Impact of advertising on sales and demand: formula sheet

Key formulas

Effect of successful advertising on demand

Advertising ↑ → demand curve shifts right (Q ↑ at each price)

This is the basic result for any advertising that raises willingness to buy. It is a shift, not a movement along the curve.

Effect of persuasion on elasticity

Brand loyalty ↑ → |PED| ↓ (demand becomes less elastic)

Persuasive advertising aims to make demand steeper. This lets the firm raise price with a smaller fall in quantity.

Price elasticity of demand

PED = (% change in quantity demanded) ÷ (% change in price)

Use it to show why lower elasticity helps revenue when price rises.

Advertising elasticity of demand

AED = (% change in quantity demanded) ÷ (% change in advertising expenditure)

Measures sales response to advertising. It is covered further in the advertising elasticity topic.

Net benefit test

Advertising is worthwhile if extra profit from extra sales > extra advertising cost

Advertising is a cost. Compare the gain with the spend.

Price elasticity of demand

PED = (% change in quantity demanded) ÷ (% change in price)

Usually negative; many texts quote the absolute value. Demand is elastic if |PED| > 1 and inelastic if |PED| < 1.

Advertising elasticity of demand

AED = (% change in quantity demanded) ÷ (% change in advertising expenditure)

Positive for a good whose sales rise with advertising. A larger value means sales respond more strongly.

Total revenue

TR = P × Q

Use it to test whether a price rise after advertising still increases revenue.

Net gain from advertising

Net gain = change in profit before advertising cost − advertising cost

Advertising is worthwhile only if this is positive.

Shift versus movement

Advertising → shift of the curve; own price → movement along the curve

State this clearly in written answers.

Advertising elasticity of sales (point/percentage form)

E_A = (%ΔQ) ÷ (%ΔA) = (ΔQ ÷ Q) ÷ (ΔA ÷ A)

Q is sales quantity (or revenue, if stated) and A is advertising spend. Other factors are held constant.

Point elasticity using a derivative

E_A = (dQ/dA) × (A ÷ Q)

Use when the sales response function Q = f(A) is given. Evaluate at the stated value of A.

Arc (midpoint) elasticity

E_A = [(Q₂ − Q₁) ÷ ((Q₁ + Q₂) ÷ 2)] ÷ [(A₂ − A₁) ÷ ((A₁ + A₂) ÷ 2)]

Use for larger changes. It gives the same answer whichever direction you move.

Marginal sales response

Marginal response = dQ/dA ≈ ΔQ ÷ ΔA

Extra sales per extra rupee of advertising. Diminishing returns means this falls as A rises (d²Q/dA² < 0).

Constant-elasticity response function

Q = k × A^b, so E_A = b

Here the elasticity is the same at every level of A. With 0 < b < 1, returns diminish.

Interpretation rule

E_A > 1 elastic; 0 < E_A < 1 inelastic; E_A = 0 no effect

Describe the size of the response, not just the number.

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.

Long-run equilibrium, monopolistic competition

P = AC (including advertising cost) and MR = MC

Normal profit in the long run. Advertising cost is included in AC, so the price is higher than without advertising.

Advertising-to-sales ratio

Advertising ratio = advertising expenditure ÷ sales revenue

A high ratio suggests advertising is an important competitive tool or entry barrier. Interpret it with care, since it does not prove a barrier on its own.

Dorfman-Steiner condition

A ÷ R = e_A ÷ |e_P|

A is advertising spending, R is revenue, e_A is advertising elasticity of demand and e_P is price elasticity. It is a profit-maximising rule for a firm with market power. Revise it under optimal advertising spending.

Profit rule

Profit-maximising output where MR = MC

Advertising shifts demand and so changes MR. The rule itself stays the same.

Welfare test

Net welfare effect = benefits (information, lower search costs, scale economies) − costs (higher price, barriers, wasteful spending)

A qualitative rule. Use it to structure the evaluation.

Quick revision

• Informative advertising gives facts; persuasive advertising tries to change preferences and build brand loyalty.
• Advertising aims to raise demand, reduce price elasticity, build loyalty, or deter entry.
• Successful advertising shifts the demand curve to the right at each price.
• It can also make demand less elastic, which lets the firm raise price.
• Advertising elasticity = % change in quantity demanded ÷ % change in advertising expenditure.
• Dorfman-Steiner: advertising spend ÷ sales revenue = advertising elasticity ÷ |price elasticity|.
• The rule assumes the firm maximises profit and that price elasticity is measured as a magnitude.
• Higher advertising elasticity or less elastic demand means a higher optimal advertising-to-sales ratio.
• Advertising has diminishing returns, so extra spend adds less and less to sales.
• Advertising is most important where products are differentiated, such as monopolistic competition and oligopoly.
• Welfare effects are mixed: more information and choice versus higher prices, barriers to entry and waste.
• State your assumptions in written answers and show each step of the working.

Common mistakes

• Treating informative and persuasive advertising as the same thing. Fix: Ask what the advert mainly does. Giving facts is informative. Changing tastes or building loyalty is persuasive.
• Showing advertising as a movement along the demand curve. Fix: Advertising changes a non-price determinant, so the whole curve shifts. Only a price change moves along it.
• Showing advertising as a movement along the demand curve. Fix: Advertising is not the price. Draw a new curve to the right and label it D2.
• Saying advertising always makes demand inelastic. Fix: Say it can make demand less elastic if it differentiates the product. Comparative price advertising can make demand more elastic.
• Confusing advertising elasticity with the marginal response dQ/dA. Fix: Elasticity is a ratio of percentages with no units. Marginal response is in units per rupee. Multiply dQ/dA by A ÷ Q to convert.
• Using the new value instead of the original as the base for percentage change. Fix: Divide changes by the starting values unless the midpoint method is requested. Write the base next to each calculation.
• Using the negative price elasticity directly, giving a negative advertising ratio. Fix: Always write |ηP| and state that you took the absolute value.
• Inverting the ratio as |ηP| ÷ ηA. Fix: Remember: advertising elasticity on top. High responsiveness to advertising means a higher ratio.
• Saying advertising is always harmful or always beneficial. Fix: Give both sides, then conclude that the effect depends on the market and the type of advertising.
• Claiming monopolistic competition earns supernormal profit in the long run. Fix: Free entry removes supernormal profit. State that long-run profit is normal and AC includes advertising.

Exam tips

• Always name the type of advertising before you discuss effects. Examiners reward correct classification.
• When asked about effects, mention both the shift of the demand curve and the change in elasticity.
• Link advertising to non-price competition and to market structure in any written answer.
• In evaluation, mention cost and rival response. A one-sided answer loses marks.
• In multiple-choice questions, look for key words: facts and features point to informative, image and loyalty point to persuasive.
• Always draw the diagram, even when the question does not insist on one. Label D1, D2, P, Q1 and Q2.
• Use the words shift and movement precisely. Examiners look for them.
• When numbers are given, include the advertising cost before judging whether it was worthwhile.