A MODEL OF PRICE ADVERTISING

The following simple model of price advertising takes an intertemporal approach based on assumptions similar to those in Sibley (1995). Each firm considers two groups of consumers - those who buy from that firm and those who do not. Only those who buy have full information about changes to that firm ’s prices. Other

consumers only find out about changes in prices through advertising or by undertaking search. As with Sibley, advertising increases the probability that a firm contacts a potential customer at any particular time.

A firm may charge two prices, ?h or (where P^ > P J . Potentially the firm has a total of m(Pj) customers (j = H or L). In reality, some consumers may not have full information about prices and so the actual number of customers at time t, (%(), may be less than m. Specifically, if the firm increases its price from P^ to all its existing customers know the new price. Those not prepared to buy at Py drop out of the market and the actual number still equals the potential number of customers.

However, if the firm decreases its price from Ph to P^, existing customers realise the price has dropped and continue to purchase. New customers who would be prepared to buy at P^ do not know that the price has changed. Here, the actual number of customers may be less than the potential number:

< m{Pj) (7.1)

In this model, information is only imperfect in the case of a decrease in price. It is in this case that the firm may have an incentive to undertake advertising which provides price information and/or for the potential consumers to undertake some search

A two period gam e is considered here. In the first period the firm decides on its

price and advertising strategy and in the second, consum ers decide whether or not to

buy the product.

Period 1: The price is set initially at ?h and n^ = m(PH). In otlier words, all customers know that the firm is charging Py. For some reason, such as a supply shock, the firm decides to reduce the price to ?l

Period 2: Under the new price, the firm would have m (P J customers under perfect information. However, since some people are unaware of the price fall there are only Ü2 actual customers. Let x be the difference between the potential and actual number

of sales in period two:

X = m{Pj) - (7.2)

When there is no advertising and no search activity, n2 = m(?H) and x is determined

purely by the price elasticity of demand of existing customers. When there is perfect information, n2 = m (P J.

Thus m(P^) < < m{Pj)

or 0 < X < [m{Pj) - m(P^)] (7.3)

Information on prices may be revealed in two ways: potential customers may undertake search activity or they may receive advertisements from firms. Search activity (S) involves a cost to the consumer and any level of advertising (aj, which

may include information on prices, involves a cost to firm i.

In Period 1, firms decide how much price advertising to undertake following the price decrease, given the amount of search they would expect consumers to do. In Period

2, consumers decide how much search to undertake, given the amount of price

advertising they receive. Thus, as in Robert and Stahl (1993), advertising and search activity are interdependent. The more a firm advertises, the less incentive there is for consumers to search, and vice versa.

The intensity of search activity will depend on its expected costs and benefits. Laband (1991) argues that the value of search for information about the quality of the good can be approximated by the price of the product. The higher is the price, the greater is the loss to the consumer if the product is a disappointment. However, there are many factors other than price which affect the benefits of search. Stigler (1961), for example, suggests that consumer search will be less worthwhile for final, than for intermediate, consumers. A firm buying an expensive piece of machinery is much more likely to search around for the best deal than someone thinking about buying a chocolate bar. However, in addition, the firm buying machinery may have a host of other specifications (such as highly specialised technical requirements) which render price less important than even similarly priced consumer goods. When features such as quality or technical specifications are very important, the benefits from search on price may be very low even for quite expensive goods. Thus, in this model, the value of search in a market is modelled quite generally as depending on the relative

Laband (1991) ignored the cost of search due to lack of data. Here it is assumed that the cost of search for consumers is constant across firms and dependent solely on the number of competing firms in the market. The more firms there are to search amongst, the more expensive it is for consumers to obtain full information on prices from search.

From the firm’s point of view, their decision on how much price information to give will depend on how many extra consumers are expected to result from the advertising (at its maximum equal to x) and also on its expected cost. The former will be a positive function of the importance of price to consumers in that market and a negative function of the amount of search that consumers decide to undertake. This model focuses on the intensity of price information in a firm ’s advertisements rather than the amount of advertising itself. It is therefore assumed (following Laband, 1991) that, for any given level of advertisements, a;, the marginal cost to firm i of providing price information is constant^^. For simplicity, it is further assumed that all firms in a particular market adopt the same price advertising strategy. This gives us:

Pi = Pi(S,r) (7.4)

S = S(Pi,T,N) (7.5)

where pj = proportion of firm i’s advertisements that contain price information.

^^To be precise, Laband actually assumes that the cost of including information is zero for any level of advertising. However, presumably there is some opportunity cost in including price information rather than some other advertising content.

s = amount of search consumers undertake in firm i’s market r = relative importance of price in firm i’s market.

N = number of companies in firm i’s market.

The above discussion implies the following partial derivatives: dpJdS < 0; dpjdr > 0; dS/dpi < 0; dS/dr < 0; dS/dN < 0. In addition, it is assumed that dp/dS > -1 and dS/dpi > -1. That is, an increase in search will not cause the total amount of price advertising to decline more than proportionately and vice versa.

Combining (7.4) and (7.5) gives us a reduced form equation for price advertising:

p. = p[S(p.,T,N),T] (7.6)

Of interest here is what happens to price advertising as the number of firms and the importance of price change.

As the number of firms increase, so does the cost of comprehensive search and, all else being equal, firms expect lower levels of search. This gives firms an incentive to increase the amount of price information they provide. More formally, the total derivative of p; with respect to N is given by:

‘ip, dS ■dN

dN

, 9 5

dp,' dS

(7.7)

From the partial derivatives above, it is clear that both the numerator and the denominator of equation (7.7) are positive, implying the total derivative is also positive. This contrasts with Robert and Stahl (1993) who find that entry reduces the

total amount o f advertising (although firms compete more aggressively on price).

As the importance of price in the market increases, there are two effects. First, the number of potential new customers following a price cut is increased, suggesting that firms will engage in more price advertising. At the same time, firms expect

consumers to search more, implying an indirect negative effect on price advertising. Again, the overall effect can be formally shown through the total derivative of p with respect to r:

4c, _ dS dr dr

_ _ _ --- -- --- \l

. a s

ap/ as

The total derivative is positive only if:

as ^ ^ (7.9)

àS ÔT dr

As it has been assumed that ôp/5S > -1, the total derivative will be positive if d^Jdr is not less than bStdr. In other words, an increase in price importance will increase price advertising if the direct effect on price advertising is greater or equal to the direct effect on search. In situations where search is very important (for example in the case of some producer goods), the effect of price importance may disappear or even become negative.

7.3 TESTING THE MODEL