Foreign Penetration and Domestic Competition

Transcription

1 March 29, 2015 Foreign Penetration and Domestic Competition By Sajal Lahiri and Yingyi Tsai Abstract We consider an oligopolistic model with a number of domestic and and a number of foreign firms, and free entry and exit of domestic firms. The two sets of firms produce differentiated goods and serve the domestic market. They incur fixed costs of production. In this context, we examine, inter alia, the effect of an increase in the number of foreign firms on: (i) the free entry number of domestic firms, (ii) the optimal number of domestic firms, and (iii) domestic welfare. JEL classifications: H2, F2, L1, L5. Keywords: Foreign direct investment, domestic firms, lump-sum subsidies, oligopoly, differentiated goods. Department of Economics, Southern Illinois University, 1000 Faner Drive, Carbondale, IL , USA: ; lahiri@siu.edu Department of Applied Economics, National University of Kaohsiung, Kaohsiung University Road, Nan- Tze 811, Kaohsiung, Taiwan.; yingyi.tsai@gmail.com

2 1 Introduction The more the merrier? It is generally believed that a higher number of firms in an industry is necessarily good for the country: it increases competition, reduces price and thus increase welfare. With this theoretical underpinning, antitrust policies are typically designed so that new entries are encouraged and entry barriers are removed. However, it has been found in the literature that more competition may not increase welfare and in fact can reduce it. For example, in the context of oligopolistic models with endogenous R&D, Stiglitz (1981), Spence (1984) and Tandon (1984) found the possibility of welfare loss caused by the existence of potential entrants of rival firms. Schmalensee (1976), von Weizsäcker (1980 a, b) and Suzumura and Kiyono (1987) found that in a Cournot oligopolistic sector the optimal number of firms may well be smaller than the equilibrium number of firms with free entry and exit. 1 In these models, the existence of fixed costs plays a crucial role in deriving dis-economies of competition: while a new entry raises consumers surplus, it requires an additional fixed cost, and the latter cost may outweigh the former benefit. The above-mentioned studies work with symmetric oligopolistic model. In contrast, Lahiri and Ono (1986, 2004) show that in oligopolistic model with asymmetric firms, elimination of firms with sufficiently low market share improves welfare. A different strand of the literature examine the welfare effects of foreign direct investment (FDI). FDI has been a contentious issue for a long time in many countries. For example, it has been a major economic issue between the United States and Japan. The US has been asking countries such as Japan, India and China to open up various markets, such as construction, banking, insurance, and telecommunication to US firms, while more and more Japanese, Korean and European automobile and electric manufacturers have been establishing subsidiaries in the US. More recently, allowing FDI in multi-brand retail industry in India has been creating a lot of controversy. 1 Other studies include Agarwal and Barua, 1994; Asplund and Sandin, 1999; Hamilton and Stiegert,

3 Foreign penetration by direct investment is often taken to be a danger to host countries, especially from the viewpoint of their effect of domestic firms.the standard economic theory generally shows that improvements in consumers surplus caused by increases in supply by foreign firms dominate reductions in domestic producers surplus. However, it is not necessarily the case when the domestic market structure is oligopolistic. Ono (1990) and Lahiri and Ono (2003) derive conditions when foreign penetration is harmful under oligopoly. Their analysis assumes that FDI has no effect on the number of domestic firms. Lahiri and Ono (2015) examine how exogenous entry of domestic firms affect government policy on FDI and environment when the two sets of firms produce a homogeneous good. In this paper we combine the afore-mentioned two strands, and examine the welfare effect of FDI, including an additional channel of the effect of foreign penetration by FDI on welfare loss arising from excessive competition. In our framework, a domestic market is served by a number of identical domestic firms and a number of identical foreign firms. The two groups supply imperfectly substitute goods. There is free entry and exit of domestic firms We examine, inter alia, the effect of an increase in the number of foreign firms on the free entry number of domestic firms, on the optimal number of domestic firms, and on welfare. We also examine optimal subsidy policy when there is free entry and exit of both sets of firms. 2 The Basic Framework We consider a market in which there are two groups of firms d and f. Group d consists of n d identical domestic firms, each with constant unit variable cost c d, and Group f consists of n f identical foreign firms, each with constant unit variable cost c f. The two groups of firms produce two goods for the market to be called goods d and f that are imperfectly substitutes. The inverse demand functions are: p d = α d β d Q d γq f, p f = α f β f Q f γq d, (1) 2

4 where p k and Q k are respective the price and total demand of good k (k = d, f). That is Q k = n k q k, k = d, f, (2) where q d and q f are outputs per firm for the two groups of firms. Profits for each firm in the two groups are given by: π k = (p k c k )q k F k + S k, k = d, f, (3) where F k and S k are respectively fixed costs of, and lump-sum subsidy to, each firm in group k (k = d, f). Assuming Cournot conjectures, the first-order profit-maximizing conditions are: p k c k = β k q k, k = d, f. (4) Welfare of the country is given by W = n d π d + CS n d S d n f S f, where (5) dcs = Q d dp d Q f dp f. (6) Finally, we shall consider sub-cases depending on whether the number of firms in either group is exogenous or endogenous, i.e., whether or nor there is free and exits of the firms. In case of free entry and exit for domestic firms, we shall have: π d = (p d c d )q d F d + S d = 0, (7) and in case of free entry and exit for foreign firms: π f = (p f c f )q f F f + S f = 0. (8) This completes the description of our basic framework. 3

5 3 Optimal policies We take m and n both to be endogenous, i.e., free entry and exit for both sets of firms: π d = π f = 0 (equations (7) and (8) are both satisfied). We shall derive the signs of the optimal levels of S d and S f. Since lump-sum subsidies to the firms are instruments that target the number of firms directly, negative signs of the subsidy to one group of firms should point to restrictions on entry for that group. The welfare expression (5) in this case simplifies to W = CS n d S d n f S f, with dcs = Q d dp d Q f dp f. (9) From (4) we find: dp k = β k dq k, k = d, f, (10) and substituting (4) in (7) and (8) we get: β k qk 2 = F k S k, k = d, f, (11) which yields: dq k = (1/(2β k q k ) ds k, k = d, f. (12) Substituting (??) and (1) into (4) and then differentiating and substituting (12), we find: 2β d q d dq d + 2γq d dq f = ds d, 2γq f dq d + 2β f q f dq f = ds f, and solving these two equations yield dq d = β fq f ds d γq d ds f 2q d q f (β d β f γ 2 ), dq f = β dq d ds f γq f ds d 2q d q f (β d β f γ 2 ). (13) Differentiating (2) and substituting (12), (??) and (13) in it, we solve for dn d and dn f q d dn d = [ ] γds f 2q f (β d β f γ 2 ) + nd β f + ds 2β d q d 2q d (β d β f γ 2 d, ) (14) q f dn d = [ ] γds d 2q d (β d β f γ 2 ) + nf β d + ds 2β f q f 2q f (β d β f γ 2 f ) (15) 4

6 The above results are very intuitive. An increase in the level of lump-sum subsidy to firms in one group increases the number of firms in that group, reduces that in the other group, increases the total demand for that group s product, and reduces the total demand of the other group s product. It reduces the output of each firm in the that group and reduces the price of its product. Finally, differentiating (9) and substituting (10)-(15), we find dw = [ n ] [ d 2 a 1S d + a 2 S f ds d + n ] f 2 a 3S f + a 2 S d ds f, where (16) a 1 = 1 [ nd + 2q d β d q d a 3 = 1 [ nf + 2q f β f q f ] β f > 0, a q d (β d β f γ 2 2 = ) ] β d q f (β d β f γ 2 ) > 0. γ 2q d q f (β d β f γ 2 ) > 0, Optimal values of S d and S f are solved by setting W/ S d = W/ S f = 0. This gives: a 1 S d + a 2 S f = n d /2, a 2 S d a 3 S f = n f /2, and then solving simultaneously for optimal values of S d and S f as: 2 S d = a 3n d a 2 n f 2(a 1 a 3 a 2 2) < 0, S f = a 1n f a 2 n d 2(a 1 a 3 a 2 2) < 0, where a 1 a 3 a 2 2 > 0 from the second-order condition. From the above two equations, we obtain our first result: Proposition 1 The optimal levels of both of S d and S f are negative, i.e., both sets of firms are taxed. The revenue-raising motive is the key reason for the optimal policies being taxes, and not excessive competition. In fact, the mechanism for the determination of optimal policies is 2 These are not closed-form solutions as the right-hand side involves endogenous variables. However, the following expressions do prove the sign of the optimal subsidies. 5

7 quite different here than in the excessive competition literature. Heuristically, the arguments go as follows. In Cournot oligopolistic model with fixed costs, a higher level of fixed costs would reduce the value of the optimal number of firms and thus the policy prescription would be to restrict entry. Here, an increase in the level of fixed costs would reduce the number of firms in the industry and therefore the tax base. Thus, the optimal level of tax will be lower, implying more entry into the industry. 4 Foreign penetration The number of foreign firms n f is now exogenous, but the number of domestic firms n d is determined by the free-entry-exit condition (7). It may no longer be true now that there is excessive competition among domestic firms, i.e., the free-entry-exit number of domestic firms, ˆn d may not be higher than the socially optimal number of domestic firms n d. In this section we shall examine how an exogenous increase in n f affects ˆn d, n d and welfare. Because of free entry and exit of domestic firms, we apply (7) to obtain: ˆq d = F d /β d, (17) and then from (4) we solve for q f and ˆn d. 3 The solutions are given by: ˆn d = (a d c d β d q d )(n f + 1)β f (α f c f )γn f [(n f + 1)β d β f n f γ 2 ] q d, (18) ˆq f = α f c f γˆn d q d (n f + 1)β f. (19) Differentiating the above equation and using (??) and (4), we find dˆn d γq f β f = dn f q d ((n f + 1)β d β f n f γ 2 ) < 0, which gives (20) Proposition 2 An increase in the number of foreign firms reduces the free-entry equilibrium number of domestic firms. 3 For the time being we assume away the existence of any lump-sum subsidy. 6

8 Thus, entry of foreign firms crowd out domestic firms. However, as mentioned before, there may not be excess competition among domestic firms when the number of foreign firms is exogenous. Therefore, the above result does not necessarily prove that foreign penetration reduces excessive competition among domestic firms. This result is good (bad) for welfare if ˆn d is higher (lower) than the optimal number of domestic firms, n d. We shall now characterize n d for a given level of n f. We shall now characterize n d for a given value of n f. For this, we first of all compute dw/dn f without assuming free entry and exit of domestic firms where W = n d π d + CS. In this case, both n d and n f are exogenous and so q d and q f are solved from (4) as: q d = (α d c d )(n f + 1)β f (α f c f )n f γ, (21) q f = (α f c f )(n d + 1)β d (α d c d )n d γ, (22) where = (n d + 1)(n f + 1)β d β f n d n f γ 2 > 0. From (21) and (22), we obtain: dq d dn f = q f β f γ, dq f dn f = q f [(n d + 1)β d β f n d γ 2 ]. (23) Differentiating W = n d π d + CS given above and using (1), (4), (10), and (23), we get dw dn d = β d q 2 d(n f + 1)β d β f + n f γq d q f β d β f F d. (24) Setting dw/dn d = 0, we obtain the first-order condition for the optimality of n d as: [β d q 2 d(n f + 1)β d β f + n f γq d q f β d β f ]/ F d = 0 = f(n d, n f ) (say). (25) The first two terms represent marginal benefits of increasing in the number of domestic firms: it increases consumer surplus and profits of domestic firms net of fixed costs. The third term is the marginal cost due to an increase in total fixed costs. It is clear that an increase in per-firm fixed costs will reduce the optimal number of domestic firms. 7

9 To compare n d obtained in (25) with the free-entry n d (ˆn d ) in (18), we evaluate dw/dm when n d = ˆn d. In particular, we substitute (17) and (18) in (24) and use (1) and (4) to get: q d dw dn d = n f (β f γ)[β d (n d + 1)q d + γq f ] β d β f (n d + 1)q d < 0, which gives (26) nd =ˆn d Proposition 3 There is excessive domestic competition for any number of foreign firms. Propositions 2 and 3 however do not prove that foreign penetration reduces excessive competition as the value of n d will also shift with a change in n f. From (25), we see that an increase in the number of foreign firms does not affect the marginal cost of increasing the number of domestic firm, but it has opposing effects on the marginal benefit. It directly increases marginal benefit, but decreases it as output per firm of both sets of firms go down. The multiplier factor also goes up with n f and this will further lower marginal benefits. To obtain the net effect, differentiating (25) and substituting (25), we find: ( f nd ) β d β f dn d dn f = n d F d π d γn fq f [q fβ f γ + q d {β d β f (2n f + n d + 3) n d γ 2 }], where f nd < 0 from the second-order condition. From the above equation it follows that if the per-firm fixed costs is sufficiently high, an increase in the number of foreign firms is likely to increase optimal number of domestic firms, and then with the help of proposition 3, it will reduce the level of excessive competition ˆn d n d. Formally, Proposition 4 If the per-firm fixed cost of the domestic firms is very high, then an increase in the number of foreign firms is likely to increase the optimal number of domestic firms and thus reduce excessive competition among domestic firms. The above result can be explained intuitively as follows. A high level of per-firm fixed cost of the domestic firms mean that there are only a handful of domestic firms, but with 8

10 relatively large per-firm output. In such a situation, the direct increase in the marginal benefit of raising the number of domestic firms, due to an increase in the number of foreign firms is large and would dominate the negative indirect effect on the marginal benefit. 5 Foreign penetration and welfare Finally, we examine the effect of foreign penetration on domestic welfare. Since we want to incorporate the additional effect of foreign penetration on excessive competition, we shall assume free entry and exit of domestic firms. Welfare in the present case equals to consumers surplus, i.e., W = CS and, using (6) and (10), dw = ˆn dˆq d dp d n f q f dp f = ˆn dˆq d β d dˆq d n f q f β f dq f, where ˆq d is given by (17). From (17), we find that dq d = 0, and from (18) and (19) that 1 dq f (β d β f γ 2 ) = q f dn f (n f + 1)β d β f n f γ < 0. 2 Thus, the effect of an increase in n f on welfare is unambiguously positive. To summarize: Proposition 5 An increase in the number of foreign firms unambiguously increases welfare of the domestic/host country when there is free entry and exit of domestic firms. The direct effect of an increase in n f is to reduce the per-firm output of the foreign firms. An increase in n f also increases the the number of domestic firms (proposition 2), and this will increase the per-firm output of the foreign firms. The direct effect dominates the indirect effect and the net effect of an increase in n f on q f is negative. Since domestic firms make no profits, foreign penetration does have any effect on domestic profits. Because of free entry and exit of domestic firms, foreign penetration also does not have any effect on consumers surplus out of the goods produced by domestic firms. The only effect of foreign penetration is unambiguous increase in consumers surplus from the good produced by foreign firms. 9

11 6 Conclusion What are the consequences of an inflow of foreign direct investment (FDI) for domestic industrial policy and welfare? This is the main research question that we have considered in this paper. We did so by considering a Cournot oligopolistic model with two sets of firms. One set consists of domestic firms and the other foreign, and the two sets producing two imperfectly substitute goods. There is free entry and exit of domestic firms, but we consider both free entry and exit, and fixed number, of foreign firms. We find that FDI unambiguously increases domestic welfare. We also find conditions under which FDI reduces excessive competition among domestic firms. When there are free and entry exit among both sets of firms, the optimal policy is to apply lump-sum tax on both sets of firms because of the revenue-raising aspect of such a tax. 10

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