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Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Model and the Results
  5. 3. Conclusion
  6. Appendix
  7. References
  8. Biographies

It is usually believed that higher competition, implying more active firms, benefits consumers. We show that this may not be the case in an industry with asymmetric cost firms. A rise in the number of more cost-inefficient firms makes the consumers worse off in the presence of a welfare-maximizing tax/subsidy policy. A rise in the number of more cost-inefficient firms also reduces social welfare.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Model and the Results
  5. 3. Conclusion
  6. Appendix
  7. References
  8. Biographies

It is usually believed that higher product market competition reduces price and benefits the consumers (Metzenbaum 1993, Hausman and Leibtag 2007). However, the evidence does not support this view always. Caves, Whinston, and Hurwitz (1991), Grabowski and Vernon (1992), and Perloff, Suslow, and Seguin (2006) show that entry triggers price in the U.S. pharmaceutical industry. Using simulations, Thomadsen (2007) shows that price in the fast food industry may be higher under duopoly than under monopoly.

We provide an explanation for the price raising effect of higher competition. Considering an industry with asymmetric cost firms, we show that a rise in the number of more cost-inefficient firms makes the consumers worse off in the presence of a welfare-maximizing tax/subsidy policy.1 However, the consumers are better off if either the number of more cost-efficient firms increases or the costs of the more cost-inefficient firms reduce.

To understand the reasons for our results, let us first consider the situation with no tax/subsidy policies of the government. We encounter two types of inefficiencies under oligopoly with cost asymmetry. One type of inefficiency is due to the oligopolistic competition, and the other type of inefficiency is due to cost asymmetry. If the number of firms increases, it tends to reduce the inefficiency due to oligopolistic competition, irrespective of the entrant's marginal cost. If the number of more cost-efficient firms increases, it also tends to reduce the effect of inefficiency due to cost asymmetry. However, if the number of more cost-inefficient firms increases, it tends to increase the inefficiency due to cost asymmetry. In the absence of tax/subsidy policies, the effect of inefficiency due to oligopolistic competition dominates the effect of inefficiency due to cost asymmetry, and more firms or lower marginal costs of the more cost-inefficient firms increase total output and make the consumers better off.

However, the situation changes in the presence of a welfare-maximizing uniform tax/subsidy policy.2 A uniform tax/subsidy can eliminate the effects of inefficiency due to oligopolistic competition, but it cannot eliminate the effect of inefficiency due to cost asymmetry. Hence, any change that increases the inefficiency due to cost asymmetry affects the consumers adversely. Therefore, a rise in the number of more cost-inefficient firms reduces consumer surplus in the presence of a uniform tax/subsidy policy. However, more cost-efficient firms or lower marginal costs of the more cost-inefficient firms make the consumers better off.

One should not get confused between our result and Lahiri and Ono (1988) and Klemperer (1988), which suggest that higher competition, either due to lower marginal cost or due to entry of a firm, always makes the consumers better off, although entry of a more cost-inefficient firm may reduce welfare. Our result does not support the results of Lahiri and Ono (1988) and Klemperer (1988) in the sense that a rise in the number of more cost-inefficient firms in our analysis makes the consumers worse off.

Since the endogenous tax/subsidy policies can be viewed as a way to regulate the equilibrium outcomes, our paper can be related to Gans and Quiggin (2003) and Mukherjee and Wang (2012), which show, respectively, that higher competition may hurt the consumers in the presence of “regulation with scale economies” and “welfare-maximising nationalised firm.” Hence, our analysis, along with Gans and Quiggin (2003) and Mukherjee and Wang (2012), suggests that the price raising effect of competition can be a more common phenomenon under regulatory mechanism.3

2. The Model and the Results

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Model and the Results
  5. 3. Conclusion
  6. Appendix
  7. References
  8. Biographies

Consider an economy with inline image firms, each with the marginal cost of production 0, and inline image firms, each with the marginal cost of production inline image, competing like Cournot oligopolists with a homogeneous product. We assume that the welfare-maximizing government of the country imposes a per-unit tax, t,4 on each firm.

We assume that the inverse market demand function is P = aq, where P is price and q is the total output. We show in the appendix the condition under which our result holds under a general demand function.

We consider the following game. Given the number of firms, at stage 1, the government determines t to maximize welfare, which is the sum of total profits of the firms, consumer surplus and tax revenue. At stage 2, the firms compete like Cournot oligopolists and the profits are realized. We solve the game through backward induction.

Given the tax rate, each of the n firms maximizes inline image to determine its output, where inline image, and each of the m firms maximizes inline image to determine its output, whereinline image. The equilibrium outputs of the ith firm, inline image, and the jth firm, inline image, can be found as inline image and inline image, respectively. We assume that inline image and inline image, which ensure positive outputs of all firms.

The total output and price of the product are, respectively,

  • math image(1)

It is clear from (1) that, for a given tax rate, more firms (regardless of their marginal costs) and lower costs of the more cost-inefficient firms increase inline image, thus making the consumers better off. Hence, higher competition makes the consumers better off under exogenous tax/subsidy.

Now, we show the effects of the strategic tax/subsidy policy. To show this, we solve the first stage of the game, where the government determines t to maximize welfare, which is the sum of total profits (Π), consumer surplus (CS), and tax revenue (TR). Hence, the government maximizes the following expression to determine t:

  • math image(2)

where inline image.

We get the equilibrium tax rate as inline image. Incorporating the equilibrium tax rate, we get the equilibrium outputs of the ith firm, inline image, and the jth firm, inline image, as inline image and inline image, respectively. The equilibrium outputs of all firms are positive if inline image, which is assumed to hold.

The total equilibrium output is inline image. Since inline image, inline image, and inline image, the following proposition is immediate.

PROPOSITION 1. (a) An increase in n increases inline image, thus making the consumers better off. (b) An increase in m reduces inline image, thus making the consumers worse off. (c) A reduction in c increases inline image, thus making the consumers better off.

The reason for our interesting result, which is Proposition 1(b), is as follows: We have seen that, for a given t, an increase in m increases total output. However, if m increases, it reduces subsidy (i.e., inline image), which tends to reduce the total output. Since the tax policy internalizes the inefficiency due to oligopolistic competition but not the inefficiency due to the cost asymmetry, an increase in m reduces the total output by reducing subsidy.5 We show in the appendix the condition under which this result holds under a general demand function.

It is intuitive that if the products are differentiated in our analysis, more firms, irrespective of their marginal costs, create a positive effect on the consumers by increasing the number of varieties. Hence, the variety effect tends to reduce the negative effect of a rise in the number of more cost-inefficient firms. Therefore, more cost-inefficient firms makes the consumers worse off if the products are not very much differentiated so that the inefficiency due to the cost asymmetry dominates the effect of product differentiation.

It is also worth mentioning that uniform tax/subsidy is important for Proposition 1(b). It is intuitive that the government could eliminate the inefficiencies created by oligopolistic competition as well as cost asymmetry if it could charge discriminatory tax/subsidies. In this situation, the number of firms would not affect the total output and consumer surplus. However, as mentioned in the introduction, institutional reasons or the implementation costs may be responsible for the uniform tax/subsidy policy, and in the presence of which a rise in the number of more cost-inefficient firms makes the consumers worse off.

Finally, the presence of more cost-efficient firms in our analysis does not prevent the more cost-inefficient firms from entering the industry, implying that there is limited number of more cost-efficient firms in the industry. However, this may not be the case with free entry of more cost-efficient firms, where the entire market can be served by the more cost-efficient firms only. Hence, our analysis is applicable in industries where both types of firms co-exist.

3. Conclusion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Model and the Results
  5. 3. Conclusion
  6. Appendix
  7. References
  8. Biographies

We show that, in an industry with asymmetric cost firms, a rise in the number of more cost-inefficient firms hurts the consumers in the presence of a welfare-maximizing tax/subsidy policy. Hence, instead of increasing competition, reducing inefficiency due to cost asymmetry may be more desirable under endogenous tax/subsidy policy.

Appendix

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Model and the Results
  5. 3. Conclusion
  6. Appendix
  7. References
  8. Biographies

Output Reducing Competition under a General Demand Function

Assume that the inverse market demand function is inline image with inline image and inline image.6 Given the tax rate, each of the more cost-efficient firms and each of the less cost-efficient firms maximize the following expressions, respectively, to determine their outputs:

  • display math(A1)
  • display math(A2)

The equilibrium outputs are given by the following conditions, respectively:

  • display math(A3)
  • display math(A4)

The total outputs of the firms are determined by the following expression:

  • display math(A5)

where inline image, and it depends on t.

The government maximizes the following expression to determine the tax rate:

  • math image(A6)

The equilibrium tax is determined by the following expression:

  • math image(A7)

It follows from (A7) that inline image, i.e., a rise in the number of more cost-inefficient firms increases the equilibrium tax, since inline image from (A4).

Now we want to see the effect of m on the total output. We get from (A5) that

  • math image(A8)

Since inline image, we get that inline image if

  • math image(A9)

It is immediate from (A9) that if the tax rate is exogenous, we have inline image and (A9) does not hold since inline image from (A4). That is, for a given tax rate, a rise in the number of more cost-inefficient firms increases total output. However, if the government chooses welfare-maximizing tax, a rise in the number of more cost-inefficient firms may reduce total output by making inline image.

  1. 1

    The implications of indirect tax in imperfectly competitive markets have been discussed in different contexts. See Suits and Musgrave (1953), Delipalla and Keen (1992), Seade (1985), Stern (1987), Tam (1991) and Hamilton (1999) for a representative sample.

  2. 2

    The consideration of a uniform tax/subsidy can have the following justification. It is often argued that uniform tax rates are simpler and easier to implement. As mentioned in Coşgel (2006, p. 333), “The cost of administering a system with discriminatory rates can be very high when the characteristics of tax payers do not differ systematically or when these differences cannot be easily observed. It is generally easier to identify differences between the sectors of the economy than within each sector, making it harder to implement discriminatory rates within a sector.”

  3. 3

    There are some other papers challenging the price reducing effects of competition. The factors responsible for the price-raising effects of competition in those papers are consumers’ search costs (Janssen and Moraga-González 2004), the presence of the loyal and switching buyer groups (Rosenthal 1980) and the consumers’ preferences for differentiated products (Chen and Riordan 2008). See also the references in Chen and Riordan (2008) for the papers showing the price-raising effects of competition in the spatial models of product differentiation. In contrast, our result is due to the endogenous tax/subsidy policies, and do not depend on the above-mentioned factors.

  4. 4

    If t is negative, it implies that the government is subsidizing the firms.

  5. 5

    It is also worth mentioning that we get inline image for inline image, since inline image due to the requirement for positive equilibrium outputs. Hence, more cost-inefficient firms reduces welfare whenever all firms produce positive outputs.

  6. 6

    Our result holds as long as the industry marginal revenue is downward sloping. Our assumption of inline image satisfies this requirement.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Model and the Results
  5. 3. Conclusion
  6. Appendix
  7. References
  8. Biographies
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Biographies

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Model and the Results
  5. 3. Conclusion
  6. Appendix
  7. References
  8. Biographies
  • Soumyananda Dinda, Department of Economics, Sidho Kanho Birsha University, Purulia, West Bengal, 723101, India (sdinda2000@yahoo.co.in).

  • Arijit Mukherjee, School of Business and Economics, Sir Richard Morris Building, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK (A.Mukherjee@lboro.ac.uk).