Download Marketing and the Economics of Convenience

Marketing and the Economics of Convenience
Bart J. Bronnenberg∗
September 25, 2012
Preliminary and incomplete!
Abstract
This paper develops a simple economic theory about mass-marketing and convenience. Without manufacturer-provided distribution and communication, consumers
spend more resources visiting sellers and gathering information about their products.
Travel- and search costs are fixed to quantity. They limit the demand for variety like
prices limit the demand for quantity. To avoid being an unwanted variety, competing
manufacturers seek to change demand for their variety, i.e., to create customers. In
equilibrium, they invest in providing convenience and achieve a socially desirable division of the cost of using the market into a consumer cost of buying and a manufacturer
cost of selling.
JEL: D11, L1, M3
∗
Professor of Marketing and CentER Research Fellow at Tilburg University, The Netherlands. I thank
Jan Boone, Pradeep Chintagunta, Yufeng Hwang, Matthew Gentzkow, Thomas Otter, Carlos Santos, Jesse
Shapiro, Benjamin Tanz, Frederic Vermeulen, Naufel Vilcassim, Birger Wernerfelt and seminar participants
at Duke University, New York University, and Tilburg University for comments and suggestions. I thank the
Netherlands Foundation for Scientific Research (NWO Vici Grant) for financial support. All errors are mine.
1
“Now the problems of market distribution are no less worthy of systematic study than
are the problems of factory production. It is as essential that the finished goods be moved
from the stock room of the producer to the hands of the consumer, as it is that operations
be performed upon the raw material to produce the finished goods. And the problems
of marketing are even more complicated than the problems of manufacturing, because the
human factor is of more importance.”
A.W. Shaw (1912, p. 704), Quarterly Journal of Economics.
The cost of using the market is high. In 2007, the United States of America laid out US$2.4
trillion to connect producers to consumers, an amount equal to 17% of the United States Gross
Domestic Product (GDP).1 It has been high for a long time. At least since the end of the
American Civil War (1861-1865), the combined retail and wholesale margin of manufactured
goods has been between 30% and 45% of retail value. It is also high everywhere. Across
the 209 countries in the United Nations database, the percentage of 2007 GDP allocated to
retailing, wholesaling, and communication averages 23% with a standard deviation of 8%.
In light of the ubiquitous activity involved, it is surprising that the contribution to society of manufacturer-provided distribution to consumers has received little study from the
economic sciences (and the business sciences), especially relative to the role of manufacturing. Economic models of general equilibrium mostly assume frictionless exchange between
producers and consumers where the role of the distributor of products and the provider of
information is played by a costless Walrasian auctioneer. Such a view of the society is however at great odds with reality and places the institutions that operate the market at the
side-lines of analysis.
In this paper, I treat distribution of products and information as economic activity. In
particular, I study when a costly system of distribution and communication emerges as
as a complement to a system of mass production from the decisions of profit maximizing
manufacturers and when it serves society. This system is referred to as mass marketing.2 To
1
I provide calculations in Appendix A.
My definition of marketing is limited to the distribution of products and information, i.e., the provision
of convenience. There is also a “persuasive” marketing system intended to change the understanding or the
2
2
evaluate the merits of mass marketing, I first propose a “no-marketing” model of demand
and supply to serve as a benchmark.3 It consists of an economy with many differentiated
manufacturers who each sell a single variety, quietly and from the factory-door. To buy a
given variety, even to learn about its price, a consumer visits, at some cost, the manufacturer
who produces it. Once there, the consumer can buy any quantity that maximizes utility.
The consumer’s cost of buying therefore contains a fixed “per-variety” component, which is
high when marketing is absent.
Introducing fixed costs of buying into economic analysis, changes the nature of demand,
of competition, and of the functions that firms perform in fundamental ways. In particular,
demand for variety is curtailed by the consumer’s cost of using the market, just like demand
for quantity is limited by price. The manufacturer’s fear of becoming an unwanted variety intensifies competition. In equilibrium, a costly marketing function emerges from the decisions
of profit maximizing manufacturers depending in an interesting way on a few key parameters. In other words, when consumers face per-variety fixed costs, manufacturers become
marketeers. Consumers benefit from this non-price competition relative to competition in
price alone. Surprisingly, in the circumstances considered, welfare can not be bettered by a
social planner.
To bear out these ideas in the most straightforward fashion, my formalization comes at
the cost of simplicity. In particular, I use a setup where consumers have constant elasticity
of substitution (CES) preferences and differentiated manufacturers compete with each other
until profits are driven down to 0.
The paper contains six parts. Section I informally discusses the role of convenience and
sets out the main ideas carried through in analysis. Section II presents the demand model
perception of what is offered to the consumer. Albeit important (see e.g., McCloskey and Klamer 1995) this
system is not studied here.
3
This idea is not new. Alderson (1948) proposes “If there were no distribution system at all, each consumer
would have to visit the farm or factory or handicraft shop in which desired products were made; make their
own selections; and arrange for transportation to their home. What actually happens may be compared
against this standard of zero distribution and the difference represents the output of the distribution system.”
3
that takes into account consumer fixed costs. Section III adds the “no-marketing” supply
side and shows that, in equilibrium, variety can be in short or excess supply relative to the
demand for it. Section IV considers when manufacturers use marketing to lower transaction
costs and whether the market provides the socially desired amount of marketing. Section V
applies the theory to an enduring debate about the cost of distribution. Section VI concludes
with suggestions for future research.
I.
Transaction costs and marketing
Coase (1937) defined transaction cost as the cost of using the price mechanism. In his theory,
firms eliminate certain exchanges from the market and replace them by managed coordination
at a lower cost. This view helped explain vertical integration and the boundaries of the firm
in terms of production, e.g., the decision to either make or buy products.
This paper uses a somewhat similar logic to broaden the role of the firm from production to
also include the engineering of transactions by means of marketing. Drucker (1973) is among
the first to observe that an important purpose of a business firm to engineer transactions, or
to “create a customer.” But, why are not all consumers also customers? In this paper, it is
because the cost associated with the consumer’s unassisted use of the market is high, which
in turn makes a variety expensive. In order to sell in this situation, firms need to “create
a customer” by lowering that consumer’s cost of using the market. Considering the costly
nature of transactions between consumers and producers thus expands the function of the
firm to include the economic decision to serve a customer.4 This is the role of marketing.
A key question about this function in the context of its social desirability is then: “How
should the costs of using the market be shared between buyers and sellers?” The answer
provided in this paper requires expanding the economic model of the consumer from “how
4
Recently, Arkolakis (2010) studies the implications of a reduced form model of how firms strive to create
a customer in international trade.
4
much to buy?” to “who to buy from?” In the proposed model, per-variety fixed costs of
using the market enter the consumer’s problem of “who to buy from” as a constant “price”
for variety which is traded-off against diminishing marginal love for variety. In effect, this
gives rise to a demand system consisting of two interrelated parts. The first is the more
traditional demand function for quantity, whereas, as a result of the aforementioned tradeoff,
the second is a demand function for variety. With limited demand for variety and for quantity,
marketing and its relation to price competition become important.
This research is related to existing work in economics in several important ways. Much
has been written about whether the market produces the right amount of variety. Indeed, the
question of how many manufacturers should enter for the social good has been at the heart
of research in economics (Dixit and Stiglitz 1977; Mankiw and Whinston 1986; Spence 1976)
and marketing (Bayus and Putsis 1999; Kim, Allenby and Rossi 2002). Whereas these studies
look at optimal variety from the supply side, I focus on the role of the demand side. When
transaction costs are high, the consumer forgoes variety. In this situation, manufacturers
face an extensive consumer margin. Because marketing lowers the consumer’s transaction
cost at a business expense, its effect in the aggregate is to raise demand for variety while
reducing its supply. This frames the question about the right amount of variety as a question
about coordination of demand and supply for variety by the institutions in the market place.
Like price regulates the demand and supply of quantity, i.e., produces the “right” quantity,
so does the costly engineering of transactions regulate the demand and supply of variety.
Another relation to the literature is formed by how welfare is produced. Welfare rises
in my model because consumers buy more variety and firms make better use of economies
of scale. It shares this explanation with the literature on trade and increasing returns (e.g.,
Krugman 1979, 1980). However, the mechanism behind these benefits differs and is complementary. International trade creates a world market which allows more firms to recoup
their entry costs than separately in each domestic market. This generates more variety from
5
which consumers benefit. In contrast, in my paper consumers have fixed costs and firms’
actions to lower them allows consumers to buy more variety, keeping the number of firms
constant. Also, economies of scale do not arise from access to larger markets. Instead, they
arise from manufacturer exit due to the cost of marketing. Although paradoxical at first, this
type of exit is beneficial. Namely, in equilibrium, exit is limited to excess-supply of variety,
i.e., variety for which consumers had no demand. The setup costs saved are put to better
use by investing in marketing and lowering the consumer’s total cost of buying. Thus, when
the market is not coordinated, marketing converts entry cost associated with excess variety,
through business rivalry over customers, into more convenience and lower prices. Further,
marketing competition produces an efficient outcome. Among all combinations of prices and
transaction costs that equate demand for variety to supply, marketing competition produces
those that maximize welfare to consumers.
A formalization of these arguments starts next with a model of demand.
II.
A.
Demand for quantity and variety
Introduction
Consider a one-period economy consisting of a continuum of differentiated firms each producing a single unique variety ω ∈ Ω. Ω denotes the total set of supplied varieties. There
is a unit mass of consumers who have constant elasticity of substitution (CES) preferences
(Dixit and Stiglitz 1977) over a continuum of varieties as follows,
Z
U (x, Ω) =
x (ω)
σ−1
σ
dω
σ
σ−1
.
(1)
ω∈Ω
In this formulation, σ is the elasticity of substitution between two varieties ω1 and ω2 . Two
varieties are closer substitutes when σ is larger. I consider markets for substitutes, which
6
is the case when σ > 1. Using a continuum of varieties, rather than a discrete set, is for
analytical convenience.
Consumers are endowed with L units of labor that they supply to the market inelastically
at a wage w = 1, which is the numeraire. The quantity L has the interpretation of total
consumer income (e.g., Becker 1965), i.e., income if the consumer only worked.
There are costs to using the market that arise from differences in location and information
between manufacturers and consumers. To obtain each variety, the consumer allocates part
of his resources to travel where it is sold, learning about price and other terms of purchase,
negotiation with sales agents, etc. As argued above, many of these costs are “per-variety,”
i.e., they are fixed with respect to quantity. The consumer’s fixed cost of using the market
to buy variety ω is µ (ω) and manufacturers charge prices p (ω). Transaction costs µ are
expressed in monetary units, in this case in hourly wage.5
Fixed costs enter the model via the income constraint. This effectively causes a difference
between total income L, and income disposable for consumption Y . In particular, income
available for consumption is equal to
Y =L−
Z
ω∈Ω0
µ (ω) dω,
(2)
where µ (ω) is the transaction cost of obtaining variety ω, and Ω0 is the set of varieties
purchased by the consumer, {ω ∈ Ω0 : x (ω) > 0}..
Fixed transaction costs affect the consumer’s demand for variety. If the consumer visits
only a subset of manufacturers Ω0 ⊂ Ω, he can save on transaction costs. From equation
5
The assumption relies on consumers’ willingness to trade money for convenience. Studies report that
consumers are willing to pay to avoid spending time shopping for books (Clay, Krishnan and Wolff 2001),
fast food (Thomadsen 2007), financial products (Hortaçsu and Syverson 2004), and groceries (Chintagunta,
et al. 2011). Barger (1955) reports that the profit margin of distribution services has been high since the
1860’s, i.e., that consumers value convenience in money terms. One way to interpret the assumption is that
the consumer’s resource is time, which can be allocated to working or shopping. Another interpretation is
that the consumer faces monetary travel costs.
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(2), this leaves him with more disposable income Y for consumption. Demand for varieties
is determined by the trade-off between the marginal benefit from additional variety and the
marginal cost of obtaining it via the market. This argument curbs the extent to which “love
of variety,” present in many consumer models, translates into demand for variety. It will give
rise to a demand system that specifies both a demand for quantity and a demand for variety
as well as the substitution between them.
Figure 1 provides a stylized graphical illustration of this trade-off involving two varieties.
A consumer can purchase all quantities on the budget constraint (i). All bundles on the CES
indifference curve through A and B have the same utility, i.e., the consumer is indifferent
between variety 1 at quantity B and the bundle A. The utility maximizing bundle is A. When
the consumer buys less variety, and visits one less manufacturer, the income constraint shifts
out from (i) to (ii) because of a savings in fixed costs. Consumption of variety 1 at quantity
C, as is shown here, is preferred over consumption of variety 1 at quantity B, i.e., {B} ≺ {C},
whereas consumption of B is equally preferred to consuming quantities represented by A,
i.e., {A} = {B} . By transitivity, the consumer prefers C units of variety 1 to the bundle at
A, i.e., {A} ≺ {C}.
B.
The consumer problem
Moving to the formalization of demand, assume that the consumer has an information set
consisting of variety-specific prices, p (ω), and transaction costs, µ (ω) and maximizes utility
with respect to the subset of varieties, Ω0 , and quantities, x (ω),
max
U, s.t. L =
0
Ω ,x
Z
ω∈Ω0
(µ (ω) + p (ω) x (ω)) dω.
(3)
This formulation treats variety and quantity as separate decision variables. Although my
model is mathematically equivalent to maximizing utility with respect to quantity x ≥ 0
8
variety 2
(ii)
(i)
A
variety 1
B
C
Figure 1: Variety reduction and transaction costs
Note – Point A denotes the optimal bundle of goods where the indifference curve touches the income
constraint indicated by (i). The consumer obtains the same utility from consuming just variety 1 at the
quantity represented by B. But, buying only variety 1 shifts out the income constraint to the dashed line
(ii). The consumer prefers to limit variety when point C is to the right of B, i.e., when the shift in the
income constraint is large enough or when the indifference function is not too curved.
9
only, i.e., allowing for corner solutions, it is useful to think of the consumer problem as explicitly choosing to buy from a particular manufacturer or not. In addition, the standard
Kuhn-Tucker conditions apply only within a given set Ω0 . I therefore decompose the maximization problem by first maximizing utility with respect to quantity for a given purchase
set Ω0 . This gives the demand for quantity in closed-from similar to that Dixit and Stiglitz
(1977). Substitution of optimal quantities in utility next yields the indirect utility function
υ (p, µ, L, Ω0 ), which depends on the size of Ω0 , and the vector of prices and transaction costs
in Ω0 but not on those outside Ω0 . Finally, the demand for variety can be solved from a maximization of indirect utility over all possible subsets Ω0 ⊆ Ω. In more compact representation,
I reformulate the maximization problem (3) into
0
max
U (Ω , x) = max
max U (Ω , x) = max
(υ (Ω0 , p, µ, L))
0
0
0
Ω ,x
Ω
0
x
(4)
Ω
and solve it in Appendix B.
Demand for quantity.– Write utility maximizing quantity as x∗ and the utility maximizing
set as Ω∗ . If ω is a member of the set Ω∗ purchased by the consumer, then the quantity x (ω)∗
desired by the consumer is of the familiar Dixit-Stiglitz form
x∗ (ω) = A (Ω∗ ) p (ω)−σ .
(5)
The scalar A = Y P σ−1 is a demand shifter, Y is disposable income, i.e., Y = L−
R
and P is the Dixit-Stiglitz price index P =
R
ω∈Ω∗
p (ω)1−σ dω
1
1−σ
ω∈Ω∗
µ (ω) dω,
, all defined over the op-
timal set Ω∗ . Because of the presence of many varieties, any single price does not affect the
price index. Therefore the demand function (5) is a constant elasticity demand function over
the optimal set, with price elasticity equal to −σ. This is the standard Marshallian demand
as in Dixit-Stiglitz, except it is defined on a utility maximizing subset Ω∗ ⊆ Ω and income
10
is reduced because of the accumulation of transaction costs of purchasing an assortment of
variety.
Demand for variety.– Next, demand for variety can be expressed as a sorting rule and a
stopping rule.
First, the consumer creates a list by sorting varieties on a scalar index, µ (ω) p (ω)σ−1 .
This index only involves the price and transaction costs of a given variety. When varieties
are more unique (the elasticity of substitution σ is close to 1), varieties at the top of the
list are those with low transaction costs µ (ω). The consumer sorts on convenience because
he receives high utility from diversity. When, on the other hand, varieties are similar (the
elasticity of substitution σ is large), the top of the list contains varieties with low prices
because the consumer receives comparatively more utility from quantity. More generally, in
a later section on welfare, it is shown that the sorting rule organizes varieties in decreasing
utility per dollar of total income L.
Second, the consumer selects varieties ωs from the top of this list and includes them in
the purchase set as long as
µ (ωs ) p (ωs )σ−1 ≤
A (Ωs )
,
σ−1
(6)
where A (Ωs ) is the demand shifter that belongs to the set formed by the first s varieties
on the list.6 As more varieties are added, the left hand side of the inequality increases or
stays constant because of the application of the sorting rule. At the same time, because new
varieties in the set draw demand from all other varieties, the demand shifter A (Ωs ) on the
right hand side decreases. If the level of inconvenience µ is high, the inequality (6) will be
6
These results are not very specific to the assumption that the consumer’s use of the market affects his
income. An alternative formulation where transaction costs are not incurred in terms of income but in terms
of time gives nearly the same results. Suppose income is L and the time available for shopping is M. Both
budgets are fixed. Utility is now maximized subject to an income and a time constraint. This alternative
formulation gives the same demand function as equation 5, the same ordering of varieties to be included
in the set, but a right hand side of equation (6) that reflects the total time available for shopping, i.e.,
σ−1
µ (ω) p (ω)
≤ M P σ−1 where P is the Dixit-Stiglitz price index and M is the total time budget. The main
points in the analysis do not change in a meaningful way in this alternative formulation.
11
violated before the consumer includes the entire supply of varieties in the set. The location
of the variety in the sorted list for which equation (6) holds in equality defines the optimal
set Ω∗ whose mass in turn defines the demand for variety D. Only when µ = 0, as is the
case in Dixit and Stiglitz (1977), equation (6) is guaranteed to hold and the consumer will
buy the entire supply of variety.
A simple interpretation of the demand for variety can be given as follows. Substituting
demand-for-quantity (equation 5) into demand-for-variety (equation 6) and rearranging terms
gives an expression for how the consumer allocates his income to buying quantity versus
variety. In particular, the consumer would buy any variety for which
µ (ω)
1
≤
.
p (ω) x∗ (ω) + µ (ω)
σ
(7)
The denominator of the left hand side is equal to the total expenditure on variety ω. Therefore, the left hand side is the fraction of expenditure on ω allocated to transactions. As
varieties are more differentiated (σ closer to 1), the consumer is willing to allocate a larger
and larger fraction of his resources to making transactions in a no-marketing economy.
The demand system is non-homothetic. For a consumer who’s income L rises, demand
for varieties will expand, via an increase in the demand shifter A, in the direction of more
inconvenient and expensive varieties.
There are several earlier studies which share with the current demand model that some
varieties may not be bought. For instance, there is a literature on incomplete demand
systems (see, e.g., von Haefen 2010), quantity rationing (Muellbauer and Portes 1978; Neary
and Roberts 1980), and the literature on demand with corner solutions (Kim, et. al 2002;
Wales and Woodland 1983). However, the rationing of variety in these models goes through
prices and not fixed costs.
The demand system proposed here has the richness to account for different types of
12
restrictions on the demand for variety. For instance, µ can be taken as a measure of travel
cost. This gives rise to spatial demand systems. Bell et al., (1998) discuss the impact of
distance between consumers and outlets on the selective demand for stores. Atkin (2011),
Bronnenberg et al. (2009), and Bronnenberg et al. (2012) show that taste for substitute
food products is local. Alternatively, when µ has the interpretation of the cost of collecting
and processing information, the demand model fits in a search-theoretic framework, and can
be used to rationalize consideration and purchase of a select number of varieties (see e.g.,
Kim, et al. 2002; Roberts and Lattin 1991) or the existence of awareness sets (e.g., Sovinsky
Goeree 2008; Arkolakis 2010).
Finally, there is a connection of this demand model to models of household-production.
Becker’s (1965) new consumption theory formalizes the demand for goods from an underlying
household production function. My demand model can be thought of as containing a simple
model of household production where the consumer faces fixed or setup costs from using the
market as a necessary condition to produce utility from a variety. Independently, Howell and
Allenby (2012) recently developed an empirical model of such demand with fixed costs.
III.
A.
The demand and supply of variety
Manufacturer sales
The purpose of this section is to provide a simple equilibrium analysis of a no-marketing
economy as a benchmark. Consider henceforth the special case of symmetric varieties and
constant and equal transaction costs per variety. This is limiting, but as Dixit and Stiglitz
(1977) note “even the symmetric case yields some interesting results,” and sticking to this
tradition increases the validity of using the Dixit and Stiglitz (1977) model as a direct comparison. I assume that the consumer knows how much effort it takes to visit a manufacturer,
i.e., the consumer knows µ. However when determining the amount of variety to buy, the
13
consumer does not know prices p but instead holds expectations about them. The consumer
next visits manufacturers, possibly a subset of them, and makes quantity decisions based on
the actual prices learned. Manufacturer level unit sales is the aggregation of individual level
demand across consumers and quantity.
Because of symmetry, consumers expect manufacturers to price equally (it will be shown
below they do). When the consumer buys D varieties, disposable income is equal to Y = L −
µD. With equal prices and symmetric varieties, per-variety expenditure is disposable income
equally divided among all D varieties. Substituting per-variety expenditure in equation (7)
and solving gives an explicit expression for the demand for variety
D=
L
.
σµ
(8)
The amount of variety desired is negative in transaction costs and in the similarity of varieties.
It further increases proportionally to total income L. Increases in L are used to buy more
variety while the expenditure on each variety remains constant. Equation (8) is a constant
and unit elasticity demand function for variety, D (µ), in the “price,” µ, that the consumer
pays for a variety.
Next, manufacturer-level unit sales for each variety is an aggregation of demand for quantity across those consumers who buy from a manufacturer, i.e., across customers. An important characteristic of demand is that consumers prefer a certain amount of variety, but at the
same time they are impartial to who supplies it, i.e., consumers do not care about the identity
of manufacturers. Therefore, any subset of varieties of size D is equally preferred. In these
conditions, it seems reasonable to take as a benchmark that consumers will spread equally
among all possible subsets.7 Consequently, if there is a mass of T varieties on the market, a
7
Clearly one explanation simply involves independent consumers who each randomly draw a particular
subset. Another explanation involves transaction cost in terms of time spent in a manufacturer-specific
service queue. When consumers always choose varieties by visiting the manufacturer with the shortest line,
consumers will spread evenly across all manufacturers.
14
fraction of min
D
,1
T
consumers buys from a given manufacturer. Other aggregation rules
may apply. However, they share that when transaction costs are high, demand and supply
of variety differ simply because consumers will generally not all buy the exact same subset
of varieties. Neither D nor T depend on the price of any single manufacturer.
The demand from each customer of ω is x (ω) = A (D) p (ω)−σ , where, with some abuse
of notation, A (D) is the demand shifter for a set of size D. A (D) does not depend on any
single price either. Aggregating equation (5) over consumers, unit sales qω for firm ω in the
market is equal to
D
qω (p) = min
, 1 × A (D) × p (ω)−σ ≡ Ã (D) × p (ω)−σ ,
T
(9)
where à (D) is a market level demand shifter.
B.
Supply
Each variety is produced by a single firm who lays out a fixed cost of F units of labor to
acquire a production technology, which uses one unit of additional labor to produce
1
c
units
of output.8 Manufacturers compete monopolistically, and enter the market only if doing so
covers their cost. The mass of manufacturers that enters defines the total supply of varieties
and is denoted by T.
Dropping the subscript ω, the profit function for each symmetric firm is
π = (p − c) q (p) − F = (p − c) Ã (D) p−σ − F.
(10)
Taking first and second order conditions and solving for the profit maximizing price in this
8
These are the only firms in the market. In particular, they displace a cottage industry of home producers.
The conditions under which industrial firms displace local home producers are outlined in Murphy, et al.
(1989). This eliminates the scenario where consumers engage in home production to avoid transaction costs.
The conditions under which industrialization might become infeasible due to transaction costs, constitute a
separate and possibly interesting avenue for research but are not investigated here.
15
no-marketing benchmark yields that manufacturers charge monopoly prices.
p=c
σ
.
σ−1
(11)
The consumer’s expectation that all prices are the same when determining the size of their
purchase sets is rational because all firms face the same pricing problem and price the same.
These are the same prices as in Dixit and Stiglitz (1971). But, contrast to their work,
there may be insufficient demand for variety and it is puzzling that prices for a variety do
not drop in such a case. Prices remain high because consumers do not know actual prices
in order to determine which varieties to buy. This result is related to Diamond (1971) that
even undifferentiated firms will charge high prices. Like in Diamond (1971), the seller can
not attract consumers using price. Manufacturers selling quietly from their factory door are
not competing for customers.
Going back to the supply of variety, the total mass of variety in the market is determined
by the mass of manufacturers who can cover their fixed costs F . This is equal to the number
of times fixed costs F can be recouped from the margin
p−c
p
=
1
σ
that the manufacturing
sector is able to charge on disposable income Y . Thus the mass of manufacturing firms in
the benchmark economy is
T =
Y
.
σF
(12)
Equation (12) is the benchmark variety supplied by the market when consumers carry the
full cost of using the market.
C.
The “no-marketing” equilibrium
Demand (8) for and supply (12) of variety depend on primitives that are unique to each.
The supply of variety is restricted by the setup cost F to the manufacturer, associated with
16
setting up production. The demand for variety is restricted by the cost µ to the consumer,
associated with making a transaction with a manufacturer.
The analysis now shifts to if and when the demand for variety differs from its supply.
First, consider the opposite, namely that D = T . The consumer spends Dµ on making
transactions, which, using equation (8) , is equal to
L
σ
and has the remainder Y =
σ−1
L
σ
disposable for quantity. This implies that the demand for variety is equal to its supply when
σ
the fixed costs on the demand side and supply side are related as follows µ = F σ−1
≡ µ̃.
When transaction costs in the no-marketing economy are low (µ < µ̃) consumers buy
all varieties on the market because their demand for variety exceeds supply. In this case,
their income is Y = L − µT and a total mass of T =
Y
σF
manufacturers enters. Solving for
disposable income and the variety produced by the market,
σF
Y =L
σF + µ
!
and T =
L
.
σF + µ
(13)
Disposable income and the market supply of variety depend negatively on transaction costs
µ. However, whereas the supply of variety drops from the setup costs F , disposable income
rises in F from reduced supply (entry).
In contrast, when transaction costs are high (µ > µ̃) consumer demand for variety is less
than the variety supplied. Income is Y = L − µD and a total mass of T =
Y
σF
manufacturers
enters. Solving for disposable income and the supply of variety provided by the market once
more,
σ−1
Y =L
σ
L
and T =
σF
σ−1
σ
(14)
Thus, when high transaction costs cause consumers to buy only a subset of varieties on the
market, the consumer uses a fixed budget for transactions equal to
1
σ
times full income L.
When transaction costs increase, the consumer spends the same resources on transactions but
buys less varieties. Like income, the total mass of manufacturers on the market is independent
17
of transaction costs.
In sum, when the consumer faces per-variety fixed costs, the demand and supply of variety
are not automatically coordinated. What is the consequence of this? Dixit and Stiglitz
(1977) write in their introduction “It is useful to think of the question [of optimum kinds
and quantities of commodities] as one of quantity versus diversity. With scale economies,
resources can be saved by producing fewer goods and larger quantities of each. However this
leaves less variety [supplied], which entails some welfare loss” (terms in brackets added). This
argument has been at the center of the debate on the social optimality of variety.
The present analysis adds to this argument a parallel on the demand side. The consumer
commonly faces fixed costs, which produce scale economies in household production. Resources can again be saved by buying fewer varieties and larger quantities of each. This, too,
entails a welfare loss.
When the consumer’s fixed cost is high, the question arises whether fixed costs by manufacturers continue to cause a welfare loss. I argue that the second argument can overrule
the first. So, the answer is “no,” when demand for variety is less than its supply. In this
case, consumers are not harmed by the reduction of variety from the fixed cost of entry.
This is because consumers’ own fixed costs reduce variety purchased even more. Moreover,
consumers would continue to be unharmed if manufacturers incurred more fixed costs as long
as reduced entry leaves enough variety to cover demand. Even better, the consumer would
benefit when the manufacturer invests in lowering the fixed costs of consumers. The next
section considers when and why the manufacturer will do so.
18
IV.
A.
Competing for customers
Marketing technology
Now consider that manufacturers have a technology (refer to it as “marketing”) that lowers
transaction costs to consumers and provides information to consumers about price. Manufacturers lower transaction costs by opening manufacturer outlets, e.g., a Gap store or a
Bang & Olufsen store. Manufacturers can communicate price by advertising. The purpose
of this section is to derive if and when an equilibrium exists involving non-price competition
and when it yields outcomes that are preferred to pure-price competition. For reasons of
parsimony, the analysis is limited to symmetric equilibria.
Like the cost of entry in manufacturing, the cost of marketing is assumed to be fixed (see
Spence 1976; Sutton 1990) to quantity. A manufacturer who invests G, shifts the consumer
transaction costs to µ (G). I assume that the marketing technology obeys the following
conditions: µ0 (G) < 0, µ00 (G) > 0, and µ (∞) = 0. Under these assumptions, investment
leads to lower transaction costs, but more investment is needed to keep lowering them to
consumers at a constant rate. If the manufacturer invests nothing, the maximum transaction
cost to the consumer is bounded, i.e., µ (0) = µ.
Next, if a manufacturer wants to communicate its prices to all consumers in the economy they can do so using advertising. To be conservative about the prospects of non-price
competition, I assume that advertising is inexpensive relative to distribution,9 effectively
costless.
In sum, marketing is formalized with two competitive instruments which manufacturers
can use in isolation or together. They can invest G and reduce transaction costs to the
consumer. Alternatively, they can communicate prices to the market at no cost, and lower
9
It is reasonable to assume that the cost of advertising is low relative to distribution. The total 2007 bill
of distribution of retailed goods in the United States was $B2,200. The cost of advertising spent on those
goods is estimated to be around $B200 (see Appendix A).
19
prices.
B.
Low transaction cost
When transaction costs are low, µ < µ̃, manufacturers are serving all consumers in the
market. So the incentive to invest in marketing can only come from selling more to existing
customers. However, the quantity sold to consumers by a manufacturer does not depend on
the transaction cost of its own variety. This cost is fixed to consumers and does not enter
their quantity decisions. Therefore, when transaction costs are low enough for consumers to
buy all varieties, lowering transaction costs benefits consumers but not manufacturers, and
hence the latter will not provide for it. Manufacturers charge monopoly prices as in equation
(11), and consumers know all the prices in the market.
C.
High transaction cost
When transaction costs are high, µ > µ̃, manufacturers behave differently. To preview the
analysis, first consider an informal introduction. With high transaction costs, consumers
want a limited amount of variety. Consumers care more about the breadth of assortment
than about the identity of individual firms. When there is an abundance of variety relative
to demand, the consumer can choose from multiple assortments, each of similar value. Consumer indifference among limited assortments forces manufacturers into fierce rivalry over
customers.10 Interestingly, these are the same type of manufacturers who would behave as
monopolists had the consumer’s transaction cost been lower, as in the previous section.
Manufacturers can compete for customers by providing lower transaction costs, by informing consumers and asking lower prices, or by combinations of these actions. Providing
more convenience makes manufacturers incur more fixed costs and reduces their number in
10
Although consumer indifference makes it “cut-throat,” business rivalry over customers will result from
consumer fixed costs even when consumers have some degree of preference heterogeneity.
20
entry. Decreasing price erodes manufacturer margins and also reduces the number of manufacturers that enter. In both cases, demand for variety rises. Therefore, marketing makes
demand for variety rise toward a supply falling from marketing cost and margin erosion. It
closes the gap between demand for variety (of which there was too little) and the supply of
variety (of which there was too much).
There are two conditions for the existence of an equilibrium. First, prices, p, and investments in lower transaction costs, G, must be best responses, i.e., maximize profits given
the actions of others. Second, prices and investments must equate the demand and supply
of variety on the market. The second requirement is because competitive forces compel the
manufacturer to keep lowering transaction costs and prices in order to win customers as long
as there is an extensive consumer margin left.
I use these conditions to solve for the equilibrium. All proofs are in Appendix B. A
manufacturer maximizes profits taking competitors’ actions as given. He needs to worry
about not being dropped by consumers who might not buy all varieties. Therefore, the best
responses [p∗ , G∗ ] need to pass the stopping rule of the consumer’s purchase set, i.e., equation
(6). The manufacturer problem is then to pick the most profitable policy, subject to being
included in the assortment purchased by the consumer.
max (p − c) x − (F + G) , subject to pσ−1 µ (G) ≤
p,G
A (Ω0 )
and G ≥ 0.
σ−1
(15)
The policies of others enter via the demand shifter A (Ω0 ). One might solve for best responses
using the Kuhn-Tucker conditions. However, as explained above, p and G are additionally
related because the best responses also need balance the demand and supply of variety. The
combinations of p and G that equate demand to supply of variety can be written in the form
21
of a price as a function of marketing investment G and productivity µ (G),
p (G) = c
σ
σ−
(16)
σ (F +G)
(σ−1) µ(G)
Instead of choosing both G and p, the manufacturer chooses only one of them. Notice that,
holding demand equal to supply, investment in convenience G raises equilibrium prices p (G).
Indeed, if demand rises from lower transaction cost, it is required that profit margins rise to
accommodate more entry.
I now present the results organized by strategic combinations of deciding to lower transaction costs (yes/no) and deciding to communicate prices (yes/no). For reference, the benchmark in the previous section considered the “no-no” case.
No reduction in transaction costs, communication of prices.– When marketing is not
sufficiently productive, manufacturers will not invest in lowering transaction costs and instead
compete on price.
More precisely, when the derivative of transaction costs with respect to marketing inµ(0)
vestment is too close too zero, µ0 (0) > − µ(0)−µ̃
, investments G are ineffective at lowering
transaction costs µ even at low levels of G. In this case, manufacturers will not lower transaction costs and set G∗ = 0.
Instead, a manufacturer will use price to secure demand from all consumers by being
slightly less expensive than the competition and communicating this to consumers. Because
this results in a jump in sales in return for a marginal decrease in price, manufacturers will
all lower price until no more customers can be won. Equilibrium prices follow equation (16)
∗
and are p = c
σ
µ̃
σ− µ(0)
. Recall that transaction costs are large, µ (0) > µ̃, or
µ̃
µ(0)
< 1.
σ
Also recall that prices are c σ−1
when manufacturers do not communicate them. Therefore,
providing information about price via advertising leads to reduced margins in competitive
22
equilibrium.11
The price reduction from advertising relative to monopoly prices can be substantial.
When transaction costs in the no-marketing economy, µ (0), are high or fixed costs F are
low, µ (0) µ̃, communication of prices causes them to approach competitive rates (p∗ → c),
despite varieties being differentiated. Manufacturers all wish to raise their prices, and they
would if they could secure assortment membership. But in the presence of transaction costs,
consumers choose a limited assortment and raising price would mean being dropped entirely
by consumers, because other firms stand ready to sell at a low price.
In sum, price-cost margins can erode for two reasons in my model. The more traditional
reason is that products are not differentiated (high σ). To this is added the reason that
consumers have high transaction costs, µ.
Compared to the “no-marketing” benchmark of the previous section, the consumer will
buy the same amount of variety, and larger quantities.
Reduction in transaction costs, no communication of prices.– When advertising is not
possible or legal, the manufacturer does not communicate its price and assortment membership is not impacted by price. Manufacturers thus set monopoly prices, i.e., p = c
σ
σ−1
.
They face an extensive consumer margin that can be captured with slightly more convenience than the competition. Each manufacturer now invests in marketing if it wants to
stay in the market. The urge for an individual manufacturer to invest more is only stopped
when all manufacturers individually have reached a level of investment that balances demand
and supply of variety at monopoly prices. In particular, setting equation (16) to monopoly
prices, investment levels follow
σ (F +G)
(σ−1) µ(G)
= 1. This equation does not involve the derivative
of µ with respect to investment. Manufacturers will invest in lowering transaction costs to
“compete away” excess variety, no matter how inefficient marketing is at lowering transac11
This is consistent with the literature on informative advertising (e.g., Kaldor 1950). A nice example of
empirical support is given in Benham (1972). A comprehensive overview of this literature on this effect is
given in Bagwell (2007).
23
tion costs. Demand for variety is increased because for any positive G, transaction costs are
decreased.
Compared to the benchmark of the previous section, the consumer will buy more variety,
yet the total quantity purchased remains the same.
Reduction in transaction costs, communication of prices.– Finally, under circumstances
typically observed, manufacturers can advertise. When marketing is sufficiently productive,
manufacturers will lower transaction costs even when advertising is free.
µ(0)
More specifically, the manufacturers will invest when µ0 (0) < − µ(0)−µ̃
. The necessary
conditions for equilibrium can be expressed as
σ (F + G∗ )
µ (G ) = − 1 −
(σ − 1) µ (G∗ )
0
∗
!−1
(17)
and
p (G∗ ) = c
σ
.
σ − 1 − µ0 (G∗ )−1
(18)
µ(0)
, and increases to 0 by the assumptions
The left hand side of (17) starts at less than − µ(0)−µ̃
on the function µ (G). At the same time, it is easy to see that the right hand side decreases
µ(0)
from − µ(0)−µ̃
at G = 0 toward −∞ as G increases (before flipping sign and staying positive).
It then follows that both sides of equation (17) cross exactly once at a bounded value G∗ for
µ(0)
which µ0 (G∗ ) is below − µ(0)−µ̃
. This implies two things.
µ(0)
First, at the equilibrium level of investment, G∗ , if µ0 (G∗ ) < − µ(0)−µ̃
, it is also smaller
than −1. This means that in equilibrium, investments to lower the consumer’s transaction
costs require that a manufacturer is better than a consumer at carrying the latter’s transaction
costs.
Second, substituting µ0 (G∗ ) < −1 into equation (18) it is easily seen that equilibrium
prices are less than monopoly prices. However, it is also true that prices that prevail under
positive investment G∗ > 0 are larger than equilibrium prices when there is no investment
24
(a) price and transaction cost
do not
communicate
strategies
communicate
prices
prices
do not lower
high µ
high µ
transaction
high
p
low p
costs
lower
low µ
medium µ
transaction
high
p
medium p
costs
⇐⇒
(a) price and transaction cost
do not
communicate
strategies
communicate
prices
prices
do not lower
least variety
least variety
transaction
least
quantity
most
quantity
costs
lower
most variety
medium variety
transaction
least
quantity
medium
quantity
costs
Table 1: Summary of results in terms of manufacturer actions and consumer outcomes
and only price competition exists. The analysis will return to this observation in the next
section on welfare.
Compared to the benchmark of the previous section, the consumer will buy more variety
and larger quantities of each.
Summary.– Table 1 summarizes the results qualitatively. The left part of the table summarizes the results with respect to prices and transaction costs that the consumer faces. The
right part translates this into diversity and quantity. In each of the two parts of the table,
the benchmark “no-marketing” case is the upper left cell. What can be concluded from the
table is that compared to when firms do nothing to provide products or information, consumers enjoy more than or equal variety and lower than or equal prices with marketing, with
at least one of the two weak inequalities holding strongly. I now turn to whether non-price
competition raises welfare.
D.
Welfare
Some have argued that competition in marketing between firms is wasteful duplication of
costs (Braithwaite 1928; Kaldor 1950). Others level the critique at marketing that it changes
consumers’ behavior from its natural state and makes that manufacturers sell at high prices
(Galbraith 1967).
I now discuss the welfare implications of the model above for the case when marketing
emerges, i.e., when µ > µ̃. I compare welfare in an economy with marketing to that of an
25
economy when the consumer carries the cost of using the market in full. Similar to the ideas
by Alderson (1948), I consider this comparison informative about the product of marketing.
Society welfare in my model is equal to consumer welfare (manufacturers enter until
profits are negligible). In turn, consumer welfare is equal to the utility derived from buying
and consuming D varieties. Substituting equal quantities in the utility function (1), welfare
σ
is equal to W ≡ U = D σ−1 x. At equal prices, x =
case, demand for variety is D =
L
,
µσ
Y
.
pD
For the benchmark “no-marketing”
disposable income is Y = L σ−1
and firms set monopoly
σ
σ
prices p = c σ−1
, as derived above. Therefore, welfare is,
W0 = D
1
σ−1
Y
=
p
L
σµ
!
1
σ−1
L σ−1
c
σ
2
(19)
.
Note that welfare in the benchmark case does not depend on the fixed cost of entry, F .12
This is because manufacturer setup costs do not constrain the variety that the consumer
purchases when µ > µ̃. In this case, the consumer carries the cost of using the market and
the latter provides too much variety. Consumer welfare decreases in variable manufacturing
cost c, and in transaction cost µ. A 1% reduction in manufacturing costs leads to a 1%
increase in welfare, whereas a 1% decrease in transaction costs µ leads to a
1
%
σ−1
increase in
welfare. That is to say, lowering transaction costs µ is more welfare enhancing than lowering
manufacturing costs c when varieties are not too close substitutes, i.e., σ < 2.
Recalling the conclusion of the previous subsection, when firms compete in the provision
of low transaction costs and information, consumers never have less variety D (G∗ ) ≥ D
and never pay more than monopoly prices p (G∗ ) ≤ p, with at least one of the two weak
12
By substituting D =
L
µσ ,
into welfare, another way of expressing welfare is
W0 = D
1
σ−1
Y
=
p
LY σ−1
σµpσ−1
1
σ−1
.
The denominator contains the term µpσ−1 which is the sorting criterion used by the consumer to create a
purchase set (equation 6). Sorting varieties with different µ and p on this criterion is therefore the same as
sorting varieties on utility from a fixed total income, L.
26
inequalities holding strongly. In addition, consumers allocate the same amount of income to
transactions, whether firms provide convenience or not, i.e., Y (G∗ ) = Y. For welfare, this
means that
1
W1 = D (G∗ ) σ−1
1
Y
Y
σ−1
>
D
(0)
= W0
p (G∗ )
p (0)
(20)
Convenience, i.e., manufacturer-provided distribution of goods and information, improves
the welfare of consumers relative to that in their natural state, i.e., W0 is strictly less than
W1 . Marketing by manufacturers creates value to consumers with high transaction costs by
providing convenient access to variety, lower prices, or both.
Both elements of mass marketing, i.e., low-cost access to variety and advertising of prices,
are valuable to consumers. Making use of advertising of prices guarantees that manufacturers
produce transactions at a lower cost than consumers. That is, communicating prices to create
customers avoids that manufacturers compete away the entire extensive consumer margin
with transaction cost reductions that become ever more costly. Advertising prices therefore
has two beneficial effects in this theory: it allows consumers to select varieties based on price,
and therefore enhances price competition, and it ensure that firms do not spend inefficiently
on distribution and reduce too much variety. Advertising prices, even if it were not free but
came at some cost, is therefore not wasteful.
Mankiw and Whinston (1986, p. 49) conclude “when firms must incur fixed set-up costs,
the regulation of entry is often desirable.” In the context where firms and consumers incur
fixed costs, it would seem that it is of interest to see whether the form of competition discussed
above is socially efficient. Are the outcomes generated by forces of the market desirable
or would a social planner do better at raising welfare by regulating entry? For example,
communication is cheap in this economy. A planner might prefer that manufacturers use this
instrument over costly distribution and just compete on price only, i.e., behave as in the first
27
case above.
I prove in the appendix that taking the non-competitive behavior of manufacturers in
the post-entry game as given, the planner sets the same marketing levels, G, as those set by
profit maximizing firms. That is, directly maximizing welfare with respect to G and p in
1
max D (G) σ−1
G,p
Y
,
p (G)
(21)
subject to equation (16), leads to equations (17) and (18). Thus, competing manufacturers
produce a second best solution13 to the presence of a cost of using the market. Cut-throat
competition between manufacturers to create or keep a customer makes manufacturers maximize profits by best serving customers. Loosely stated, this adds a new economic role to the
firm, from being a manufacturer to also being a marketeer.
Finally, going back to the statement in the first paragraph of this section, i.e., that
marketing makes prices go up, consider the relation between investments in convenience G
and prices p (G) . Demand for variety only equals its supply when higher investment levels in
convenience, G, go hand in hand with higher prices p (G). Thus, when in equilibrium firms
invest more in marketing, indeed, prices rise. This seems consistent with marketing making
products expensive. However, this is not so. Prices rise not because of marketing-induced
monopoly power. To the contrary, firms compete cutthroat. Prices rice because consumers
demand variety (want convenience). Keeping demand for variety equal to supply, rising prices
are a condition for the supply of variety that consumers want. As an aside, the perspective
that prices rise is dependent on which is the benchmark. Prices are highest when firms do
nothing to provide information or low transaction costs.
13
Obviously the existence of fixed costs precludes the possibility that there are first-best solutions to the
allocation problem. The role of marketing is more in the spirit of Bowles and Gintis (2000, p 1412-1413) who
write that “we must judge policies and institutions not by how close they approximate the assumptions of
the fundamental theorems of welfare economics, but rather according to their ability to function effectively
in the second-best world of ineradicable state and market failures.”
28
In sum, it is welfare enhancing for consumers that firms provide convenience, not just
low prices. Another way of saying this is that prices do not allocate goods in a socially
optimal way when consumers have fixed costs. Non-price competition, such as competition
in marketing, is a solution to this problem in as much as yielding a second best outcome.
The next section considers two simple applications of the analysis in this section.
V.
A.
Discussion
Does distribution cost too much?
In 1929, the United States underwent an effort to study the distribution sector and conducted
a census of distribution to determine how much society spent on connecting manufacturers
to consumers. Estimates of the cost of distribution were reported by Galbraith and Black
(1935), Malenbaum (1941) and Stewart and Dewhurst (1939) in line with those reported in the
appendix. Shaw (1990) summarizes these estimates and discusses how they intensified rather
than resolved the debate about the height of the distribution bill. As a simple application
of the theory laid out above, this section revisits an age old question “Does distribution cost
too much?”.14
One valid approach to answering the question is to focus on welfare, as was done above. In
this case, welfare rises, so one might conclude distribution does not cost too much. However,
it is also insightful to look at cost and output separately. Because competition in convenience
14
This question traces back to the writings on the economic organization of Greek city states by Plato and
Aristotle. Plato argues that facilitating exchange and distribution of goods is important to societies that owe
their prosperity to the gains from division of labor. In Book II, at 371c, Plato asks: “If the farmer or any
other craftsman brings what he has produced to the market, and he doesn’t arrive at the same time as those
who need what he has to exchange, will he sit idle, his craft unattended?” He suggests it may be better
to pay someone to operate the market rather than for a productive worker to sit idle: “Not at all: there
are men who see this situation and set themselves to this service.” However, the foremost qualification of
these ancient-Greek marketeers was to be socially cheap: “in rightly governed cities [they] are usually those
whose bodies are weakest and are useless for any other job.” Trading and retailing are also discussed by early
economists. Adam Smith (Wealth of Nations, Book II, Chapter V) believed that retailers and merchants
perform an essential service to society. See Cassels (1936) for a more detailed overview of early marketing
thought in economics.
29
occurs only when transaction costs are high, I focus on this case (µ > µ̃).
I first compare the cost of production with and without investment in marketing. The
total setup cost for the uncoordinated manufacturing sector in the no-marketing equilibrium
is (see equation 14),
TF =
L σ−1
Lσ−1
F =
.
σF σ
σ σ
(22)
On the other hand, in the equilibrium with market-provided convenience, the total amount
of manufacturer setup cost is equal to
L
L (F + G∗ )
∗
T (G ) (F + G ) =
(F + G ) =
,
σµ (G∗ )
σ µ (G∗ )
∗
∗
(23)
where the second step comes from the equality of demand and supply of variety in equilibrium.
Comparing equation (22) and equation (23), an economy without distribution costs more than
an economy with distribution when the following inequality holds,
σ (F + G∗ )
< 1.
(σ − 1) µ (G∗ )
(24)
It is easily verified that this is true in equilibrium.15 Therefore, the total setup cost T F in
the no-marketing economy is more than or equal to the setup cost T (G∗ ) (F + G∗ ) when the
market provides convenience. Therefore, the cost of convenience to society is covered by a
reduction in variety, which - given the transaction costs faced by consumers - was unwanted.
Another way of saying the same is that marketing re-allocates resources inefficiently tied up
in the supply of variety, of which there was too much, to increased convenience, of which
there was too little.
Next, move from cost to output. The total output of the manufacturing sector is equal
to demand for quantity. Total demand for quantity is equal to disposable consumer income
15
In particular, this result follows immediately from the right hand side of equation (17) being negative in
equilibrium.
30
divided by price. Disposable income is not impacted by investment in marketing when µ > µ̃
(see again equation 14). Therefore the ratio of outputs with and without marketing is just
the inverse of the ratio of prices. Since prices are lower from the competition caused by
communicating price, total output rises with competition for convenience.
In sum, the distributive marketing system provides more efficient use of the economies of
scale used in manufacturing. To society, the cost of distribution is offset by a reduction in
the cost of manufacturing. In this example, distribution does not cost too much. Is is free.
B.
The size of the marketing sector and productivity shocks
Another question about the size of the distribution system is its relation to changes in marketing productivity. For instance, how should the size of the marketing sector change as it
becomes cheaper to create a customer?
For this analysis, I make use of an example of functional form of the relation between
investment and transaction costs, in particular µ (G) = µ (0) exp (−τ G). It is trivial to verify
that this obeys the assumptions made in the previous section about the effects of investment,
i.e., µ0 (G) < 0, µ00 (G) > 0, and µ (∞) = 0. Marketing productivity rises in τ. Figure 2
shows the equilibrium levels G∗ and the cost of distribution to society T (G∗ ) G∗ at different
values of τ . Starting at low productivity, τ = 0 no marketing activity emerges. Then as
productivity increases, firms start to invest16 and will do so more and more as productivity
increases further. Finally, when productivity increases even more, firms will invest less, and
eventually even the total size of the marketing sector will decrease with it.
This non-monotonicity is observed in data. Starting in the late 1800’s when transportation
and communication were not very productive, cost shocks in marketing, from the introduction
of mass media, the Interstate Highway System, etc., initially made the marketing sector
larger. Expenditures on distribution grew over the years from about 31% of total retail
16
µ(0)
Firms start to invest when µ0 (0) < − µ(0)−µ̃
. This means they will invest when τ >
31
1
µ(0)−µ̃ .
value of manufactured goods in 1869 to about 37% in 1950 (see Appendix A). An even
stronger trend is reported in Wallis and North (1986), who divide the U.S. economy in a
manufacturing sector and a transaction sector, and estimate that the share of the transaction
sector increased from 25% in 1870 to 45% in 1970. However, whereas the long-term trend in
the cost of distribution is upward sloping, there is recent evidence of a decline in the share of
distribution in consumption expenditure and in GDP. For instance, using the United Nations
national accounts data for 1970-2010, the joint cost of distribution and communication fell
from 26% to slightly below 21% of GDP.
In the context of future research, the question arises whether this recent decline is related
to productivity shocks in marketing. Although speculative, the broad adoption of information
technology has made products and product information available online at a fraction of the
time it takes to visit manufacturers, computerized tracking systems have enabled a high speed
parcel delivery system, etc. A deeper inquiry seems appropriate about the effects of marketing
on productivity of the economic system because marketing makes society productive in nontraditional ways. As an example, the right hand graph of Figure 2 demonstrates that cost
effectiveness in marketing (i.e., rising τ , improves society’s efficiency in producing utility
but degrades its efficiency of producing quantity. Rising prices, necessary for the market to
supply variety, cause that the total quantity produced in the economy actually drops.
VI.
Conclusion
In this paper, Coase’s (1937) ideas about the boundaries of the firm are extended to include
other functions than manufacturing. When the consumer’s transaction costs of dealing with
manufacturers are fixed to quantity, the latter find it in their interest to provide convenience
and create customers, especially when there are economies of scale in dealing with the cost
of using the market.
32
output/hr
cost
TG
G
utility
quantity
τ
τ
Figure 2: The cost and output of distribution as a function of marketing productivity
Note – In both graphs, the horizontal axis displays marketing productivity τ . In the left graph, G is the
cost of marketing per firm, and T G is the cost of the marketing sector. In the right graph, total quantity
produced and total welfare produced per hour of labor are displayed.
Consumers benefit from this non-price competition, as it leaves more variety in their
hands than price competition alone. In the context of asking “How to best share the costs
of using the market between manufacturers and consumers?”, I thus find that it may be
best for society when specialized and costly institutions carry a part of these costs instead
of consumers.
In terms of future research, there are at least two additional benefits of marketing which
are directly obvious from the model proposed here and should be studied independently.
First, manufacturers will not lower transaction costs below the level that creates a customer.
This makes them ineffective at lowering the consumer’s total cost of using the market. The
consumer will namely use lower transaction costs to buy more variety, and thus face a high
total expense of using the market. It may be of interest to study under which conditions
this gives rise to an additional sector of general retailers or shopping centers, to provide
assortment at a single low transaction cost.
Second, I have not considered firm-heterogeneity. Along with it, the analysis remained
silent on how marketing investment interacts with firm survival. In particular, related to
33
important research on firm-selection effects of international trade (e.g., Melitz 2003), it is
useful to study whether investment in marketing affects the equilibrium distribution of firms,
e.g., the survival of more productive firms over less productive ones.
To close, inefficiency and fixed costs on the supply side are central topics in welfare
economics. I hope to have made a contribution in demonstrating that inefficiency and fixed
costs on the demand side are also relevant in the economic analysis of welfare. They affect
competition and market structure profoundly. Mass marketing, in the sense of marketprovided distribution and communication is a response to such fixed costs. It balances the
demand and supply of variety, and contributes by providing more variety, lower prices, or
both.
34
References
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37
A
Market distribution
A.
Distribution and communication expense in the United States
At the macro level, one way to measure the size of the distribution and communication industry is to add up the margins of wholesaling and retailing, and next add marketing expenses
by manufacturers. In principle, this covers marketing expenditures across all agents in the
distribution, communication, and transaction channels between producers and consumers.
Using the Business Expenses Survey from the Economic Census in 2007, I compute the
gross-margins of wholesaling and retailing to be $B1,10217 and $B1,106 respectively (see Table 2). To proxy for other marketing costs, I use advertising outlays. I start with data on
advertising to sales ratios. For the US, these data are available across 200 industries monitored by Schonfeld & Associated and reported by Advertising Age.18 The average advertising
to sales ratio is 3.3%. Applied to total 2007 manufacturing shipments of $B5,319, total advertising is approximately $B176.19 By this approximation, the total cost of marketing sums
to $B2,384. This is about 17% of the 2007 GDP.
The total value added by manufacturing is also available from the 2007 Economic Census
and is $B2,383. The similarity of the margins in distribution and manufacturing also holds
earlier in the 20th century. Galbraith and Black (1935, p. 401) estimate that the total
marketing bill for the US in 1929 was $B24.4, whereas the value added by manufacturing
was $B28.3.
Table 2: Wholesale and retail expense in 2007
United States
2007 (in US$B)a
A. sales
B. inventories
C. inventory growth
D. purchases
E. margins = A-D+C
F. margins as % of sales
Wholesale
with MSBO’sb
5889
546
33
4820c
1102
18.7%
Wholesale
without MSBO’s
4174
427
27
3416
785
18.8%
Retail
(NAICS 44,45)
3999
494
14
2907
1106
28%
a
Data were last accessed 28 June 2012 from http://www.census.gov/econ/bes/
manufacturer sales and business office
c
This is computed from the ratio between A. and D. from “Wholesale without MSBO’s”
applied to A. from “Wholesale with MSBO’s.”
b
17
This number accounts for manufacturer’s wholesaling costs. It is obtained by applying the percentage
margin for Wholesaling Except MSBOs to the sales of Wholesaling Including MSBOs.
18
See http://adage.com/article/datacenter-advertising-spending/advertising-percent-sales-2006/109934/.
19
This number is likely a conservative estimate. Total advertising in 2007 has been reported to be
about $B290 (see, http://adage.com/article/mediaworks/u-s-ad-spending-growth-slows/118852/). But, this
amount includes advertising of services also.
38
B.
The cost of distribution in historical perspective
Data about U.S. wholesaling and retailing margins have been collected incidentally since the
1860’s. I draw from the 1929 Census of distribution,20 Barger (1955), the Annual Retailing
Trade Survey (ARTS) and Annual Wholesale Trade Survey (AWTS) which have been in
existence at the Census since 1992. Barger (1955) conducts a long term study of the combined
margin of wholesale and retailing as a percentage of retail value. He calls this the “cost of
distribution.” It does not cover transport and advertising. For reasons of data availability,
Barger (1955) reports margins averaged over industries by commodity output from 1869-1929,
and margins averaged by sales share from 1929-1948.
Figure 3 shows that the margin of retailing has steadily increased from 23% in 1869 to
about 29% in 1948. From Table 2, it is 28% in 2007.
The margin of wholesaling drops slightly from 10% to 8% of retail value over the years
1860-1950. Table 2 gives a more recent estimate using percentages of wholesaler revenue. To
express wholesaling as a percentage of retail value, divide wholesale margin by 1 plus the
retail margin of 0.28. The wholesale margin is then to 18.7%/1.28=14.6% of retail value in
2007. Similar numbers can be obtained for the years 1992-2008.
Taken together, by these estimates the total margin of distribution has been high for
many years and rose from 31% in the second half of the 19th century to about 43% of retail
value in the first decade of the 21st century.
Cost as a fraction of retail value
0
5
10
percentage
15 20 25
30
35
1860−1950
1860
1880
1900
1920
1940
1960
year
retail
wholesale
Figure 3: Historical margins of retailing and wholesaling (1860-1950)
There are other earlier estimates of the cost of distribution, which use different data
and different methods but nonetheless arrive at similar numbers. Malenbaum (1941) for
instance estimates that consumers pay about 51% of total consumer outlays to marketing
(this estimate includes transportation). Wallis and North (1986), dividing the U.S. economy
20
http://www.census.gov/prod/www/abs/decennial/1930.html
39
Cost as a % of GDP
0
5
percentage
10
15
20
25
1970−2010
1970
1980
1990
year
intermediation
2000
2010
transp_comm
Figure 4: Historical margins of retailing and wholesaling (1970-2010)
in a manufacturing sector and a transaction section, estimate that the share of the transaction
sector increased from 25% in 1870 to 45% in 1970.21 Shaw (1990) summarizes and discusses
similar estimates from the 1929 census.
However, there are more recent data that suggest that the total amount spent on retailing
and wholesaling is decreasing as a fraction of GDP. Figure 4 shows that the cost of intermediation (wholesaling and retailing) as a percentage of GDP has declined. The same is true
for the cost of communication and transportation.
C.
The cost of distribution and communication across nations
Finally, I draw from the United Nations National Accounts data base22 which holds data on
economic activity by International Standard Industrial Classification (ISIC). I use the year
2007. To measure the size of distribution and communication in each country in the United
Nations data base, I focus on three industries: G. Wholesale and retail trade; repair of motor
vehicles, motorcycles and personal and household goods, H. Restaurants and Hotels, and I.
Transport, storage and communications. For the Main Aggregates data, the ISIC Codes G
and H are not separated, but for a sub-sample of countries in the database they are. For
another sub-sample, ISIC I is split into two subcategories comprising of I:60-63 which covers
physical transportation23 and I:64 which covers post and telecommunications.
21
Wang (2003) notes that a positive relation between the size of nations and the share of the transaction
sector should be expected. His reasoning is that the origins of economic growth are in specialization and that
larger countries have more of it. But, with more specialization comes the likely possibility that intermediate
goods and services change through more hands, raising the total fraction of transaction efforts and costs.
22
http://unstats.un.org/unsd/nationalaccount/
23
In particular, 60 - Land transport; transport via pipelines; 61 - Water transport; 62 - Air transport; 63
- Supporting and auxiliary transport activities; activities of travel agencies
40
Table 3 shows 4 measures of distribution and communication as fractions of GDP, total
consumer expenditures, and total added value. As can be observed from any of the listed
measures, the allocation to market distribution and communication for a typical country is
high and the standard deviation in the measures across geography is relatively low. The
number of countries used to compute the summary statistics in Table 3 differs because not
all countries report results at the industry level used in measures 3 and 4.
Table 3: Distribution and Communication - National Accounts
measure (and definition)
1. [ISIC(G-H)+ISIC(I)]/GDP
2. [ISIC(G-H)+ISIC(I)]/Consumption
3. [ISIC(G)+ISIC(I60-63)]/Total Added Value
4. [ISIC (G+H)+ISIC(I)]/Total Added Value
B
mean
0.227
0.378
0.187
0.249
std.dev.
0.076
0.179
0.056
0.069
min
0.007
0.055
0.049
0.061
max
0.538
1.697
0.380
0.489
N
209
209
93
126
Proofs of selected results
Proof of equation (5) Define the Lagrangian of the consumer problem as:
L=
Z
ω∈Ω0
x (ω)
σ−1
σ
dω
σ
σ−1
+λ L−
Z
ω∈Ω0
[p (ω) x (ω) + µ (ω)] dω .
The Kuhn-Tucker conditions are
∂L
∂x(ω)
≤0
x (ω) ≥ 0
∂L
x (ω) ∂x(ω)
=0 ,
and
∂L
∂λ
≤0
λ≥0
λ ∂L
=0 .
∂λ
Note that at x = 0 the derivative of the Lagrangian contains a jump. This is because at
x = 0 the derivative of the integral
Z
ω∈Ω0
.



∂L
=
∂x 

x (ω)
σ−1
σ
dω
σ
σ−1
Ux − λ (p + µ) if x = 0
Ux − λp if x > 0
Starting with the first order condition (FOC)
∂L
∂x(ω)
= 0,
−1
1
∂L
= 0 → U σ x (ω) σ = λp (ω) .
∂x (ω)
Taking the ratio of this FOC for quantities for varieties ω1 and ω2 in Ω0 gives
x (ω1 )
=
x (ω2 )
p (ω1 )
p (ω2 )
41
!−σ
,
(B.1)
which reveals the constant elasticity-of-substitution property of the model
Multiply by x (ω2 ) p (ω1 ), integrate over ω1 , and use the first order condition for λ, i.e.,
L−
Z
ω∈Ω0
Z
µ (ω) dω =
ω∈Ω0
p (ω) x (ω) dω
This will give for each ω2 ∈ Ω0 the following expression
x (ω2 ) =
The effect of p (ω2 ) on
above as
R
ω∈Ω0
µ (ω) dω) p (ω2 )−σ
R
1−σ
dω1
ω1 ∈Ω0 p (ω1 )
(L −
R
ω∈Ω0
p (ω)1−σ dω is negligible. Therefore, we can write the equation
x (ω) = A (Ω0 ) p (ω)−σ ,
(B.2)
where A (Ω0 ) = Y P σ−1 is a demand shifter, income Y (Ω0 ) = L −
is the Dixit-Stiglitz price index P (Ω0 ) =
0
A Ω
R
p (ω)1−σ dω
ω∈Ω0
L−
= R
1
1−σ
R
ω∈Ω0
µ (ω) dω, and P (Ω0 )
, i.e.,
R
µ (ω) dω
.
1−σ
p
(ω)
dω
0
ω∈Ω
ω∈Ω0
(B.3)
The demand function in equation (B.2) is the usual Marshallian demand as in Dixit-Stiglitz,
except it is defined on the subset Ω0 and disposable income is reduced due to transaction
costs. This proves that in any set Ω0 demand is of the form in equation (B.2). Therefore,
when thinking about the optimal set Ω∗ , one can use that demand will be of the same form.
Proof of equation (6) Consider the following rule about forming a purchase set.
1. Include a variety ω from outside the purchase set into the set Ω0 ⊆ Ω if
µ (ω) p (ω)
σ−1
A (Ω0 )
.
<
σ−1
2. Remove a variety ω from the purchase set if the opposite holds.
3. Cycle over 1. and 2. until no varieties are switched in a completed cycle.
The proof is constructed by showing that (1) from any initial subset Ω0 ⊆ Ω, indirect utility
rises from repeated application of this rule and (2) starting from any subset, the same set
emerges from repeated application of the rule in an arbitrary sequence of adding or dropping.
Therefore, from any initial subset, an increasing utility path leads to the same set. This set
is therefore the utility-maximizing set Ω∗ .
1. Start with the indirect utility, i.e., the utility U =
42
R
ω∈Ω0
x (ω)
σ−1
σ
dω
σ
σ−1
at quantities
x (ω) = A (Ω0 ) p (ω)−σ . This is equal to
Z
0
υ (Ω , p, µ, L) =
ω∈Ω0
0
=
L−
A (Ω ) p (ω)
Z
= A (Ω )
−σ
0
ω∈Ω0
σ−1
σ
−σ+1
p (ω)
σ
σ−1
dω
dω
σ
σ−1
Z
Z
ω∈Ω0
µ (ω) dω
ω∈Ω0
p (ω)
1−σ
dω
1
σ−1
.
(B.4)
This indirect utility function depends on the set Ω0 , prices p, transaction costs µ, and
income L. Adding incremental variety reduces the first term in brackets (disposable
income) and raises the second.
Now, derive the incremental indirect utility from adding variety ωs . The derivative of
Rb
a g (h) dh with respect to b is g (b) (i.e., the Fundamental Theorem of Calculus). The
change in indirect utility when expanding the set of varieties by ωs is
1
σ−1
∂υ
= −µ (ωs )
p (ω)1−σ dω
+
0
∂ωs
ω∈Ω
Z
1 −1
Z
σ−1
1
1−σ
L−
µ (ω) dω
p (ω)
dω
p (ωs )1−σ
σ−1
ω∈Ω0
ω∈Ω0
Z
1 σ−1
1
1−σ
1−σ
0
−µ (ωs ) +
A (Ω ) p (ωs )
=
p (ω)
dω
σ−1
ω∈Ω0
1
−1
A (Ω0 ) p (ωs )1−σ
(B.5)
= P (Ω0 )
−µ (ωs ) +
σ−1
Z
The contribution to utility from including ωs does not depend on prices or transaction
costs of any other variety except through the demand shifter A (Ω0 ) and the price index
P (Ω0 ) . Indirect utility rises from including a variety, i.e., the right hand side of equation
(B.5) is larger than 0, when
µ (ωs ) p (ωs )σ−1 <
A (Ω0 )
σ−1
(B.6)
and falls when the opposite is the case.
2. To complete the proof, show that the same set Ω∗ emerges from any initial subset, using
any non-decreasing utility path of adding or dropping varieties. Using the expression
for A (Ω0 ), equation (B.3), and taking derivatives
∂A
= −µ (ωs )
∂ωs
= −
L−
Z
ω∈Ω0
ω∈Ω0
= −P
ω∈Ω0
σ−1
−1
dω
−
Z
Z
Z
p (ω)
1−σ
µ (ω) dω
p (ω)1−σ dω
−1 1−σ
ω∈Ω0
p (ω)
dω
µ (ωs ) + Ap (ωs )1−σ
µ (ωs ) + Ap (ωs )1−σ < 0
43
−2
p (ωs )1−σ
0
Therefore, adding varieties decreases the demand shifter A Ω . The intuition is that
with more market entry, every variety will have less demand.
From any subset Ω0 , use the rule to add any sequence of varieties until the variety with
the highest µ (ω) p (ω)σ−1 in the set makes equation (B.6) bind. Call this variety ωt .
If such a variety does not exist after all varieties on the market have been added, the
consumer buys all varieties.
If, on the other hand ωt does exist, there still may be utility enhancing varieties ωs
outside the set. For instance, when µ (ωs ) = 0, the associated variety ωs is guaranteed
to pass the equation (B.6). If ωs exists ⇔µ (ωs ) p (ωs )σ−1 < µ (ωt ) p (ωt )σ−1 . In words,
if there are utility enhancing varieties left that can be added to the set, the set does
not consist of the varieties with the lowest µ (ω) p (ω)σ−1 , and vice versa.
Next, adding ωs increases utility and reduces the demand shifter A. Therefore, it is
also utility enhancing to drop ωt . Thus, adding a utility enhancing variety not only increases utility directly, it also replaces varieties with the largest µ (ω) p (ω)σ−1 in the set.
Repeated application of the rule improves utility and sorts the varieties on µ (ω) p (ω)σ−1 .
It leads to the same set, i.e., when varieties are organized in two groups, one with low
values for µ (ω) p (ω)σ−1 and one with high values, with the marginal variety ω ∗ that
defines the set size obeying
µ (ω ∗ ) p (ω ∗ )σ−1 =
A (Ω∗ )
.
σ−1
Combining (1) and (2), from any initial set Ω0 , the same set Ω∗ emerges on a non-decreasing
utility path from repeated application of equation (B.6). Therefore Ω∗ is the optimal set. Proof of equation (16) The equality of demand and supply means that in equilibrium,
L σ−1p−c
L
=
.
σµ (G)
F +G σ
p
The left hand side of this constraint is the consumer’s demand for variety (equation 8), and
the right hand side is the free-entry number of firms that can recoup fixed costs F + G from
the margin p−c
on disposable income L σ−1
. The result follows immediately from rearranging
p
σ
this equation. Proof of equations (17) and (18) Consider a single manufacturer using the deviation G∗ and p∗ . Consumers will buy its variety as long as equation (6) holds, i.e., p∗ x∗ ≥
(σ − 1) µ (G∗ ) and will drop the variety otherwise. The manufacturer maximizes profit taking
the strategy of others given.
max
(p∗ − c) x∗ − (F + G∗ ) , subject to (σ − 1) µ (G∗ ) ≤ x∗ p∗ and G∗ ≥ 0
∗
∗
p ,G
Substitute Marshallian demand x = Ap∗−σ , where A is the demand shifter that belongs to
all manufacturers using the policy [p, G]. The demand shifter does not depend on pd or Gd .
44
Define the Lagrangian
L = (p∗ − c) Ap∗−σ − (F + G∗ ) + λ Ap∗−σ+1 − (σ − 1) µ (G∗ ) .
The Kuhn-Tucker (KT) conditions for G are
∂L
∂G∗
G∗ ≥ 0
≤0
∂L
G∗ ∂G
∗ = 0 ,
The derivative of the Lagrangian with respect to Gd is
∂L
= −1 − λ (σ − 1) µ0 (G∗ ) ≤ 0
∂G∗
1. First consider that G∗ is positive. Then,
λ=−
∂L
∂G∗
= 0, and
1
(σ − 1) µ0 (G∗ )
which is also strictly positive.
Taking the derivative of the Lagrangian with respect to p∗ ,
p∗ − σ (p∗ − c) − (σ − 1) λp∗ = 0
from which follows after substituting for λ that the profit maximizing price is
p∗ = σ
σ − 1 − µ0 (G∗ )−1
(B.7)
c.
Finally, in symmetric equilibrium p = p∗ and G = G∗ for each firm. Therefore they
need to obey equation (16), i.e., that in symmetric equilibrium
p∗ = σ
σ−
σ F +G∗
σ−1 µ(G∗ )
c.
This gives two equations and two unknowns from which we can solve that the necessary
and sufficient conditions for equilibrium are equation (17)
σ F + G∗
µ (G ) = − 1 −
σ − 1 µ (G∗ )
0
!−1
∗
and equation (18)
p∗ = c σ
σ − 1 − µ0 (G∗ )−1
2. Next consider that the equilibrium level of investment is 0. When G∗ = 0, equation
(16) directly solves equilibrium prices as
p∗ = c σ
σ−
σ F
σ−1 µ
45
= c
σ
σ−
µ̃
µ
,
and we can use the KT conditions to find the conditions under which this is optimal
for a single manufacturer. Setting the derivative on price to 0, yields a solution for λ.
∂L
Substitute this in the KT conditions for G, in particular that ∂G
∗ < 0,. I find that
∗
G = 0 when
µ
µ0 (0) > −
µ − µ̃
Proof of equation (21)
1
max D (G) σ−1
G
Y
, subject to p (G) = c
p (G)
σ−
σ
σ (F +G)
(σ−1) µ(G)
Substitute the constraint into the objective function, and substitute the expressions for Y
and D. Rearranging this gives
L
max
G
σµ (G)
!
1
σ−1
L σ − 1 ((σ − 1) µ (G) − F − G)
L
= max
G
c σ
(σ − 1) µ (G)
σµ (G)
!
σ
σ−1
((σ − 1) µ (G) − F − G)
c
σ
Maximizing the function above yields the same G as maximizing µ (G)− σ−1 ((σ − 1) µ (G) − F − G).
Taking the first order condition and rearranging gives the result that
µ0 (G) =
µ (G)
σ
−µ (G) + σ−1
(F + G)
which is the same as equation (17)
46
(B.8)