Sunk Costs, Market Structure And Welfare:
A General Equilibrium Interpretation
Nelson S
Duke University
This version: November 10, 2007
Abstract
This paper develops a general equilibrium model with the purpose of identifying
fundamental determinants of market structure and their welfare impact. The main
effects are derived from the interaction between horizontal and vertical differentiation,
induced by different sets of exogenous and endogenous sunk costs. The former are
found to be positively correlated with market concentration and market power, but
their relation to welfare approaches an inverted U-shaped curve. On the other hand,
endogenous sunk costs parameters are found to be positively correlated with market
concentration, but negatively with market power, as long as no price coordination
takes place. Their relation to welfare approaches a U-shaped curve. These results
carry important policy implications, detailing new reasons why simple concentration
indicators are not a sufficient statistic for welfare evaluations. The model also suggests
new tools in order to improve these assessments., making use of observable variables to
proxy for unobservable determinants.
Keywords: Market Structure, Sunk Costs, Vertical Differentiation, Welfare.
JEL Classification Numbers: E10, L16, L40, L50
I would like to thank Pietro Peretto and Michelle Connolly for their guidance and encouragement. I alsothank Huseyin Yildirim and seminar participants at the Triangle Dynamic Macro Group at Duke Universityfor helpful comments and suggestions.
Duke University, Department of Economics, nelson.sa@duke.edu
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1 Introduction
This paper examines how different types of fixed costs, either exogenous or endogenous,
drive the relationship between market structure and welfare. That is done in the context
of a general equilibrium model where market concentration, market power and productivity
arise from the interaction between horizontal and vertical differentiation. This can be used
to determine the number of alternative varieties supplied, the scale of consumption for each
one of them and their degree of cross-substitutability in the preference space. The combi-
nation of these elements offers a comprehensive depiction of welfare outcomes. The policy
implications are particularly relevant, offering additional insights to a wide range of economic
literature on antitrust regulation. A new indicator is proposed, using the relative weight of
endogenous sunk costs (embodied in advertising and research activities) and exogenous sunk
costs (embodied in setup and fixed operational expenditures) to distinguish between positive
and negative structural features within more concentrated markets.
Early theory suggests two possible effects of market concentration on welfare. Structural-
ist views posit that low firm numbers, resulting from exogenous setup barriers, enhance the
likelihood of collusion and reinforce market power, to the detriment of welfare. Conversely,
efficiency views hypothesize that high concentration is simply the result of exogenous in-
dividual cost disparities, which enable firms with comparative productivity advantages to
gain larger market shares. A more refined approach has later been provided by game the-
oretical interpretations. Exploring models of strategic interaction applied to oligopolistic
environments, they have succeeded in establishing a simultaneous and endogenous relation-
ship between concentration and profitability. In addition, they have drawn attention to the
price elasticity of demand as a strong explanatory variable behind profit-revenue ratios. How-
ever, some questions remain open. First, these models lack a formal assessment of welfare
implications in the broader context of horizontal variety and vertically enhanced quality.
Second, empirical studies uncover mixed evidence concerning the relative incidence of neg-
ative market power effects and positive efficiency gains in different industries with identical
concentration features. As a result, a growing tendency has emerged to focus in increasingly
specific industry studies, in detriment of broader and simpler statistical regularities.
The model proposed in this paper revisits these questions in two new ways. In the first
place, its general equilibrium framework affords greater analytical flexibility in order to draw
systematic cross-sectional associations between welfare variables and cost parameters. It
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also enables new interaction channels to be introduced between these elements. Downstream
market structure affects the incentives for the development of new intermediate goods by
suppliers, thus influencing overall productivity. In the second place, it is well accepted that
variety matters for welfare purposes. This model examines the quality of industry diversity
by making cross-product substitutability endogenous. The relevance of this feature becomes
obvious when noting that demand elasticity depends on how close multiple varieties of a good
are in the preference range. This will in turn affect market power for each final producer and
carry new welfare implications.
The mechanisms explored in this paper can be described as follows. On the one hand,
exogenous sunk costs require the creation of market power, so that the firm is able to gen-
erate enough revenues to break even. This can be achieved through vertical differentiation,
supported either by technological innovation or persuasive advertising. However, larger sunk
costs limit the number of firms the market can sustain and constraint horizontal differentia-
tion. In such cases, concentration and price-cost margins are positively related. On the other
hand, more difficulty in increasing the willingness to pay from consumers induces stronger
product homogeneity, reducing market power and prices. Since exogenous fixed costs must
still be compensated, outlays on vertical differentiation eventually increase in order to sus-
tain a necessary threshold of imperfect competition. The higher research (or advertising)
expenditures once again discourage market entry and horizontal differentiation. Under such
conditions, concentration and price-cost margins may display a negative relation across in-
dustries, as long as collusion does not take place. The overall correlation between structure
and performance indicators reflects the joint product of these distinctive partial effects.
Where exogenous sunk costs are involved, this model yields results that are generically
consistent with a large body of literature inspired by structuralist views of industrial or-
ganization, linking high concentration to negative welfare outcomes. However, this occurs
here in the context of a hump shaped relationship, implicitly defining an ideal value of fixed
operational costs. In case these are excessively low, too much entry and horizontal differ-
entiation takes place, reducing market shares and the return from investments in vertical
differentiation. The resulting product homogeneity may be enough to generate a negative
welfare impact within lower ranges of concentration.
Endogenous sunk cost parameters may influence the fundamental links between market
concentration, market power, and welfare in less conventional ways. In case vertical differ-
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entiation is difficult to introduce, the market can become increasingly concentrated, while
the heterogeneity of consumption alternatives decreases adversely. However, beyond a cer-
tain threshold of substitutability, the loss from having fewer varieties becomes relatively less
important and is more than compensated by the higher consumption associated to larger
production scales and lower market power. This effect is reinforced by external economies,
since additional demand generates entry incentives for suppliers, enabling the development
of more efficient production methods. Welfare gains may then be attained in this way, but
these must be measured against the risks of collusive behavior eventually introduced when
markets become more concentrated and homogeneous.
The insights provided by this paper carry important policy implications. They confirm
that concentration is a misleading statistic for welfare evaluation. Identical market features
may conceal different cost structures and social value, according to diverse combinations of
exogenous and endogenous fixed costs. In order to help identify these alternative settings, one
additional tool for market assessment is proposed here. This consists of vertical differentiation
outlays (embodied in advertising and/or research activities) weighted by a per period measure
of fixed operational costs for each consumption variety. Using observable variables, a better
appraisal of the relative importance of both sunk costs might thus be achieved, shedding new
light on how these forces shape market structure and yield different welfare outcomes.
The paper is organized in the following manner. Section 2 presents an overview of the
concentration-performance debate, set in historical perspective. This will enable a more
complete understanding of the objectives and contributions of this work in the context of
the past literature. Section 3 lays out the theoretical model, exploring both its positive and
normative facets. Finally, section 4 c
