost 80.

  2. Find the highest revenue and highest profit among those choices. Explain the difference.

  3. Raise fixed costs. Check whether the best price changes in this model, and whether operating remains profitable.

What this model leaves out

  • Demand is an invented deterministic line, not an estimate supported by customer data.

  • Competition, taxes, capacity, repeat customers and uncertainty are omitted. This is not personal financial advice.

Take it further

High school: Design a fictional fundraiser and distinguish revenue from surplus.

College: Derive the profit-maximizing price and study demand sensitivity.

Working professionals: Write a pricing experiment plan with uncertain demand estimates and guardrails.

5 · Apply

Try a fresh case

A different shop sells 30 units at 9 credits, pays 3 credits per unit and 50 fixed credits. What is profit?

This is a public practice check. Retries support learning; matching a number does not certify independent proficiency.

Take the investigation further

Choose any extension. These are project prompts for you to carry out; they are not automatically assessed.

School investigation

Design a fictional fundraiser and distinguish revenue from surplus.

College investigation

Derive the profit-maximizing price and study demand sensitivity.

Workplace investigation

Write a pricing experiment plan with uncertain demand estimates and guardrails.

6 · Continue

Keep the evidence, choose your next step

Completion records your own decision that you have worked through this investigation. Practice checks and independent project evidence are separate.