Measuring and Testing Advertising-Induced Rotation in the Demand Curve



can rotate a demand curve as well by changing the spread of the WTP. The former
case is illustrated in figures (1a-1c), and the latter case is illustrated in figures (1d-
1f), wherein the dotted and boldfaced curves denote scenarios before and after a
hypothetical successful advertising campaign for milk, respectively. Suppose the
WTP for milk before the advertising follows a normal distribution with a mean of
three and a variance of one. The dotted curve in figure (1a) represents the
probability distribution function (pdf) of the milk WTP. A successful milk
advertising campaign was usually assumed to shift the pdf of the milk WTP outward
without changing its spread, implying that the advertising increased the WTP of all
milk consumers unanimously. If the milk advertising increases every consumer’s
WTP by two (a large number to make the curves before and after advertising look
distinct), then the pdf of the milk WTP after the advertising follows a normal
distribution with a mean of five and a variance of one, represented by the boldfaced
curve in figure (1a). An outward shift of the pdf results in an outward shift of the
cumulative distribution function (cdf), which is shown in figure (1b). Note that any
point cdf(WTP
0) on the cdf curve indicates the proportion of consumers that will not
purchase milk since their WTP’s are less than WTP
0. Therefore, q (=1- cdf(WTP0))
is the proportion of consumers that will purchase milk for a given price of WTP
0.
Mapping the WTP to the vertical axis and corresponding q to the horizontal axis, we
have the familiar inverse demand curves in figure (1c), which shows that an outward
shift of the pdf caused by the advertising finally leads to an outward shift of the
demand curve.

At issue here is that advertising may change the spread of the pdf by



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