When the Threat is Stronger than the Execution: Trade Liberalization and Welfare under Oligopoly

Transcription

1 When the Threat is Stronger than the Execution: Trade Liberalization and Welfare under Oligopoly Dermot Leahy Maynooth University J. Peter Neary Oxford, CEPR and CESifo ESEM 2016, Geneva August 24, 2016 Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

2 Aron Nimzowitsch Introduction Aron Nimzowitsch, The threat is stronger than the execution Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

3 Introduction Introduction Trade policy: Gains from trade liberalization The magnitude of the gains is still a central issue in international trade. Recent work sheds light on the quantitative extent of gains under perfect competition and monopolistic competition with heterogeneous firms. Less work has been done on trade liberalization under oligopoly. Despite growing evidence that trade is dominated by large firms. Mayer and Ottaviano (2008), Freund and Pierola (2015) IO: Oligopoly with cost asymmetries Who gains and who loses as best-practice technology disseminates? Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

4 Our Contribution Introduction We compare trade liberalization under Cournot and Bertrand oligopoly in a unified framework with product differentiation. Common perception that the results of oligopoly trade models are highly sensitive to the mode of competition. We show that many of the predictions are qualitatively robust to whether firms compete on quantity or price. But: There are important differences between the two cases. Details: We use duopoly with linear demands to obtain explicit solutions. Then extend the analysis to oligopoly and more general functional forms: results are qualitatively robust. Take-Home: Firms compete more aggressively under Bertrand than under Cournot. This affects outcomes even when there is no trade under Bertrand. Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

5 Introduction Background Literature Quantity versus price competition: Singh and Vives (1984), Vives (1985) Oligopoly with cost asymmetries: Lahiri and Ono (1988), Neary (1994) Welfare effects of trade liberalization under oligopoly: Use the reciprocal-markets model first developed by Brander (1981) and Brander and Krugman (1983). Extended by Bernhofen (2001) - Product differentiation. Clarke and Collie (2003) - Bertrand. Brander and Spencer (2015), Collie and Le (2015). For a survey see: Leahy and Neary (2011). A simultaneous-move game, not about entry deterrence: Spence (1977), Dixit (1980), Fudenberg-Tirole (1985), Neary (2002) Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

6 Outline Introduction 1 The Model 2 Equilibria with Trade 3 The Nimzowitsch Region 4 General Demands 5 Conclusion Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

7 Outline The Model 1 The Model Utility and Demand Technology and Firm Behavior 2 Equilibria with Trade 3 The Nimzowitsch Region 4 General Demands 5 Conclusion Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

8 The Model Utility and Demand The Model A symmetric two-country model, with segmented markets. A home and foreign firm compete in both home and foreign markets. Demand: A representative consumer in the home country with quasi-linear utility: U = z 0 + u(x, y) We first assume a quadratic sub-utility function: u(x, y) = a(x + y) b 2 (x2 + 2exy + y 2 ) Maximization of utility subject to the budget constraint yields linear inverse demand functions: p = a b(x + ey) and p = a b(y + ex) Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

9 The Model Technology and Firm Behavior Technology and Firm Behavior Costs: Marginal costs are constant and we ignore fixed costs. Profits: Home market profits of the home and foreign firm are: π = (p c)x π = (p c t)y Symmetric multilateral trade liberalization under: 1 Quantity/Cournot competition 2 Price/Bertrand competition The symmetric case, where the home and foreign firms face symmetric demands, the same production cost functions, and the same trade cost. Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

10 Outline Equilibria with Trade 1 The Model 2 Equilibria with Trade Quantity Competition Price Competition Bertrand vs. Cournot 3 The Nimzowitsch Region 4 General Demands 5 Conclusion Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

11 Equilibria with Trade Quantity Competition Quantity Competition: Outputs and Profits Home market outputs: Free trade: x CF = y CF = A b(2+e) A a c Prohibitive trade cost: y = 0 t C = 2 e ( x C = x CF 1 + e ) t 2 t C 2 A ( and y C = y CF 1 t ) t C Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

12 Equilibria with Trade Quantity Competition Quantity Competition: Outputs and Profits Home market outputs: Free trade: x CF = y CF = A b(2+e) A a c Prohibitive trade cost: y = 0 t C = 2 e ( x C = x CF 1 + e ) t 2 t C 2 A ( and y C = y CF 1 t ) t C Profits of home firm: Due to symmetry, home exports x equal home imports y, home firm s profits on its exports are π = (p c t)x = (p c t)y. Effect of a multilateral change in trade costs on total profits: d (π + π ) dt = 2(ex 2x ) 4 e 2 So: Profits are U-shaped in t. { < 0 when t = 0 (so x = x ) > 0 when t = t C (so x = 0) Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

13 Equilibria with Trade Quantity Competition Cournot Profits Trade is locally bad for profits, in the neighbourhood of autarky. Must it be globally bad? Anderson, Donsimoni, and Gabszewicz (1989) showed that it is when goods are perfect substitutes. However, trade liberalization is less bad for firms when e is lower. t t^c 0.8 t min 0.7 t eq e Loci of t and e that yield Autarky, Minimum Profits, and Autarky Profits Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

14 Equilibria with Trade Welfare under Cournot Quantity Competition Consumer surplus rises monotonically as trade costs fall. (Prices of both goods fall) Hence, the range of t where welfare is lower than autarky is smaller than that where profits are lower. Welfare is also U-shaped in t. It falls below the autarky level between the upper and lower loci reaching a minimum along the middle locus. 1.0 t t^c t min 0.7 t eq e Loci of t and e that yield Autarky, Minimum Profits, and Autarky Welfare Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

15 Equilibria with Trade Bertrand Competition Price Competition To compare Bertrand and Cournot competition we use the same demand and cost functions. x = To solve for Bertrand equilibrium we use direct demand functions: 1 b (1 e 2 ) [(1 e)a (p 1 ep )] y = b (1 e 2 ) [(1 e)a (p ep)] Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

16 Equilibria with Trade Bertrand Competition Price Competition To compare Bertrand and Cournot competition we use the same demand and cost functions. x = To solve for Bertrand equilibrium we use direct demand functions: 1 b (1 e 2 ) [(1 e)a (p 1 ep )] y = b (1 e 2 ) [(1 e)a (p ep)] Home market outputs: Free trade: x BF = y BF = A b(2+e e 2 ) Prohibitive trade cost: y = 0 t B = (1 e)(2+e) A ( x B = x BF 1 + e ) t 2 e 2 t B 2 e 2 ( and y B = y BF 1 t ) t B Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

17 Equilibria with Trade Bertrand vs. Cournot Bertrand vs. Cournot Straightforward to show that: t B < t C Profits and welfare also behave similarly to quantity competition for trade costs between zero and t B. As shown by Vives (1985): price competition is more competitive than quantity competition in symmetric equilibrium: price competition leads to lower prices and higher outputs and thus higher welfare. With linear demands, even with asymmetric firms, price competition always leads to higher welfare for t t B : { W B W C = 1 e 2 ( ) ( 4 + e b (1 + e) (4 e 2 ) 2 4 e 2 2 ) } 2e A(A t) + 2(1 e) t2 Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

18 Equilibria with Trade Bertrand vs. Cournot Bertrand vs. Cournot Welfare Qualitatively similar as trade costs fall, but also differences: W WB-WA WC-WA t Effects of Trade Liberalization on Welfare in Cournot and Bertrand Competition Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

19 Outline The Nimzowitsch Region 1 The Model 2 Equilibria with Trade 3 The Nimzowitsch Region The Nimzowitsch Region: Home Best Response Welfare in the Nimzowitsch Region 4 General Demands 5 Conclusion Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

20 The Nimzowitsch Region The Nimzowitsch Region A region of trade costs too high for trade in Bertrand, but low enough to allow the threat of trade. Between t B and t C no trade occurs under price competition. Yet (with linear demands) the pro-competitive threat of trade raises welfare above the Cournot level. The threat of trade raises welfare more than actual trade under Cournot. We call the region of parameter space in which this outcome holds the Nimzowitsch Region. Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

21 The Nimzowitsch Region Trade under Price and Output Competition t M B C N e Regions of Trade B: y B > y C ; C: y C > y B > 0; N: Nimzowitsch Region; A: Autarky Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

22 The Nimzowitsch Region The Nimzowitsch Region The Nimzowitsch Region: Home Best Response At t B there is no trade under Bertrand but the domestic firm s price is below the monopoly level. The home firm does not raise its price, since its rival would then make positive sales lowering the home firm s domestic profits. When t reaches t C the home firm can act as an unconstrained monopolist. When t B t t C, the home firm chooses a price at which the foreign firm is just unable to produce. Domestic output is: x = A t be which falls in t. Since x falls in t in the region t B t t C and y = 0, welfare is falling in t in that region. Hence under price competition, unlike under quantity competition, trade liberalization starting from autarky initially raises welfare Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

23 The Nimzowitsch Region The Nimzowitsch Region: Home Best Response Bertrand vs. Cournot Outputs xc yc xb yb XC XB Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

24 The Nimzowitsch Region Welfare in the Nimzowitsch Region Welfare in the Nimzowitsch Region Welfare under price and output competition: W WB-WA WC-WA Nimzovitsch Region t Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

25 The Nimzowitsch Region Welfare in the Nimzowitsch Region Strategic Interactions in the Nimzowitsch Region p * c t B* ( p; t) ~ p* ( p ) ~ B* ( p; t) p * C c tˆ B ( p*) ~ B ( p * ) ~ p( p * ) p * ~ B ( p * ) ~ B* ( p; t) B c tˆ p M p p p (a) Foreign Best-Response Function (b) Home Best-Response Function (c) Equilibrium in the Nimzowitsch Region Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

26 The Nimzowitsch Region Welfare in the Nimzowitsch Region Minimum versus Maximum Import Constraints Contrast: 1 Here: Imports are non-negative: y 0 2 Krishna (JIE 1989): Import quota: y ȳ Both extend classic results to product differentiation: 1 Low-cost firm prices at marginal cost of high-cost 2 No pure-strategy equilibrium with capacity constraints [Edgeworth] In both, home firm s best response is a choice between two options: When import constraint binds, a high price yields monopoly profits When it does not, a low price leads to a standard Bertrand equilibrium For both options, profits given p are concave in p 1 Here: Maximum profits is the lower envelope Which is itself concave 2 Krishna: Maximum profits is the upper envelope So: no equilibrium in pure strategies Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

27 The Nimzowitsch Region Welfare in the Nimzowitsch Region The Nimzowitsch Region: The Home Firm p* c+t C c+t c+t B p M p y=0 M B y>0 y=0 p Price Competition: The Home Firm s Perspective Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

28 Outline General Demands 1 The Model 2 Equilibria with Trade 3 The Nimzowitsch Region 4 General Demands Free Trade and Autarky The Volume of Trade Welfare 5 Conclusion Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

29 General Demands General Demands Do these results continue to hold with general demands? p(x, y) for the home good and p (y, x) for the foreign? We assume that the demand functions are twice differentiable and strictly decreasing in own price, p x < 0 and p y < 0. We also assume that p (0, x) < so that foreign demand has a choke price and a prohibitive trade cost exists. We assume that the demand system can be inverted to get: x(p, p ) for the home good and y(p, p) for the foreign. Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

30 General Demands Free Trade and Autarky Free Trade and Autarky We impose a few additional mild restrictions such as: Marginal revenue is always downward-sloping Home marginal revenue falls in a symmetric equilibrium following an equal increase in the outputs of both goods We do not restrict quantities to be strategic substitutes under Cournot nor prices to be strategic complements under Bertrand Given these we are able to show: 1 At t = 0, the volume of trade is higher under Bertrand than Cournot. Prices at t = 0 are lower under Bertrand than Cournot. (This result is implicit in Vives (1985) who did not look at trade) 2 t B < t C Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

31 The Volume of Trade General Demands The Volume of Trade The volume of trade under price and output competition: Here a single intersection but in general there could be many. y B (0) y C (0) t B t C t Volume of Trade under Quantity and Price Competition Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

32 Welfare General Demands Welfare Welfare change dw = dχ + dπ can be written as: dw = (p c)dx + (p c t)dy ydt ) y < 0 under both quantity and price competition. So at free trade an increase in trade costs is bad. This generalises the result under linear demands. 1 At t = 0 this is dw dt = (p c)( dx dt + dy dt 2 At t C under Cournot we have dx/dt > 0 (if outputs are strategic subtitutes) so dw dt = (p c) dx dt > 0. A small fall in trade costs is bad. Unlike the linear demand case these results can only be stated at particular points. Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

33 General Demands Welfare Welfare in the Nimzowitsch Region The Nimzowitsch Region: { t B, t C } Consider Bertrand competition only: Equilibrium has y = 0. Hence p (0, x) c t = 0, implying that x must decrease in t dx/dt = 1/p x(0, x) < 0 So a decrease in t between t B and t C raises welfare. At t B a small fall in trade costs under Bertrand lowers welfare (if dx/dt > 0 ). This allows us to sign the following derivatives: dw B dw < B 0 dw > B 0 < 0 dt ˆt C, dt ˆt B, dt ˆt B,+ Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

34 General Demands Welfare Welfare with General Demands: Summary W (1) WB-WA WC-WA (2) (3) (4) (5) t (6) (3) With general demands, we can only sign the end-points But the results confirm qualitatively the results with linear demands: dw B dt (1) > 0 (4) ˆt B, dw B dt dw B dt < 0 (2) t=0,+ < 0 (5) ˆt B,+ dw C dt dw B dt < 0 t=0,+ < 0 (6) ˆt C, dw C dt > 0 ˆt C, Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

35 Outline Conclusion 1 The Model 2 Equilibria with Trade 3 The Nimzowitsch Region 4 General Demands 5 Conclusion Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34

36 Conclusion Conclusion We have compared trade liberalization under Cournot and Bertrand in a unified reciprocal-markets framework using general demands: The trade cost that chokes off trade is higher under Cournot. The critical level of trade costs below which the possibility of trade affects the domestic firms behavior is the same under Cournot and Bertrand competition. The pro-competitive effects of trade are stronger under Bertrand competition despite the fact that for trade costs close to the critical level the volume of trade is higher under Cournot competition. Tighter results if we assume linear demands: At any trade cost, welfare is higher under Bertrand than under Cournot True even in the Nimzowitsch Region, where Bertrand trade is zero Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, / 34