Business Economics · Impact of advertising on sales and demand

Optimal Advertising Spending: Dorfman-Steiner Condition Explained

Updated 11 October 2026 · Fact-checked

The Dorfman-Steiner condition says a profit-maximising firm should spend on advertising until the extra revenue from one more rupee of advertising equals one rupee. In ratio form, advertising spending as a share of sales equals advertising elasticity divided by the absolute price elasticity of demand: A/(PQ) = ηA ÷ |ηP|.

Understand Optimal Advertising Spending (Dorfman-Steiner)

A firm that advertises faces a simple trade-off. More advertising raises demand and sales. But advertising costs money. The firm should keep advertising only while the extra profit from it is more than its cost.

This is the usual profit rule applied to a new input. Spend on advertising until the marginal revenue from advertising equals the marginal cost of advertising. The marginal cost of one more rupee of advertising is one rupee. The marginal revenue is the extra revenue (net of extra production cost) that rupee brings in.

The Dorfman-Steiner condition turns this into a neat result. It uses two elasticities. Price elasticity of demand (ηP) tells you how sales change when price changes. Advertising elasticity of demand (ηA) tells you how sales change when advertising spending changes by 1%. The condition says the firm's advertising-to-sales ratio should equal ηA ÷ |ηP|.

Why does this make sense? If demand is very responsive to advertising (high ηA), advertise more. If demand is very price elastic (high |ηP|), the firm has little mark-up to earn on each extra sale, so extra sales are worth less and it should advertise less relative to sales.

The standard model assumes the firm sets both price and advertising to maximise profit, with a constant marginal cost of production. Sales depend on price and advertising. The full condition also links to the monopoly mark-up rule: (P − MC) ÷ P = 1 ÷ |ηP|. Exams usually give you the elasticities and ask for the ratio, or give sales and ask for the budget.

Key rules to remember

Dorfman-Steiner condition: A ÷ (P × Q) = ηA ÷ |ηP|; A is advertising spending, P price, Q quantity, so PQ is sales revenue. Use the absolute value of price elasticity.
Advertising elasticity of demand: ηA = (% change in Q) ÷ (% change in A) = (ΔQ ÷ Q) ÷ (ΔA ÷ A); Measured holding price and other factors constant.
Price elasticity of demand: ηP = (% change in Q) ÷ (% change in P); Negative for a normal demand curve. Use |ηP| in the condition.
Profit-maximising price mark-up: (P − MC) ÷ P = 1 ÷ |ηP|; Holds for a firm with market power, setting price at MR = MC.
Optimal advertising budget: A* = (ηA ÷ |ηP|) × P × Q; Rearranged form for finding the rupee amount.
Marginal rule for advertising: Marginal revenue from advertising = marginal cost of advertising; Spend until the extra net benefit of one more rupee equals ₹1.

How to solve Optimal Advertising Spending (Dorfman-Steiner) questions

Use this method for any question on optimal advertising spending.

1Identify what is asked: the advertising-to-sales ratio, the rupee budget, or a comparison with the current budget.
2List the data: price elasticity ηP, advertising elasticity ηA, price P, quantity Q or total sales revenue.
3Take the absolute value of ηP. Do not use the negative sign.
4Compute the optimal ratio: A ÷ (PQ) = ηA ÷ |ηP|.
5If a budget is needed, find sales revenue PQ and multiply it by the ratio to get A*.
6Compare with the current spending. If current A is below A*, the firm under-advertises. If above, it over-advertises.
7State the assumptions: profit maximisation, price and advertising both chosen optimally, elasticities constant at the optimum.
8Give the answer with units, in rupees or as a percentage of sales.

Quickest way: Ratio shortcut

When to use it: Use this for multiple-choice questions and for any question that gives both elasticities.

Write ηA ÷ |ηP| first.
Convert to a percentage of sales.
Multiply by sales revenue if a rupee figure is needed.
Check the answer is smaller than 100% of sales: a sensible ratio usually is.

Common mistakes in Optimal Advertising Spending (Dorfman-Steiner)

Using the negative price elasticity directly, giving a negative advertising ratio.
Price elasticity is usually negative and students forget the condition uses its absolute value.
Fix: Always write |ηP| and state that you took the absolute value.
Inverting the ratio as |ηP| ÷ ηA.
The two elasticities are easy to mix up under time pressure.
Fix: Remember: advertising elasticity on top. High responsiveness to advertising means a higher ratio.
Applying the ratio to quantity or profit instead of sales revenue.
Students read 'sales' as units sold.
Fix: The base is revenue, P × Q. Multiply price by quantity first.
Treating the condition as a fixed ratio that always holds for every firm.
It is memorised as a formula without its conditions.
Fix: State that it holds at the profit maximum, when price and advertising are both chosen optimally.
Confusing advertising elasticity with price elasticity of demand.
Both are 'elasticity of demand' and the labels look alike.
Fix: Check the denominator of the percentage change: advertising spending or price.
Saying a firm should advertise until sales are maximised.
Students ignore the cost of advertising.
Fix: Stop where marginal benefit equals marginal cost, not where sales stop rising.

Worked examples

Example 1

A firm has advertising elasticity of demand 0.3 and price elasticity of demand −2.5. Its sales revenue is ₹50,00,000. Find the optimal advertising budget under the Dorfman-Steiner condition.

Show the solution

Take |ηP| = 2.5 and ηA = 0.3.
Optimal ratio = 0.3 ÷ 2.5 = 0.12, which is 12% of sales.
A* = 0.12 × ₹50,00,000 = ₹6,00,000.

Answer: The optimal advertising budget is ₹6,00,000, which is 12% of sales.

Example 2

A firm sells 20,000 units at ₹400 each and spends ₹8,00,000 on advertising. Its price elasticity is −4 and advertising elasticity is 0.5. Is it advertising optimally? Say what it should do.

Show the solution

Sales revenue = 20,000 × ₹400 = ₹80,00,000.
Current ratio = ₹8,00,000 ÷ ₹80,00,000 = 0.10, or 10%.
Optimal ratio = 0.5 ÷ |−4| = 0.5 ÷ 4 = 0.125, or 12.5%.
Optimal budget = 0.125 × ₹80,00,000 = ₹10,00,000.
Current spending of ₹8,00,000 is below ₹10,00,000.

Answer: The firm under-advertises. Taking the elasticities as given, it should raise spending by ₹2,00,000 to ₹10,00,000, which is 12.5% of sales.

Exam tips

Always write the formula first. Examiners award method marks even if arithmetic slips.
Check which elasticity is which before substituting. Look for the word 'advertising' in the definition.
In written answers, explain the economic reasoning: marginal benefit of advertising equals its marginal cost.
State the assumptions: profit maximisation, optimal price and advertising, and constant elasticities at the optimum.
In multiple-choice questions, a negative or inverted ratio is usually a distractor. Check your sign and order.

Practice questions from Impact of advertising on sales and demand

Optimal Advertising Spending (Dorfman-Steiner): frequently asked questions

What is the Dorfman-Steiner condition?

It is a rule for a profit-maximising firm that chooses both price and advertising. It says advertising spending as a share of sales revenue equals advertising elasticity divided by the absolute price elasticity of demand.

Why do we use the absolute value of price elasticity?

Price elasticity of demand is normally negative because demand falls when price rises. The condition compares magnitudes, so you use |ηP| to get a positive ratio.

What happens if demand is more price elastic?

The optimal advertising share of sales falls, other things equal. A more elastic market means a smaller mark-up on each extra unit, so extra sales add less profit.

Does the condition mean firms should always advertise a fixed share of sales?

No. The share is optimal only when the elasticities are as given and the firm has set price and advertising to maximise profit. If the elasticities change, the optimal share changes.