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```									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

P

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
A-S curve
C
30
B
20
A
10

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

A

AS

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

T
R
25

0           80            261         263                    Q

1
Using the arc elasticity formula, compute   εA   between A = \$25 and A = \$ 30

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

(P – MC) ΔQ . Equating additional costs and additional net benefits gives

(P – MC) ΔQ = ΔA
or
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.

1
But,                     MR = P(1 -            )
| ε D|
so
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