Product Liability, Entry Incentives and Industry Structure

Transcription

1 Product Liability, Entry Incentives and Industry Structure by Stepen F. Hamilton Department of Agricultural Economics Kansas State University 331B Waters Hall Manattan, KS and David L. Sunding Council of Economic Advisers Executive Office of te President Old Executive Office Building, Room 319 Wasington, D.C Marc, 1997 Submitted for te Western Agricultural Economics Association Reno, July We acknowledge elpful conversations wit Josep Stiglitz, Jeffrey Perloff and David Zilberman.

2 Product Liability, Entry Incentives and Industry Structure Abstract Numerous studies suggest tat increasing producer liability in azardous sectors stimulates small firm entry as incumbent firms divest risky activities. Tis paper considers te effect of increased producer liability in a fully-capitalized industry and sows tat te effect on industry structure depends on te sape of te marginal injury relationsip. 2

3 I. Introduction A great deal of debate as centered on te relationsip between liability and industry structure. In an important paper, Ringleb and Wiggins (1990) examine a large number of azardous product industries and find tat increasing product liability is associated wit te entry of small firms. Te mecanism by wic tis occurs, tey assert, is tat liability rules create an incentive for large, incumbent firms to avoid paying damages by vertically divesting risky activities. Suc divestiture is liability reducing wen small firms conducting te risky task ave insufficient assets to pay damages and declare bankruptcy wen suits are filed or, in te case of latent arm, exit te industry before injury emerges. 1 Tis paper considers entry incentives created in an industry by an increase in producer liability. Te analysis concludes tat wile Ringleb and Wiggins empirical observations may be sound, incomplete capitalization and vertical divestiture are not te only possible motivations for canges in market structure following increases in producer liability. Our results indicate tat an incentive for divestiture is sufficient but is not necessary for liability to increase te market sare of small firms. In tis regard, te paper suggests tat te effects of product liability on market structure are even more pervasive tan previous analyses indicate. We base our observations on an oligopoly model wit asymmetric costs, endogenous entry and complete capitalization. Te model employs a general specification of liability tat incorporates several commonly used rules as special cases. Utilizing tis framework, we explore te marginal effects of an increase in liability on several indicators of industry structure: output per firm (for various cost types), total industry output, small 3

4 firm entry and small firm market sare. In particular, we demonstrate tat small firm entry is a likely result of increased producer liability wen marginal injury is increasing in te level of industry output, even wen divestiture incentives do not exist. Te intuition is straigtforward. If marginal arm is increasing in output, producer liability sifts te marginal benefit scedule of eac incumbent firm downward, but also makes it more inelastic. Imposing producer liability in an industry wit increasing marginal damages may tus increase te equilibrium price-cost margin and create an incentive for small firms to enter. Te well-known empirical finding tat an increase in producer liability precedes small firm entry can terefore be explained by more tan simply divestiture incentives or incomplete capitalization in an industry. Te rest of te paper is organized as follows. Section II develops te basic liability model and discusses its relation to oter models of oligopoly and to oter models commonly used in te liability literature. Section III presents te marginal analysis and derives te impacts of an increase in liability on output levels and entry incentives. In Section IV, we igligt te importance of te damage function for te comparative statics results. In particular, we empasize te eretofore unrecognized point tat entry incentives depend on te sign of te marginal injury relationsip. Section V contains concluding comments. II. Te Model We consider a Cournot oligopoly wit endogenous entry as in Besley (1989), Konisi (1990), and Seade (1980a). Te model distinguises between small, ig-cost firms and 1 Anoter analysis based on incomplete capitalization is Boyd and Ingberman (1994). 4

5 large, relatively cost-efficient firms on te basis of differences in marginal production costs as in Dierickx et al. (1988) and Kimmel (1992). Denote te initial number of firms producing in equilibrium as N = m + n, were m is te number of omogeneous low-cost firms, eac wit te cost function c l (y l ), and n is te number of omogeneous ig-cost firms, eac wit cost function c (y ). Te output of a representative firm of eac type is denoted y l and y, respectively, for te low- and igcost firm. All firms maximize profit wit respect to output; consumer and worker safety considerations are suppressed by limiting attention to unavoidable portions of liability exposure. All firms in te industry are assumed to be fully capitalized. Te expected liability from azardous production is modeled as a function of total industry output, as in te case of common pool environmental ealt risks. Te profit of eac firm is [ ] = PY ( ) gy ( ) y c( y) F, i = (, l ), π i i i i i were Y = my l + ny, P(Y) is te inverse demand function, and g(y) is marginal per-unit liability. Tis framework incorporates common liability rules and a special case of te model occurs wen eac firm s liability is determined solely by its own output. We describe te relative efficiency of a representative firm in eac sub-group as follows: Firm l is more efficient tan firm wenever l l dc ( y ) dc ( y ) l <. (C1) dy dy l y * y * Condition (C1) states tat te marginal cost of te representative low-cost producer is less tan te marginal cost of a ig-cost producer at te respective equilibrium output levels. Also, to derive te comparative statics effects of a cange in liability structure, we define 5

6 te efficiency of low- and ig-cost firms wit respect to marginal canges in output. Specifically, we wis to eliminate from consideration te somewat unusual case in wic a small, ig-cost firm as a iger marginal cost of production tat te representative low-cost firm, yet as a greater capacity to expand production. Tat is, wile we do not wis to excessively restrict te model by expressing te difference in efficiency in a global sense, it is important maintain te identity of ig- and low-cost firms by assuming tat large, low-cost firms ave greater scale economies tan small, ig-cost firms. Te following condition represents te case in wic low-cost firms ave a cost advantage for a marginal expansion of output: 2 l l c ( y ) l 2 ( y ) 2 c ( y ) 2. (C2) ( y ) l y * y * Condition (C2) states tat a marginal expansion of output does not raise te marginal cost function of a low-cost firm by more tan tat of a ig-cost firm. Restricting attention to tis case eliminates ambiguity wen we refer to low-cost firms by ruling out te situation in wic ig-cost firms switc identity wit low-cost firms as output levels expand. 2 Differentiating te profit expression of a representative firm in sub-group i yields te first-order condition = P g+ ( P' g') y c = 0 (1) πy i i y i i i and second-order condition 2 Condition (C2) is sufficient, toug not necessary, for te results tat follow. Te condition is likely to be met in practical applications, since low-cost firms may ave iger marginal costs at low levels of output, yet be operating at a scale wic is well beyond any crossing of marginal cost wit tat of igcost firms. It is somewat implausible to imagine ig-cost firms sufficiently investing in te unused, excess capacity to make tem more efficient tan low-cost producers at ig levels of output. 6

7 = 2( P' g') + ( P'' g'') y c < 0. (2) πyy i i yy i i i i i were identical conditions can be written for te representative firm of type j. Te entry condition is described by treating te number of firms as a continuous variable following Besley (1989), Mankiw and Winston (1986), and Seade (1980a). We assume tat canges in liability structure are modest enoug to not affect te number of low-cost firms (altoug liability may affect large firm output decisions), tereby restricting attention to small firm entry. 3 Entry occurs in te model until profit is driven to zero for firms in te ig-cost industry sub-group. In equilibrium, te number of ig-cost firms in te industry, n*, is te solution to [ ] * = PY ( *) gy ( *) y * c ( y*) F = 0, (3) π were Y* = my l * + n*y * in a symmetric sub-group equilibrium. Te equilibrium value of n* is determined simultaneously wit y l * and y * using first-order conditions (1) and te entry condition (3). It is assumed tat n* is unique, as is te case wen at least a portion of fixed costs are sunk (Vickers, 1989). We assume te usual conditions for stability of a Cournot equilibrium. Following Dixit (1986), and Seade (1980b), expected marginal benefit is a decreasing function of firm output and declines faster tan te marginal cost curve of eiter type of firm, or and B' = P' g' < 0, (C3) 3 Tis modeling assumption is based in part on te desire to isolate te marginal effects of entry. Low cost firms not currently producing (i.e., potential entrants wit superior tecnology), ave incentives to enter unrelated to industry liability. Tus, we restrict attention to industries tat are in long run equilibria and identify conditions in wic an increase in liability induces ig-cost entry tat would oterwise be unprofitable. 7

8 i i V = B' c < 0. (C4) In te context of te asymmetric-cost equilibrium it is possible to sow tat te output of low-cost firms is greater tan tat of ig-cost firms using expressions (1). Manipulating te first-order conditions for low- and ig-cost types yields yy i i l l B'( y y ) = c c, wence y l > y follows from conditions (C1) and (C3). III. Marginal Effects of Canging Product Liability Te effect of modifying te product liability rule can be expressed as a sift in te expected liability function. Following Dixit (1986), let q be a sift parameter in te yl y expected liability function g = g(y; q). 4 Te expected liability function is expressed as l g = g( y + ( m 1) δ + y + ( n 1) γ; θ ), (4) were d and g are introduced purely for notational convenience and denote te output levels of low- and ig-cost rival firms. Te effect of a cange in expected liability is computed by totally differentiating equation (1) for bot low- and ig-cost types and expression (3), making use of equation (4), te envelope teorem, and te identities d = y l and g = y. Combining equations, l l l l l l l πyy + πyδ πyy + π γ π y y dy πy l l l l l ln lθ πyy + πyδ πyy + πyγ πyn dy πy θ l =. (5) πy + πδ πγ π n dn π l θ = π < 0, Evaluating te determinant of coefficient matrix (5) yields D y B[ V ] 2 l ( ) ' yy 4 If liability rules are newly imposed in an industry, suc as occurred in te late 1960s in te U.S., we can tink of initial expected liability, g(y), as being infinitesimally small so as to avoid complications arising from a discontinuous expected liability function. 8

9 were te inequality olds by stability conditions (C3) and (C4). Te effect of te cange in expected liability on te output of te representative ig- and low-cost firm is dy = y Ω B' π yy, (6) and dy = [ V y + B'( y y )] l l l l BV ' π yy Ω, (7) respectively, were W = [g Yq B - g q B ]. Note tat te sign of expressions (6) and (7) are te same as te sign of W. Canging liability as te following effect on te number of ig-cost firms: l l l l { gv θ π yy Ω [( n ) yv myv mb'( y y ) ]} dn y = 1 + +, (8) D were te expression in square brackets is negative. Expression (8) provides a condition tat defines te entry and exit of ig-cost firms in a azardous sector following a cange in expected liability. Te sign of expression (8) depends on te value of two parameters, te cange in expected liability per unit of output, g q, and te value of te cross-elasticity parameter, W. Using (6), (7), and (8), te effect of producer liability rules on industry output is dy dn y n dy m dy l = + +, wic is written as dy = gθπ yy B' π Ωy yy. (9) 9

10 Expression (9) sows tat an increase in producer exposure to liability reduces te total output of te azardous product wenever W ³ 0. An increase in expected marginal liability increases output in (9) iff θ[ yy ] g 2( B' + B'' y ) c gyθb' y > 0. Increased liability leads to greater industry output wen te level effect of te sift in expected liability is small relative to te slope effect. If te expected marginal liability is an increasing function of industry output (g Yq > 0), for example, a perverse output effect can occur as te expected marginal benefit scedule becomes more inelastic following te liability rule. Te key component ere is te entry condition. In an oligopoly witout entry, a decrease in te elasticity of expected marginal benefit tends to increase te residual price-cost margin, compounding te downward level effect by causing an output contraction. In te present model, owever, industry output can expand wen demand becomes more inelastic due to te entry of ig-cost firms. Te ability of incumbent firms to increase residual price premiums in response to greater exposure to liability is tus constrained by te possibility of entry. We now examine te central question of interest: te effect of a cange in liability structure on te market sares of ig- and low-cost firms. Te cange in market sare for firms in eac respective sub-group is i i i ds Ydx ( ) x( dx) = X 2. Substituting terms from te analysis above, it follows tat canges in te market sares of ig- and low-cost firms are given as follows: 10

11 [ θπ Ω( ) yy ] ds s g Y y = XB' π yy (10) and l l l l l { gyv θ π Ω yy [ BY ' ( y y ) y( YV yv )]} l ds = + 2 l. (11) X BV ' π yy Te first term in eac expression represents an increase in te market sare for eac type of firm as te downward sift in expected marginal benefit troug te level effect precipitates te exit of ig-cost firms. Note tat te term in square brackets in expression (11) is positive by te definition of low-cost producers in condition (C2). Tus, for eiter type of firm, market sare unambiguously increases wen W ³ 0. Te market sare of eac type of firm can decrease wen W < 0, owever, as te entry of ig-cost firms is possible in tis region. We next describe te effect of a cange in liability structure on te entry of small, ig-cost firms. As we sall see, te sape of te expected liability function as a profound effect on market structure in te azardous product sector. IV. Liability and Industry Structure Wen producer liability rules are imposed in an industry wit latent azards, te effect can be represented by an outwards sift in expected production risk, g q > 0, or alternately, by an inward sift of te expected marginal benefit scedule, B. If production risk in te azardous sector is associated wit constant expected marginal liability, te effect is te parallel inward sift of expected net benefits represented by g q > 0 and g Yq = 0. Similarly, te case of increasing marginal liability can be expressed by te conditions g q > 0 and 11

12 g Yq > 0, wile decreasing marginal liability can be expressed by g q > 0 and g Yq < 0. Wen expected marginal liability is constant, te imposition of producer liability rules lowers profitability in te sector by a parallel inward sift of expected marginal benefit. Inspecting expressions (6) and (7), a parallel sift in expected marginal liability does not perturb te output level of representative low- and ig-cost firms in te case of a linear demand function, but decreases (increases) te output of eac firm in eac subgroup wen industry demand is convex (concave). Te exit of ig-cost firms unambiguously occurs in an industry wit constant marginal liability wen demand is concave, altoug entry can occur wen demand is sufficiently convex. Industry output decreases in all cases except wen demand is igly convex. Te market sare of incumbent firms increases wen demand is concave, but can decrease wen demand is strongly convex under te same conditions tat stimulate te entry of ig-cost firms. Similarly, te net producer price and industry profitability increase wen demand is concave and decrease wen demand is convex. 5 Wen te expected marginal liability function is decreasing, W is likely to be positive; it is unambiguously positive, in fact, wen te liability function is weakly concave and can only be negative wen industry liability is igly convex. Hence, te likely effect of a producer liability rule in te case of decreasing expected marginal liability is to create an output expansion by incumbents and an increase in te market sare of representative firms in eac sub-group. Declining marginal liability is also likely to 5 Te influence of demand convexity on te comparative statics of an asymmetric-cost oligopoly is described in Dierickx et al.,

13 stimulate te exit of ig-cost firms, reduce total industry output of te azardous product, and lead to iger expected marginal benefit and to greater industry profit. Te case of increasing expected marginal liability is te most likely scenario wen te liability arises from environmental ealt risk, suc as in te case of consumer ealt risk associated wit radiation exposure, DES, cigarette smoking, dioxin, vinyl cloride, PCB, coke-oven emissions, and oter latent azards. Increasing expected marginal liability is likely to occur for suc carcinogenic substances, as te ealt risk associated wit exposure generally increases wit exposure level (Lictenberg and Zilberman, 1989). For industries tat rely on azardous productive inputs, te expected marginal liability function, in most cases, is an increasing function of industry output. Wen te expected marginal liability is increasing in industry output, W is negative in all but te most unlikely case in wic te expected marginal benefit function is igly concave. Wen te expected marginal benefit function is at least weakly convex, it follows tat W < 0 in te case of increasing marginal liability, wence te production level of eac incumbent firm contracts, expected marginal benefit decreases and industry profitability declines. All oter effects are ambiguous and depend on te magnitude of te level effect of te cange in expected liability. Of all te possible scenarios, te case of increasing marginal injury is most likely to stimulate te entry of ig-cost firms. Te possibility of ig-cost firm entry is greater wen te level effect of te liability rule is small relative to te slope of te expected marginal liability function. Tat is, wen marginal liability is small and increasing wit industry output, entry of ig-cost firms is likely to occur. 13

14 V. Conclusion In an important paper, Ringleb and Wiggins (1990) find tat an increase in liability frequently precedes te entry of small firms and leads to increases in small firm market sare in azardous sectors of te economy. Tey ypotesize tat suc entry results from te desire of large, incumbent firms to sield temselves from liability by divesting risky activities. Tis paper sows tat wile Ringleb and Wiggins empirical observations may be sound, incomplete capitalization and latent injury are not te only possible motivations for canges in market structure following an increase in product liability. In particular, we sow tat small firm entry can occur even in a fully capitalized environment witout divestiture incentives. Our paper points out tat entry incentives are fundamentally related to te sape of te damage function. In particular, an increase in liability is likely to result in small firm entry wen marginal damage is increasing in te level of industry output. In tis case, increased liability sifts te marginal benefit scedule downward for eac incumbent firm and makes it more inelastic. Imposing liability may tus increase te industry price-cost margin and create incentives for small firm entry. Te well-known empirical finding tat an increase in liability precedes small firm entry in industries wit latent azards can terefore be explained by factors oter tan divestiture incentives or incomplete capitalization. Te implication is tat te relationsip between liability and market structure may be considerably ricer tan previously recognized. 14

15 References Besley, T., Commodity Taxation and Imperfect Competition: A Note on te Effects of Entry, Journal of Public Economics 40(1989): Boyd, J. and D. Ingberman, Extending Liability: Sould te Sins of te Producer be Visited Upon Oters?, Business, Law and Economics Center Working Paper BLE-93-07, Jon M. Olin Scool of Business, Wasington University, Dierickx, I., C. Matutes, and D. Neven, "Indirect Taxation and Cournot Equilibrium," International Journal of Industrial Organization 6(1988): Dixit, A., Comparative Statics for Oligopoly, International Economic Review 27(1986): Kimmel, S., Effects of Cost Canges on Oligopolists' Profits, Journal of Industrial Economics 40(1992): Konisi, H., Final and Intermediate Goods Taxation in an Oligopolistic Economy wit Free Entry, Journal of Public Economics 42(1990): Lictenberg, E., and D. Zilberman, Te Economics of Public Healt Regulations, Quarterly Journal of Economics (1989). Mankiw, N., and M. Winston, Free Entry and Social Inefficiency, Rand Journal of Economics 17(1986): Oi, W., Te Economics of Product Safety, Bell Journal of Economics and Management Science 4(1973): Ringleb, A. and S. Wiggins, Liability and Large-Scale, Long-Term Hazards, Journal of Political Economy 98(1990):

16 Seade, J., On te Effects of Entry, Econometrica 48(1980): Seade, J., Te Stability of Cournot Revisited, Journal of Economic Teory 23 (1980): Spence, A., Consumer Misperceptions, Product Failure and Producer Liability, Review of Economic Studies 44(1977): Vickers, J., Te Nature of Costs and te Number of Firms at Cournot Equilibrium, International Journal of Industrial Organization 7(1989):