Journal of Economic Behavior Organization Vol. 44 2001 347–362
Buyer experimentation and introductory pricing
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Edward E. Schlee
Department of Economics, College of Business, Arizona State University, Main Campus, PO Box 873806, Tempe, AZ 85287-3806, USA
Received 3 December 1998; received in revised form 1 September 1999; accepted 1 September 1999
Abstract
We study the pricing decisions of a monopolist seller in a two-period model in which buyers and the seller are all uncertain about a good’s quality. We assume that buyers not only learn from
experience, but also may experiment, that is, increase the amount of information by consuming more. We define an introductory price to be a first period equilibrium price lower than that which
maximizes period 1 profit. The motivation for introductory pricing is that, under certain conditions, the seller prefers its buyers to be better informed about quality. A lower initial price increases
consumption and hence information. We consider two versions of the model: identical buyers with a public signal of quality; heterogeneous buyers who each receive a private quality signal.
© 2001 Elsevier Science B.V. All rights reserved.
JEL classification: D8
Keywords: Experimentation; Introductory pricing; Quality uncertainty; Learning
1. Introduction
Firms often tempt potential buyers to try a good with a low “introductory price”. Indeed, in the case of free samples, the introductory price is zero for a limited quantity, or even
negative, since samples are often mailed to consumers, freeing them from the necessity of searching for the good. Intuitively, one purpose of introductory offers is to inform consumers
of the existence and attributes of a good. Implicit in this explanation is that consumers are imperfectly informed about product quality, but learn through consumption experience.
Grossman et al. 1977 formulate a model in which a buyer experiments to learn about a good’s quality while facing an exogenous time path of prices: in each period the buyer
chooses a consumption level of good, observes a noisy signal of the its quality and then up- dates beliefs. In this paper we suppose that a monopolist seller sets the prices that buyers face,
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This work revises an earlier working paper entitled “Learning about Product Quality and Introductory Pricing”. 0167-268101 – see front matter © 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 7 - 2 6 8 1 0 0 0 0 1 3 4 - 7
348 E.E. Schlee J. of Economic Behavior Org. 44 2001 347–362
taking into account the information about quality generated by first period consumption. We define an introductory price to be a first period price lower than that which maximizes
period 1 profit.
1
The motivation for introductory pricing in our model is that, under certain conditions, the seller prefers that buyers have more quality information rather than less. A
lower initial price increases consumption and hence information under our assumptions. Experimentation is essential to our explanation, since the seller would have no incentive to
lower price if larger consumption were not more informative.
We assume that the seller and buyers are all initially uncertain about quality. Much of the literature on pricing with quality uncertainty assumes that quality information is asymmetric,
usually that sellers know the quality, but buyers do not. While this case is clearly important, there are nevertheless goods for which both buyers and sellers are uncertain about quality.
New medical treatments and nutritional supplements are examples. Moreover, if we think of quality simply as how well the good fits consumer preferences, then uncertainty on both
sides of the market is surely usual, especially for new goods.
2
In our model, the seller first sets a price and then the buyers choose the period 1 consump- tion. A noisy signal of the good’s quality is then realized and they repeat the monopoly game
in period 2. We consider two versions of the model. In the first all buyers have identical preferences and information at all times, so that we can describe the demand side of the
market by a representative buyer. In particular, all agents observe a public signal of quality. We offer two interpretations of the representative buyer assumption. The first is that there is
really only one buyer. As an example, the buyer could be a downstream firm who purchases an input of uncertain quality from an upstream firm.
3
The public quality signal in that case could be the output produced by the downstream firm. The second interpretation is that there
are many buyers with identical preferences and income, each of whom observes a noisy signal of the good’s quality as well as the aggregate performance of the good; individual
experience is aggregated either by word of mouth or more formally through public statistics concerning the good’s attributes.
4
For example, if the good is a dietary supplement or one, such as alcohol, with uncertain health consequences, then the signal might be an indicator
of the health of the population. Alternatively, the aggregate experience could be revealed by publication in outlets such as consumer reports. In this second interpretation, no individual
buyer will experiment, since a single small buyer has no influence on the aggregate outcome. In the one buyer case, however, the buyer will generally have an incentive to experiment.
Thus the precise form for the first period demand will differ in the two interpretations.
The representative buyer model captures one extreme in which all information is public and buyers are identical. In the second version of the model, buyers may have different
preferences and each observes a private quality signal which is revealed neither to other
1
Another definition would be a first period price that is lower than the second period price. We cannot use this definition here since our second period price is random, and could be lower than the “introductory” first period
price as a result of a bad first period consumption experience.
2
Judd and Riordan 1994 and Bergemann and Valimaki 1996a,b, for example, adopt this interpretation.
3
Bergemann and Valimaki 1996a use this example to motivate their single buyer model.
4
Observability of the aggregate experience is maintained in Bergemann and Valimaki 1996b and McFadden and Train 1996. The last paper considers the issue of whether consumers should try a good first, or delay consumption
until more is known about the good’s quality.
E.E. Schlee J. of Economic Behavior Org. 44 2001 347–362 349
buyers nor to the seller. Hence the seller does not know what buyers have learned when it sets its period 2 price, merely that they have learned something.
Our main results are Theorems 1 and 2. Theorem 1 considers the representative buyer case, while Theorem 2 considers the case in which each buyer observes a private quality signal.
The idea underlying our results is that if higher consumption levels are more informative and the firm prefers that buyers have more information, then the firm will charge a low
first period price. After providing conditions implying that higher consumption is more informative, the issue is then to determine when the seller prefers the buyers to be better
informed.
Consider first the representative buyer, public information model. We show that if the utility function is quasilinear in a composite good representing spending on all other goods
then public quality information is valuable to the seller. Intuitively, the firm will prefer buyers to be better informed if the price it can charge at given quantity — its inverse demand — is,
on average, the same or higher with better information so that, after the firm adjusts its sales in light of the new information its expected profit will be higher with better information. The
inverse demand will be the same or higher with better information if it is a convex or linear function of beliefs. To clarify this point, let px, ρ be the inverse demand at the quantity x
with prior belief ρ that quality is high. Thus, in the absence of further information the firm can charge px, ρ for quantity x. Suppose now that agents receive one of two possible
signals of quality, and let the belief rise to ρ
g
if buyers receive good news and fall to ρ
b
if they receive bad news. Since the expected posterior must equal the prior belief about quality, the average willingness to pay is the same or higher if px, . is a weakly convex
function of beliefs.
5
With quasilinear utility, the inverse demand is linear in beliefs, hence convex.
In the representative buyer, public information case, all parties always have the same information. Hence the seller faces a deterministic demand in each period. In the hetero-
geneous buyer, private information case, the seller faces a random second period demand: for each price, the quantity sold is a random variable since it depends on the signals that
buyers observe, but the seller does not. In that case quasilinear utility no longer suffices for introductory pricing. We show, however, that the value of public information is positive to
the seller if buyer demand functions are convex in beliefs. We show that the demands will be convex in beliefs in the quasilinear case if the high quality inverse demand curve is flatter
in quantity than the low quality inverse demand, and if both demand functions are convex in price.
Many papers of course have studied pricing under quality uncertainty.
6
Our analysis is probably closest, however, to three papers. Mirman et al. 1993 study a two-period model
of a monopolist learning about its demand curve.
7
The firm faces one of two random inverse demand curves. In each period the firm decides how much to sell, and a price is
drawn from one of the two distributions. The firm then updates beliefs about demand and
5
If λ is the probability of receiving goods news, then the expected price with the information for a given quantity is λpx, ρ
g
+ 1 − λpx, ρ
b
; since the expected posterior equals the prior, ρ, this expected price will exceed the sure price with no information, px, ρ, if p is convex in ρ.
6
A sample includes Judd and Riordan 1994, Bagwell and Riordan 1991, Milgrom and Roberts 1986, Lazear 1986, Cremer 1984, and the references contained in these papers.
7
See Treffler 1993 and Creane 1994 for other experimentation models that may yield introductory prices.
350 E.E. Schlee J. of Economic Behavior Org. 44 2001 347–362
decides how much to sell in period 2. They show that the firm will sell more initially than would maximize period 1 profit if the higher mean inverse demand curve is flatter than the
lower: intuitively, selling more spreads the two distributions farther apart, making it easier to tell from which distribution the price realization is drawn. Since higher output leads to
a lower mean price, this result is consistent with introductory pricing. Interestingly, this slope condition is also part of our sufficient condition for introductory pricing in the case
of heterogeneous buyers. In their model, however, only the firm learns and information is always valuable to it; the issue is to determine whether larger quantities give the firm a
more informative demand signal. In the heterogeneous buyer version of our model, only the buyers learn and we assume that higher consumption is more informative; the issue is
to determine whether the firm prefers buyers to be better informed.
Judd and Riordan 1994 consider a two-period model in which both consumers and firms are uncertain about quality, and who each observe a private signal of quality after
making their first period choices. The firm then attempts to signal its private information to consumers with its second period price. In our model, the firm has no private information
and hence no incentive to signal in the second period. A more fundamental difference, however, is that, although consumers learn in their model, there is no experimentation:
quality information is independent of first period consumption, and so the firm has no informational incentive to lower the first period price, as it does in our model.
Bergemann and Valimaki 1996a
8
study an infinite horizon duopoly model in which the firms use price to influence buyer experimentation, while competing in each period in
prices. All agents are uncertain of quality and all agents observe the same public quality signal. They assume that the single buyer can buy at most one unit of the good from the
market and has quasilinear preferences. The focus of the paper is whether learning in the long run is efficient. They observe, however, that for a particular equilibrium of their model
the cautious equilibrium the time t price is lower than the myopic equilibrium price, so that introductory pricing arises in their model as well see their Section 4.2. By examining
a two-period monopoly, rather than an infinite horizon duopoly, we are able to consider a richer set of buyer preferences than unit demands; moreover, we also consider the case of
heterogeneous buyers who each observe a private quality signal.
9
Our model is clearly related to the literature on strategic experimentation. Aghion et al. 1993, Mirman et al. 1994 and Harrington 1995 all consider duopolists who experiment
to learn about demand while competing with one another. In each of these papers, the signal is publicly observed, so that an experimenting firm affects its rival’s information as well as
its own. In our model, the seller attempts to manipulate the learning of buyers; the foregoing papers do not explicitly model the consumer side of the market. Finally, Schlee 1996a
studies the value of public information about quality in a one-period model. The main concern of that paper, however, is to determine when the value of information is negative
to buyers; our analysis focuses on the value of information to the seller.
8
See also Bergemann and Valimaki 1996b.
9
Shapiro 1983 considers a model in which the monopolist knows the quality, but the buyers do not. The monopolist charges a low introductory price if consumer beliefs are pessimistic, i.e. if they underestimate the true
quality. In our model, however, firms and consumers have the same beliefs about quality, so introductory pricing does not arise because consumers are pessimistic. If we allowed different priors, however, then we would get an
additional motive for introductory pricing that would be similar in spirit to Shapiro 1983.
E.E. Schlee J. of Economic Behavior Org. 44 2001 347–362 351
2. The model with a representative buyer
