Strategic Cost Management · Pricing Decisions and Strategies

Demand-Based Pricing and Price Elasticity: Finding the Optimal Price

Updated 11 October 2026 · Fact-checked

Demand-based pricing sets price using how customers respond to price changes. Price elasticity measures that response. To find the profit-maximising price, write marginal revenue from the demand equation, set it equal to marginal cost, solve for quantity, then substitute that quantity into the demand equation to get price.

Understand Demand-Based Pricing and Price Elasticity

Cost-based pricing starts from what the product costs. Demand-based pricing starts from what customers will pay and how many units they will buy at each price. Demand is usually shown as a downward-sloping demand curve: a higher price means fewer units sold.

Price elasticity of demand tells you how sharply quantity reacts to a price change. It is the percentage change in quantity demanded divided by the percentage change in price. It is normally negative, so most people quote its absolute value. If the absolute value is above 1, demand is elastic: quantity falls by a larger percentage than price rises. If it is below 1, demand is inelastic. If it equals 1, demand is unit elastic.

Elasticity links to revenue. When demand is elastic, a price rise lowers total revenue. When demand is inelastic, a price rise increases total revenue. But revenue is not profit. A firm that raises price also sells fewer units and so saves variable cost. Always judge a price change by contribution, not revenue alone.

The profit-maximising rule is marginal revenue (MR) = marginal cost (MC). MR is the extra revenue from selling one more unit. Because you must cut the price on all units to sell one more, MR is less than price. As long as MR is above MC, an extra unit adds to profit. Once MR falls below MC, it reduces profit. So you stop at MR = MC. Then you read the price from the demand curve, not from the MR line.

In exam problems, MC is usually the variable cost per unit, treated as constant. Fixed costs do not change MC, so they do not affect the optimal price or quantity. They only affect the final profit figure.

Key rules to remember

Price elasticity of demand: Ed = (% change in quantity) ÷ (% change in price); Normally negative. Use the absolute value |Ed| to classify: above 1 elastic, below 1 inelastic, equal to 1 unit elastic.
Point elasticity: Ed = (dQ ÷ dP) × (P ÷ Q); For a demand equation Q = a − bP, dQ ÷ dP = −b. Use P and Q at the point asked.
Linear demand (price form): P = a − bQ; a is the price at which quantity is zero. b is the price fall per extra unit.
Total and marginal revenue: TR = P × Q = aQ − bQ²; MR = d(TR) ÷ dQ = a − 2bQ; For a straight-line demand curve, MR has the same intercept as demand but twice the slope.
MR and elasticity: MR = P × (1 − 1 ÷ |Ed|); MR is positive only when |Ed| is above 1. A profit-maximiser with positive MC therefore prices where demand is elastic.
Profit-maximising condition: MR = MC; Also check that MR cuts MC from above, so the point is a maximum. Price is then read from the demand curve.
Markup rule (constant elasticity): P = MC × |Ed| ÷ (|Ed| − 1); Valid only for |Ed| above 1. It follows from MR = MC and the MR–elasticity link.

How to solve Demand-Based Pricing and Price Elasticity questions

Use this method for any question that asks for the optimal price, output or the effect of a price change.

1Write the demand function. If it is given as Q in terms of P, rearrange it to P in terms of Q so that revenue is easy to build.
2Write total revenue: TR = P × Q. Substitute the demand function.
3Differentiate TR with respect to Q to get MR. For P = a − bQ, MR = a − 2bQ.
4Identify MC. Usually it is the variable cost per unit. Ignore fixed costs here.
5Set MR = MC and solve for the optimal quantity Q.
6Substitute Q into the demand function to get the optimal price. Do not use the MR line for price.
7Compute profit: (P − variable cost) × Q − fixed costs. Compute elasticity at that price if asked, and check MR = P(1 − 1/|Ed|).
8State a clear recommendation. Mention any limit such as capacity, or a price below which a unit would not cover variable cost.

Quickest way: MR = MC in four lines

When to use it: Use when demand is a straight line and MC is constant or a simple function. This covers most exam numericals.

Read a and b from P = a − bQ. Write MR = a − 2bQ straight away.
Equate to MC and solve: Q = (a − MC) ÷ 2b.
Price: P = a − bQ. For constant MC this equals (a + MC) ÷ 2.
Profit = (P − MC) × Q − fixed cost. Quick check: elasticity should give MR = P(1 − 1/|Ed|) = MC.

Common mistakes in Demand-Based Pricing and Price Elasticity

Setting price equal to marginal cost, or treating MR as equal to price.
Perfect-competition rules are remembered, where P = MR. For a firm facing a downward-sloping demand curve, MR is below P.
Fix: Always derive MR from TR. For P = a − bQ, MR = a − 2bQ, not a − bQ.
Substituting the optimal quantity into the MR equation to get price.
The MR equation is already on the page and looks like a price line.
Fix: Find Q from MR = MC. Then put Q into the demand equation. Price comes only from demand.
Including fixed costs in MC, or using average total cost.
Students carry cost-plus habits into this topic.
Fix: MC is the extra cost of one more unit, usually variable cost per unit. Subtract fixed costs only when computing final profit.
Differentiating wrongly when demand is given as Q = a − bP.
Revenue is built from the wrong form, so the derivative is taken with respect to the wrong variable.
Fix: Rearrange to P = (a − Q) ÷ b first. Then TR = P × Q and differentiate with respect to Q.
Concluding that a price rise on elastic demand must reduce profit.
Revenue and profit are confused. Elastic demand reduces revenue when price rises, but variable costs also fall.
Fix: Compare total contribution before and after the change. Then state the recommendation.
Dropping the sign or misreading the elasticity value.
Elasticity is negative, and books differ on whether they show the sign.
Fix: Compute with the sign, then classify using the absolute value. Say clearly whether demand is elastic or inelastic.

Worked examples

Example 1

A company sells a product with demand P = 1,000 − 2Q, where P is the price in ₹ per unit and Q is the number of units. Variable cost is ₹200 per unit and fixed cost is ₹40,000. Find the profit-maximising price and quantity, the profit, and the price elasticity at that price. Check whether a price of ₹700 would be better.

Show the solution

TR = P × Q = 1,000Q − 2Q². So MR = 1,000 − 4Q.
MC = ₹200 (variable cost per unit). Set MR = MC: 1,000 − 4Q = 200, so 4Q = 800 and Q = 200 units.
Price from demand: P = 1,000 − 2 × 200 = ₹600.
Contribution = (600 − 200) × 200 = ₹80,000. Profit = 80,000 − 40,000 = ₹40,000.
Elasticity: from P = 1,000 − 2Q, Q = 500 − 0.5P, so dQ ÷ dP = −0.5. Ed = −0.5 × (600 ÷ 200) = −1.5. Demand is elastic.
Check: MR = P(1 − 1/|Ed|) = 600 × (1 − 1/1.5) = 600 × 1/3 = ₹200, equal to MC.
Test ₹700: Q = (1,000 − 700) ÷ 2 = 150 units. Contribution = (700 − 200) × 150 = ₹75,000. Profit = 75,000 − 40,000 = ₹35,000, which is lower than ₹40,000.

Answer: Optimal price ₹600, quantity 200 units, profit ₹40,000. Elasticity at that price is −1.5 (elastic). A price of ₹700 gives a profit of only ₹35,000, so keep the price at ₹600.

Example 2

A firm sells 10,000 units a month at ₹50. Variable cost is ₹30 per unit. Management plans to raise the price to ₹55, and market research says sales will fall to 8,500 units. Calculate the price elasticity of demand, comment on it, and recommend whether to raise the price. Fixed costs stay unchanged.

Show the solution

Percentage change in price = (55 − 50) ÷ 50 = +10%.
Percentage change in quantity = (8,500 − 10,000) ÷ 10,000 = −15%.
Ed = −15% ÷ 10% = −1.5. |Ed| is above 1, so demand is elastic.
Revenue now = 50 × 10,000 = ₹5,00,000. Revenue after = 55 × 8,500 = ₹4,67,500. Revenue falls by ₹32,500, as expected with elastic demand.
Contribution now = (50 − 30) × 10,000 = ₹2,00,000.
Contribution after = (55 − 30) × 8,500 = 25 × 8,500 = ₹2,12,500.
Since fixed costs do not change, profit rises by ₹12,500 a month.

Answer: Ed = −1.5 (elastic). Revenue falls by ₹32,500 but contribution rises from ₹2,00,000 to ₹2,12,500, so raising the price to ₹55 is recommended, provided the research estimate is reliable and long-term customer loss is not expected. (If elasticity stayed constant at 1.5, the markup rule would suggest ₹30 × 1.5 ÷ 0.5 = ₹90, so there may be room for more testing, but the estimate would hold only near the current price.)

Exam tips

In the written questions, show MR = a − 2bQ and the MR = MC step clearly. Marks usually go to the method even if arithmetic slips.
End every pricing numerical with a one-line recommendation. It is a decision question, not only a calculation.
For MCQs, memorise the classification: |Ed| above 1 elastic, below 1 inelastic. Also remember that a price rise raises revenue only when demand is inelastic.
If the question gives capacity or a minimum price, check that the MR = MC answer respects it before you finalise.
When asked to compare two prices, compare contribution, not revenue. Add fixed costs only if the question asks for profit.

Practice questions from Pricing Decisions and Strategies

Demand-Based Pricing and Price Elasticity in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Demand-Based Pricing and Price Elasticity: frequently asked questions

Why is profit maximised where MR = MC?

Each extra unit adds MR to revenue and MC to cost. While MR is above MC, selling more adds profit. Once MR is below MC, selling more reduces profit, so the best point is where they are equal.

Why is marginal revenue less than price?

To sell one more unit, the firm must lower the price on all units it sells, not just the last one. The extra unit brings in its price, but the price cut on earlier units reduces revenue. The net gain is MR, which is below price.

How does price elasticity help in pricing decisions?

It shows whether a price change will raise or lower revenue and how sales will react. A firm with inelastic demand has room to raise price. A firm with elastic demand should be careful about raising it, and must compare contribution before deciding.

Do fixed costs affect the optimal price?

No. Fixed costs do not change with output, so they are not part of marginal cost. They affect only the total profit figure, and whether the product is worth continuing at all.