ECON 4415: International Economics Autumn 2006 Karen Helene Ulltveit-Moe Lecture 8: TRADE AND OLIGOPOLY
1 Imperfect competition, and reciprocal dumping "The segmented market perception": each firm perceives each country as a separate market and makes distinct quantity decisions for each. Imperfect competition may be an independent cause of trade and gains fro trade. If individual firms have market power, i.e. are not passive price takers, they will want to segment markets and undertake price discrimination. Which implies to set a high price in markets where they possess significant market power, and a low price in markets where they have less power. Limits to segmentation: arbitrage trade, consumers travel
Oligopolistic rivalry gives rice to "reciprocal dumping": each firm dumps into other firms home markets. Reciprocal dumping - is rather striking in that there is pure waste in the form of unnecessary transport costs - may entail welfare gains due to the procompetitive effect of trade (i.e. trade affects market structure) - without free entry, reciprocal dumping may entails welfare improvement, but may also entail welfare losses, depending on the magnitude of transport costs. - with free entry, trade opening and reciprocal dumping will definitely be welfare improving for the Cournot case. The procompetitive effect of having more firms and a larger overall market, dominates the loss due to transport cost.
2 A model of an international oligopoly 2 identical countries; domestic and foreign each country has one firm producing the homogenous commodity Z exports incur transport costs market segmentation: each firm regards each country as a separate market, and chooses the profitmaximizing quantity for each country separately domestic firm produces output x for domestic consumption and output x for export foreign firm produces output y for export to the domestic consumption and output y its own market
constant marginal cost of production: c iceberg transport cost 0 5 g 5 1 marginal cost of exports c/g domestic price, p foreign price, p Profits π = xp(z)+x p (Z ) c(x + x g ) F (1) π = yp(z)+y p (Z ) c(y + y g ) F (2) it follows from the assumption of constant marginal cost that the profit maximizing choice of x is independent of
x, and similarly for y and y. Each country can therefore be considered separately. The assumption simplifies the model but is not essential to the results derived. First order conditions (forthedomesticmarket) π x = p(z)+xp 0 (Z) c =0 (3) π y = p(z)+yp 0 (Z) c g =0 (4) which gives the "best-reply" functions in implicit form. Solving (3) and (4) for x and y, gives the trade equilibrium. Using σ to denote the foreign share in the domestic market y/z, and letting ε p/zp 0, the elasticity of domestic demand, the best reply functions can be rewritten as cε p = (5) ε (1 σ) p = cε g(ε σ) (6)
Equations (5) and (6) can be solved for p and σ, to give solutions cε(1 + g) p = (7) g(2ε 1) ε(g 1) + 1 σ = (8) 1+g These solutions are an equilibrium only if the second-order conditions are satisfied π xx = p 00 +2p 0 < 0 (9) π yy = p 00 +2p 0 < 0 (10) we assume that these are satisfied and also that π xy = xp 00 + p 0 < 0 (11) π yx = yp 00 + p 0 < 0 (12) which mean that own marginal revenue declines when the other firm increases its output. The two latter conditions are equivalent to assuming that reply functions are downward sloping. They imply stability and uniqueness of the equilibrium.
Reciprocal dumping occur because Each firm has a smaller share of its export market than of its own market (see Brander & Krugman for proof) perceived marginal revenue is higher in the export market Effective marginal cost of delivering an exported unit is higher than for a unit of domestic sales, but this is consistent with higher MR perceived MR can equal MC in both countries and thus gives rise to two-way trade Each firm has a smaller mark-up over cost in its export market than at home
Reciprocal dumping will occur if monopoly markups in its absence were to exceed transport costs. The Cournot equilibrium with reciprocal dumping does NOT maximize profits for the two firms in sum; hence, both firms would gain from a cooperative solution which would allow them to raise price and reduced sales. 2.1 Welfare effects of trade without free entry of firms Reciprocal dumping is not Pareto efficient. But is a situation with free trade and reciprocal dumping superior to an autarky situation? the answer relies on two counteractive effects:
1. trade (as in this model) leads to waste in transport reducing welfare 2. international competition lowers prices and thus reduces monopoly distortion Depending on the magnitude of the two there may be gains or losses from trade. (see Figures 1-5). U = u(z)+k (13) W =2[u(Z) cz ty] F F (14) where t denote per unit transport costs dw dt =2 (p c) dz dt tdy dt y (15)
starting at the prohibitive level of trade costs, p = c + t, and y =0. And since reduces to dz dt = dx dt + dy dt (16) dw dt =2 t dx =2t dx dt dt > 0 (17) because a slight fall in transport costs tends to make x fall because of import rising. Hence, for prohibitive high levels of trade costs, a fall in trade costs would reduce welfare. Why? The fall in trade costs has three effects: reduced trade costs for the current level of import (+) consumption rises, so for each extra unit consumed there is a net gain equal to price minus the marginal cost of imports (+)
a loss due to the replacement of domestic production with high cost imports for near prohibitive levels of trade costs, the first two effects are negligible, leaving only the loss 2.2 Welfare effects of trade with free entry Generalize the model above as to allow for free entry. Maintaining notation and letting there be n firms in each country in equilibrium, the after-trade price and foreign market share ny/z are given by p = cεn(1 + g) g(2nε 1) (18) σ = nε(g 1) + 1 1+g (19)
where n is the number of firmsthatsetsprofits equal to zero for each firm i. Proposition 1 Under free entry, trade improves welfare. Proof. Consider a pretrade equilibrium: In the domestic industry each firm maximizes profit, so that FOC are satisfied: and each firms earns zero profit x i p 0 + p c =0 (20) π i = x i p cx i F =0 (21) Opening to trade changes prices; a rise in the price reduces consumer surplus and thus welfare; a reduction in price increases consumer surplus and this welfare. If opening to trade is to have a positive effect on welfare, then trade must induce a price reduction. From (20), we have that x i = (p c)/p 0 (22)
dx i dp = p0 +(p c)p 00 dz/dp (p 0 ) 2 = p0 + p 00 x i (p 0 ) 2 since dz/dp =1/p 0 and p c = p 0 x i.it follows from (11) that (22) must be positive; i.e. if the price rises then output x i must fall, and if the price remains constant so must output. With trade, profits are given by π i =(p c)x i F +(p c g )x i (23) if both p and x rise or remains constant, then (p c)x i F is non-negative by (21), and (p g c )x i is strictly positive since p > g c if trade is to take place. Therefore, π i must be strictly positive, which is a contradiction. Price must fall and welfare must rise. The procompetitive effect of trade dominates, since free entry implies zero profits, and the negative trade effect related to waste of transport cost therefore vanishes (as this works through its impact on producer surplus). Thestructuralsourceofthewelfareimprovementis that firms move down their average cost curve: while x i
falls, (x i +x i ) must exceed the original production levels, and average cost must falls. Profits remain at zero and consumer surplus rises. 2.3 Extensions Reciprocal dumping is a more general phenomenon than just a feature of the Cournot model. A necessary condition for reciprocal dumping to exist is that firms believe that their behavior can affect price. If price is strategy variable, reciprocal dumping does not arise in the homogenous product case. However, a slight amount of product differentiation restores the reciprocal dumping result.
The existence of transport costs implies that firms have an incentive to save on transport costs may induce them to invest in production facilities in the foreign market movesusfromamodelofreciprocal dumping to one of two-way foreign direct investment.