The Advertising Sales Curve The goal of advertising is to by Cappadona


									The Advertising-Sales Curve

The goal of advertising is to shift the demand curve rightward. The extent of this shift
may be measured by the elasticity of advertising expenditure.

                          % Δ in Q ΔQ A
                εA =               =   ⋅ .
                          % Δ in A   ΔA Q

To understand this concept, note that demand is a function of price and advertising
expenditure, Q= D(P,A). When price is fixed at some value P , quantity demanded is a
function of advertising outlay only -- Q = D( P , A) . The graph of this function is the
advertising-sales curve. The diagram, below illustrates its derivation


                                                        A = $10 along D1
                                                        A = $20 along D2
                                                        A = $30 along D3

                      A        B        C    P

                          D1       D2       D3

           0     50        80       120          Q

                                                 A-S curve

            0    50       80       120                  Q

ε A is the elasticity of the AS curve
Example: Consider the demand curve Q = D(P,A) =100 -2P + ¼ A2 . Suppose price is fixed at
P = $10. The advertising-sales curve is

                   Q = D(10,A) = 80 + ¼ A2

The advertising elasticity when A = $25 is ε A =25 = 1.2. This means that a 10 percent increase in
advertising outlays will increase quantity demanded and total revenue by 12 percent. 1



                                                                                          slope of the ray
                                                                            ε A= 25 =
                                                                                        slope of the tan gent


               0           80            261         263                    Q

    Using the arc elasticity formula, compute   εA   between A = $25 and A = $ 30
The Optimal Level of Advertising

Advertising shifts the demand curve outward and raises fixed costs by the amount spent on
advertising: it does not alter the variable cost functions. Hence advertising raises both costs and
revenues. The optimal level of advertising balances additional revenues and additional costs.

The additional cost of advertising is ΔA. The net additional revenue due to advertising is
(P – MC) ΔQ . Equating additional costs and additional net benefits gives

                         (P – MC) ΔQ = ΔA
                          ΔQ      1
                             =        .
                          ΔA   P − MC

Multiplying both sides by A/Q gives

                             1   A     P    A
                 εA =           ⋅ ≡       ⋅   .                                     (*)
                          P − MC Q  P − MC PQ

Profit maximization requires that

                          MC = MR.

But,                     MR = P(1 -            )
                                      | ε D|
                         P − MC     1
                            P     |εD |

                                                                εA       A
Substituting into (*)gives the Dorfman-Steiner equation:              =    .
                                                               | ε D|   PQ
It says that,

The percentage of total revenue devoted for advertising must be equal to the ratio of advertising
elasticity to price elasticity of demand for profit maximization..

Problem: Peter’s Pompanos is a monopoly seller of frozen pompanos. The price elasticity of
demand for pompanos is -0.75. Peter believes that a10 percent increase in advertising will
increase sales by 1 percent. Peter is currently spending 10 percent of its sales on advertising. We
can conclude that Peter should

a. Increase advertising. b. Decrease advertising. c. Leave advertising at its current level.

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