Competition versus efficiency

Transcription

1 UNIVERSITY OF NOTTINGHAM Discussion Papers in Econoics Discussion Paper No. 0/ Copetition versus efficiency Souyananda Dinda and Ariit Mukheree October DP 0/

2 Copetition versus efficiency Souyananda Dinda Chandragupt Institute of Manageent Patna, India and Ariit Mukheree University of Nottingha and The Leverhule Centre for Research in Globalisation and Econoic Policy, UK October 00 Abstract: It is usually believed that higher copetition, iplying ore active firs, benefits consuers and encourages the antitrust authorities to foster copetition. We show that this view can be isleading, and higher copetition ay actually ake the consuers worse-off. We suggest that the antitrust authorities should be interested in reducing inefficiency instead of increasing copetition through ore firs. Key Words: Copetition; Consuer welfare; Cost asyetry; Tax JEL Classifications: L40; L3; L; H5; D43 Correspondence to: Ariit Mukheree, School of Econoics, University of Nottingha, University park, Nottingha, NG7 RD, UK E-ail: Fax: We thank Tarun Kabira for helpful coents and suggestions. The usual disclaier applies.

3 Copetition versus efficiency. Introduction It is usually believed that higher copetition, iplying ore active firs, benefits consuers (Metzenbau, 993, Gans, 005 and Hausan and Leibtag, 007) and encourages the antitrust authorities to foster copetition. We show that this view can be isleading. We show that higher copetition can actually reduce consuer welfare in the presence of governent tax/subsidy policies. Considering an industry with asyetric cost firs and strategic tax policy, we show that if the nuber of ore cost inefficient firs increases, it reduces consuer welfare. However, consuer welfare increases if either the nuber of ore cost efficient firs increases or the costs of the ore cost inefficient firs reduce. Hence, in the presence of strategic governent policies, a rise in the nuber of ore cost inefficient firs akes the consuers worse off, thus showing a conflict between copetition and inefficiency. It is therefore safe for the antitrust authorities to consider reducing inefficiency instead of increasing copetition through ore firs. To understand the reasons for our results, let us first consider the situation with no tax/subsidy policies of the governent. If we consider an oligopoly industry with cost asyetric firs, we encounter two types of inefficiencies. One type of inefficiency is due to the oligopolistic copetition, and the other type of efficiency is due to cost asyetry. In this situation, if the nuber of firs increases, irrespective of its arginal cost, it tends to reduce the inefficiency due to oligopolistic Prootion of consuer welfare is the coon goal of consuer protection and copetition policies. As entioned in the docuent by the U.S. Departent of Justice ( Consuers benefit fro copetition through lower prices and better products and services. Wooton and Zanardi (004) survey the use of anti-duping and anti-trust policies in encouraging and aintaining copetition in open econoies.

4 copetition. If the nuber of ore cost efficient firs increases, it also tends to reduce the effect of inefficiency due to cost asyetry. However, if the nuber of ore cost inefficient firs increases, it tends to increase the inefficiency due to cost asyetry by increasing the nuber of ore cost inefficient firs. If there is no governent intervention through tax/subsidy policies, the effect of inefficiency due to oligopolistic copetition doinates the effect of inefficiency due to cost asyetry, and the increase in the nuber of firs increases total output in the industry irrespective of their costs. Even if the nuber of firs reains the sae but the cost of the ore cost inefficient firs reduces it tends to reduce the inefficiency due to cost asyetry and increases total output in the industry. Hence, without governent intervention, both ore copetition, which increases the nuber of firs in the industry, and the reduction in cost asyetry ake the consuers better off, and the antitrust authority does not need to bother whether ore cost efficient or ore cost inefficient firs are entering the industry. However, the situation changes if the governent charges a welfare axiizing unifor tax/subsidy depending on the nuber of firs and the cost asyetry. The consideration of a unifor tax/subsidy can have the following ustification. It is often argued that the unifor tax rates are sipler and easier to ipleent. As entioned in Coşgel (006, pp. 333) The cost of adinistering a syste with discriinatory rates can be very high when the characteristics of tax payers do not differ systeatically or when these differences cannot be easily observed. It is generally easier to identify differences between the sectors of the econoy than within each sector, aking it harder to ipleent discriinatory rates within a sector. For exaple, the governent iposes the sae tax/subsidy even if the car producers differ in productivities.

5 If the governent charges a unifor tax/subsidy, it can eliinate the effects of inefficiency due to oligopolistic copetition, but cannot eliinate the effect of inefficiency due to cost asyetry. 3 Any change that affects inefficiency due to the cost asyetry affects the consuers. Hence, with governent intervention, a rise in the nuber of ore cost inefficient firs increases inefficiency in the industry and reduces total output in the industry, thus aking the consuers worse-off. In this situation, even if copetition increases due to the increase in the nuber of ore cost inefficient firs, the consuers are worse off, since it also increases inefficiency in the industry. However, if either the nuber of ore cost efficient firs increases or the cost of the ore cost inefficient firs reduces, both of which reduce the effects of the inefficiency due to cost asyetry and ake the consuers better-off. One should not get confused between our result and Lahiri and Ono (988) and Kleperer (988). In both Lahiri and Ono (988) and Kleperer (988), higher copetition, either due to lower arginal cost or due to entry of a fir, always akes the consuers better off. In contrast, if the nuber of ore cost inefficient firs increases in our analysis, it akes the consuers worse off. The reainder of the paper is organized as follows. Section describes the odel and derives the results under a linear deand. Section 3 concludes.. The odel and the results Consider an econoy with n ( ) firs, each with the arginal cost of production 0, and ( ) firs, each with the arginal cost of production c (> 0), copeting like Cournot oligopolists with a hoogeneous product. We assue that the welfare axiizing governent of the country iposes a per-unit tax 4, t, on each fir. 3 It is intuitive that the governent could eliinate both types of inefficiencies if it could charge discriinatory tax/subsidies, and the nuber of firs would not affect the total output of the industry. 4 If t is negative, it iplies that the governent is subsidizing the firs. 3

6 We assue that the inverse arket deand function is P a q, () where P is price and q is the total output sold. Although we prove our ain result in this section under a linear deand function, we show in the Appendix that our result holds also under a general deand specification. We consider the following gae. Given the nuber of firs, at stage, the governent charges t in order to axiize welfare, which is the su of total profits of the firs, consuer surplus and tax revenue. At stage, the firs copete like Cournot oligopolists. We solve the gae through backward induction. Given the tax rate, each of n firs axiizes ( a q t q to deterine its output, where i,,..., n, and each of firs axiizes ( a q c t) q to deterine its output, where n+, n+,..., n+. The equilibriu outputs of the ith fir, i,,..., n, and the th fir, n+, n+,..., n+, can be found respectively as ) i q i a t+ c n+ + and a t ( n+ ) c q. () n+ + We assue that a t+ c> 0 and a t ( n+ ) c> 0, which ensure positive outputs of all firs. The total output and the price of the product are respectively ( a t)( n+ ) c q n+ + (3) and a+ t( n+ ) + c P. (4) n+ + It is clear fro (3) that if the tax/subsidy is not adusted depending on the nuber of firs and/or cost asyetry, ore firs (regardless of their types) and cost reduction in the ore cost inefficient firs increase q, thus aking the 4

7 consuers better off. Hence, under exogenous tax/subsidy, ore firs in the industry ake the consuers better-off, irrespective of the type of the fir. Now we want to see the effects of strategic tax/subsidy policies. To show this, we solve the first stage of the gae, where the governent deterines t that axiizes welfare. The governent axiizes the following expression to deterine t: ( q ) Max( P t) q + ( P c t) q + + t( q + q ) t n n+ n n+ i i i n+ i n+ ( q ) Max Pq c q +, (5) t n+ n+ where n n+ i + i n+. q q q The equilibriu tax rate can be found as t a ( c) an < 0. (6) ( n+ ) We get fro () and (6) that the equilibriu outputs of the ith fir, i,,..., n, and the th fir, n+, n+,..., n+, are respectively q i an ( + ) + cn ( + ) ( n+ ) (7) and q an n c n n ( n+ + )( n+ ) ( + )( + + ) [( + )( + ) + ]. (8) It follows fro (7) and (8) that the outputs of all firs are positive if c[( n+ )( n+ ) + ] a > a, (9) ( n+ )( n+ + ) which is assued to hold. We get that the total output is c q a. (0) n+ 5

8 Proposition : (a) An increase in n increases q, thus aking the consuers betteroff. (b) An increase in reduces (c) A reduction in c increases q, thus aking the consuers worse-off. q, thus aking the consuers better-off. Proof: (a) We get that q c > n ( n+ ) 0. (b) We get that (c) We get that q nc < ( n+ ) 0 q < 0. c ( n+ ). The reason for our interesting result, which is Proposition (b), is due to the following reason. We have seen in (3) that, for a given t, an increase in increases total output. However, it follows fro (6) that if increases it reduces subsidy (i.e., t ), which tends to reduce total output. Since the governent policy internalizes the inefficiency due to oligopolistic copetition but not the inefficiency due to the cost asyetry, an increase in reduces total output by reducing subsidy. We show in the Appendix that this interesting result holds also under a general deand function. We have done the above analysis for a hoogeneous product. However, it is intuitive that if the products of the firs are differentiated, ore firs, irrespective of their types, create a positive effect on the consuers by increasing the nuber of varieties. Hence, the variety effect tends to reduce the negative effect of a rise in the nuber of ore cost inefficient firs. Therefore, a rise in the nuber of ore cost inefficient firs akes the consuers worse-off if the products are not very uch 6

9 differentiated so that the inefficiency due to the cost asyetry doinates the effect of product differentiation. 3. Conclusion It is generally believed that higher copetition akes the consuers better-off and encourages the antitrust authorities to foster copetition. We show that this view can be isleading in the presence of strategic governent tax/subsidy policies. If the firs differ in ters of arginal costs, an increase in the nuber of ore cost inefficient firs, which increases copetition but also creates ore inefficiency in the industry, reduces consuer surplus. Hence, the antitrust authority should consider reducing inefficiency instead of increasing copetition. 7

10 Appendix Output reducing entry under a general deand function: Now we show that our interesting result, i.e., a rise in the nuber of ore cost inefficient firs reduces total output, holds also under a general deand function. P 0. 5 Assue that the inverse arket deand function is Pq ( ) with P < 0 and Given the tax rate, each of the ore cost efficient firs and each of the less cost efficient firs axiize the following expressions respectively to deterine their outputs: Max( P t) q, i,,..., n (A) qi i Max( P t c) q, n+, n+,..., n+. (A) q The equilibriu outputs are given by the following conditions respectively: P t Pq i + 0, i,,..., n (A3) P t c Pq + 0,,,..., n+ n+ n+. (A4) The total outputs of the firs are deterined by the following expression: + +, (A5) ( P t)( n ) c Pq 0 where n n+ i + i n+, and it depends on t. q q q The governent axiizes the following expression to deterine the tax rate: t q n+ ( ). (A6) 0 n+ Max P q dq c q The equilibriu tax is deterined by the following expression: 5 Our result holds as long as the industry arginal revenue is downward sloping. Our assuption of P 0 satisfies this requireent. 8

11 q P n+ q n+ c 0. (A7) It follows fro (A7) that > 0, i.e., as the nuber of ore cost inefficient firs increases, it increases the equilibriu tax, since n+ n+ q < 0 fro (A4). Now we want to see the effect of on total output. We get fro (A5) that ( P t c) ( n+ ) dq d [ P ( n + + ) + P q ]. (A8) Since [ P( n+ + ) + P q ] > 0, dq 0 d < if P t c n ( ) ( + ) < 0. (A9) It is worth noting that the sign of (A9) does not depend on the curvature of the deand function, which is given by P. Hence, it is iediate that our qualitative result of Proposition (b), which is shown with a linear deand function (where P 0 ), also occurs under a general deand function P(q). The non-linear deand function only affects the quantitative result by aking P 0. It is also iediate fro (A9) that if the tax rate does not change with the nuber of firs, i.e., if the tax rate is exogenous, we have 0 and (A9) does not hold since P t c > fro (A4). That is, for a given tax, if the nuber of ore ( ) 0 cost inefficient firs increases, it increases total output. However, if the governent chooses welfare axiizing tax, a rise in the nuber of ore cost inefficient firs reduces total output by aking > 0. 9

12 References Coşgel, M.M. (006) Taxes, efficiency, and redistribution: discriinatory taxation of villages in Ottoan Palestine, Southern Syria, and Transordan in the sixteenth century, Explorations in Econoic History 43, Gans, J.S., 005, Protecting consuers by protecting copetition: does behavioural econoics support this contention?, Working Paper, University of Melbourne. Hausan, J. and E. Leibtag, 007, Consuer benefits fro increased copetition in shopping outlets: easuring the effect of Wal-Mart, Journal of Applied Econoetrics, 7: Kleperer, P., 988, Welfare effects of entry into arkets with switching costs, Journal of Industrial Econoics, XXXVII, Lahiri, S. and Y. Ono, 988, Helping inor firs reduces welfare, Econoic Journal, 98: Metzenbau, H.M., 993, Antitrust enforceent: putting the consuers first, Health Affairs, Fall: Wooton, I. and M. Zanardi, 004, Trade and copetition policy: anti-duping versus anti-trust, in E.K. Choi and J. C. Hartigan (Eds.), Handbook of International Trade, Vol. II, Blackwell Publishing. 0