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Sunk Costs, Market Structure And Welfare: A General Equilibrium

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  • 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

    2

  • 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-

    3

  • 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

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