implement sales including shelf price reductions, coupons (‘free standing inserts’ (FSI) or
electronic), mail rebates, or price packs, see Banks and Moorthy (1999). They classified models
of sales as those related to changes in fundamentals (e.g. changing demand and cost conditions),
price discrimination, and strategic price competition.2 Conslisk et al. (1984) develop a
monopoly model of intertemporal pricing. They distinguish between consumers with high and
low reservation prices, all agents are fully informed and risk neutral. Under these conditions
sales occur periodically to induce purchases by consumers with high reservation prices. Sobel
(1984) extends the model to multiple sellers and finds that in equilibrium sales occur
periodically at the same time across sellers. Inventory-based theories of sales considered by
Blinder (1982), Reagan (1982), or Blattberg et al. (1981) assume that costs of inventory holding
of goods vary across retailers and across consumers. If a significant share of consumers has low
inventory costs, then retailers can minimize their inventory costs by regularly putting products
on sale, transferring the inventory function and cost to consumers. Lazear (1986) introduced
uncertainty about the final demand as might be the case for fashion goods. He shows that
retailers generally start with higher prices reducing them through sales as the season progresses
to discriminate across consumer valuations of fashion. Pesendorfer (2000) presents a dynamic
model of demand accumulation. In every period low and high valuation consumers enter the
market. In addition, low valuation consumers are either store loyal or shoppers.3 Pesendorfer
shows that sales are a function of the time with a price path where an extended period of high
prices is followed by a short period of low prices.4 Hosken and Reiffen (2001) extend the
approach of Sobel by considering two goods, a durable and a perishable item. They show that
price changes for the durable good exceed the changes in prices of the perishable good and that
the price changes are negatively correlated.5 Other motivations for sales are given when goods
are newly introduced (Bass, 1980 or Kalish, 1983), when consumers need incentives to spread
their buying across time (Gerstner, 1986), or when firms want to forward sell products (Salop
and Stiglitz, 1982). Salop and Stiglitz (1977) analyze the impact of search costs on the price
equilibrium. They differentiate consumers with high versus low search costs and suggest there
are informed and uniformed consumers. The uniformed select the retail shop at random, the
informed always search for the lowest price store(s). Under particular parameter conditions a
two price equilibrium exists, in which some retailers charge low prices and others high prices.6
In a similar specification, Narasimhan (1984) models price discrimination between consumers
with higher and lower transaction costs by employing coupons as promotional instrument. To
receive the sale’s price consumers need time. If we assume different opportunity costs and
demand elasticities across consumers, then it is shown to be optimal to discriminate across these
groups by using coupons. For impulse goods Lal and Matutes (1994) or earlier Hess and
Gerstner (1987) show that a loss leader pricing strategy might be a rational for retailers. The loss
We do not consider entirely static approaches, such as the model by Bliss (1988), because we are primarily
interested in the dynamic behaviour of prices, in particular sales or promotional prices. Static models can
explain the occurrence of different or even negative markups (loss leader) for respective goods. However,
an essential feature of sales in our definition is the temporary character of sales’ offers. For an overview of
most of the models presented here see also Blattberg and Neslin (1990).
Shoppers are fully informed and purchase the good at the store that offers the good at the lowest price.
Pesendorfer simplifies the Sobel model by letting his consumers not behaving strategically, but he extends
the model by letting some low valuation consumers to be store loyal (Hosken and Reiffen (2001).
However, it seems to be hard to define which goods are to be considered perishable and which durable.
Hosken and Reiffen (2001) consider peanut butter to be a durable good, while margarine is a perishable
item.
Varian (1980) criticizes that consumers likely learn to know the low price stores in time and thereby
become informed. Thus, the derived two price equilibrium ought to converge to a single price equilibrium
in time.