Ch. 9: Imperfect Competition and International Trade

Based on Feenstra and Taylor, Chapter 6 (KOM chapters 7 and 8). There are no lecture slides for this topic on the site yet; check against the lecture when it is given.

The Ricardian and Heckscher-Ohlin models explain trade by differences between countries: technology or factor endowments. They predict that countries export one good and import another (inter-industry trade). But a large share of world trade is between similar countries (Germany and France, the US and Canada) and within the same industry: Germany both exports and imports cars. This chapter explains that pattern with two new ingredients: increasing returns to scale (average cost falls as output rises) and imperfect competition (firms have some control over their price). The key model is monopolistic competition, developed by Paul Krugman (Nobel prize 2008). Trade in this model creates two new sources of gains: more product varieties for consumers and lower average costs (higher productivity) for firms that survive and expand.

1. Basics of imperfect competition

Increasing returns to scale

A production technology has increasing returns to scale when average cost falls as the scale of output rises. The simplest way to get this is a fixed cost F (a factory, R&D, a design) plus a constant marginal cost c per unit:

With falling average cost, perfect competition cannot survive: the biggest firm always has the lowest cost. Markets end up with a few firms (oligopoly), one firm (monopoly) or many firms each selling a differentiated product (monopolistic competition).

FT distinguish internal economies of scale (cost per unit depends on the size of the firm, which leads to imperfect competition, the subject of this chapter) from external economies of scale (cost per unit depends on the size of the industry, not the individual firm, as in industry clusters such as Silicon Valley; industries can remain perfectly competitive).

Monopoly equilibrium

A monopolist faces the whole downward-sloping market demand curve D. To sell one more unit it must lower the price on all units, so marginal revenue (MR) is below price. With linear demand P = a minus b × Q, total revenue is aQ minus bQ², so MR = a minus 2bQ: the MR curve has the same intercept and twice the slope of the demand curve.

The monopolist maximizes profit where MR = MC, then reads the price off the demand curve. Because MR < P, the monopoly price is above marginal cost. Example: P = 100 minus Q and MC = 20. MR = 100 minus 2Q = 20 gives Q = 40 and P = 60. Profit per unit before fixed cost is 60 minus 20 = 40.

Demand with duopoly and many firms

Suppose there are two firms (a duopoly) selling a differentiated product, and they charge the same price. Each gets half of market demand: d = D/2. But the demand curve facing one firm, d, is flatter (more elastic) than total demand D. If firm 1 cuts its price below firm 2's, it gains customers from firm 2 as well as new buyers, so its sales rise more than proportionally. With more firms, each firm's demand curve d is further to the left (a smaller share) and flatter (more competitors to steal customers from).

2. Monopolistic competition

Monopolistic competition combines features of monopoly and perfect competition. The assumptions in FT are:

1. Each firm produces a good that is similar to but differentiated from the goods of other firms (different car models, different beers).
2. There are many firms in the industry.
3. Firms can enter and exit freely, so in the long run profits are zero.
4. Increasing returns to scale: average cost falls with output.
5. Demand facing each firm depends on the number of firms and on the prices charged by the other firms.
6. Assumption 6 (symmetry): all firms have identical costs and face identical demand, so in equilibrium they all charge the same price and sell the same quantity.

Because each firm sells a differentiated product, it has a downward-sloping demand curve d and acts like a small monopolist (MR = MC). Because of free entry, profits are driven to zero, as in perfect competition.

Short-run equilibrium

Take the number of firms N as given. Each firm faces demand d₀, sets MR = MC and charges P₀. At P₀, average cost AC may be below price, so firms make profits. In the diagram, P₀ lies above the AC curve at the profit-maximizing output Q₀.

Long-run equilibrium

Profits attract entry. Each new firm takes customers from incumbents, so each firm's demand curve shifts left (smaller share) and becomes flatter (more substitutes). Prices fall. Entry continues until profits are zero: the firm's demand curve d₁ is tangent to the AC curve at the profit-maximizing quantity. At that point P = AC and MR = MC hold simultaneously. Note that firms do not produce at minimum AC: they produce on the downward-sloping part of AC, so there is excess capacity. That is the cost of having many varieties.

The algebra (KOM version)

KOM make the model precise. A firm's sales are

Two curves determine the equilibrium number of firms n and the price P:

• CC curve (average cost): with symmetric firms each produces Q = S/n, so AC = F/Q + c = n × F/S + c. More firms means each produces less, so average cost rises with n: CC slopes upward.
• PP curve (price): setting MR = MC with this demand gives P = c + 1/(b × n). More firms means more intense competition and a lower markup: PP slopes downward.

The long-run equilibrium is where they cross: P = AC, so profits are zero. If n is below the equilibrium, P > AC and firms enter; if n is above it, P < AC and firms exit.

Effect of a larger market S. A larger S lowers AC for any given n (each firm sells more and spreads its fixed cost), so the CC curve shifts down (to the right). The PP curve does not depend on S and does not move. The new equilibrium has more firms and a lower price. This is exactly what trade does: it integrates national markets into one larger market.

3. Trade under monopolistic competition

Assume Home and Foreign are identical in technology, endowments and tastes. Ricardo and Heckscher-Ohlin predict no trade at all. In the monopolistic competition model, opening trade still pays.

Short run with trade

When trade opens, the number of consumers each firm can reach doubles, and the number of competing firms (and varieties) also doubles. Each firm's demand curve becomes more elastic (flatter) because consumers can choose among more substitutes. Each firm, still seeing itself as small, believes it can gain many customers by cutting price. On the new flatter demand curve, MR = MC occurs at a lower price and higher quantity. But all firms do this at the same time, so prices fall and each firm ends up with losses: price is below AC.

Long run with trade

Losses force some firms to exit. The remaining firms each serve a larger market, move down their AC curve and produce at a lower average cost. In the new long-run equilibrium:

• The price is lower than in autarky (P₃ < P_A in FT notation): a gain from trade through higher productivity (lower AC).
• Each surviving firm produces more output (moves down its AC curve).
• The total number of firms in the integrated market is larger than in either country alone but smaller than the sum of the autarky numbers: consumers enjoy more varieties.

Worked example (KOM auto industry)

Fixed cost F = $750 million, marginal cost c = $5,000 per car, b = 1/30,000. Home's market is 900,000 cars a year, Foreign's 1.6 million. Use AC = nF/S + c and P = c + 1/(bn), so P = 5,000 + 30,000/n.

Check for Home: AC = 6 × 750,000,000/900,000 + 5,000 = 5,000 + 5,000 = 10,000, and P = 5,000 + 30,000/6 = 10,000. In the integrated market: AC = 10 × 750,000,000/2,500,000 + 5,000 = 3,000 + 5,000 = 8,000 and P = 5,000 + 3,000 = 8,000. Consumers in both countries pay less and can choose among 10 brands instead of 6 or 8. The smaller country (Home) gains most: its price falls by 20%. Note that 10 < 6 + 8 = 14, so 4 firms disappear in total.

4. Empirical applications: NAFTA and the Canada-US free trade agreement

FT test the model with the 1989 Canada-US Free Trade Agreement and the 1994 North American Free Trade Agreement (NAFTA, Canada, Mexico and the United States; replaced in 2020 by the USMCA).

Gains and adjustment costs for Canada

Daniel Trefler studied Canadian manufacturing after the 1989 agreement. In the industries most affected by tariff cuts, employment fell by about 12% in the short run (an adjustment cost: firms exited, workers lost jobs), while labor productivity rose by about 15% in those industries (about 6% for manufacturing as a whole) as less efficient plants closed and survivors expanded. Real earnings rose modestly. This matches the model: exit of firms, lower average costs for survivors.

Gains and adjustment costs for Mexico

Productivity in Mexican manufacturing rose, especially in the maquiladora plants near the US border that assemble goods for export to the US. Real wages in maquiladoras rose, and wages in other manufacturing grew more slowly. The 1994 to 1995 peso crisis lowered real wages for some years, so it is hard to isolate NAFTA's effect. Adjustment costs fell in particular on Mexican agriculture (small corn farmers facing US corn imports).

Gains and adjustment costs for the United States

For the US, the main gain is import variety: the number of product varieties imported from Mexico rose strongly after NAFTA. Studies estimate the consumer value of these new varieties at a modest share of GDP for Mexico alone; for all US imports, Broda and Weinstein estimate that the growth in import variety between 1972 and 2001 was worth about 2.6% of US GDP. Adjustment costs: US workers displaced by imports from Mexico were eligible for trade adjustment assistance (TAA). The number of displaced workers was small relative to total US job turnover, but the costs were concentrated in specific industries and regions.

5. Intra-industry trade and the gravity equation

Index of intra-industry trade

In the monopolistic competition model, Home and Foreign export different varieties of the same good to each other: intra-industry trade (two-way trade in the same industry). Trade between different industries (cloth for wine) is inter-industry trade. The share of intra-industry trade in an industry is measured by the Grubel-Lloyd index:

FT's table for US trade shows high indexes for differentiated manufactured goods (for example vaccines, golf clubs, telecommunications equipment, cars) and low indexes for goods that depend on natural resources or on cheap labor (for example footwear, toys, crude oil, tropical fruit). Industries with differentiated products and scale economies show intra-industry trade; industries driven by comparative advantage show one-way trade. Two caveats: the index depends on how finely industries are defined (more aggregation raises the index), and intra-industry trade is highest between countries at similar levels of development.

The gravity equation

The monopolistic competition model also explains the strong empirical regularity that large countries trade more with each other. The gravity equation (by analogy with Newton's law of gravity) is:

Intuition: in the monopolistic competition model, each country produces many varieties in proportion to its size, and each country buys varieties in proportion to its own income, so trade is proportional to the product of the two GDPs. Distance captures transport costs and other trade frictions.

Border effects. The gravity equation fits trade between Canadian provinces and US states well, but John McCallum found that in 1988 Canadian provinces traded about 22 times more with each other than with US states of the same size and distance. Later work (Anderson and van Wincoop) shows a smaller border effect after correcting the method, but borders still reduce trade substantially. Tariffs, quotas, different currencies, regulations and language all act like extra distance. The gravity equation is widely used to estimate the trade effects of free trade agreements and currency unions.

6. Firm heterogeneity: who exports? (KOM chapter 8)

KOM extend the model to firms with different marginal costs (the Melitz model). Within an industry, firms differ in productivity. Two results follow:

• Trade increases average productivity of the industry: when markets integrate, competition intensifies; the least productive firms (highest marginal cost) cannot cover their costs and exit, while the most productive firms expand. The industry's average productivity rises even if no single firm becomes more efficient.
• Only the most productive firms export: exporting involves extra costs (transport, a fixed cost of setting up abroad). Only firms with low enough marginal cost earn enough abroad to cover them. Empirically, exporters are larger, more productive and pay higher wages than nonexporters, and a small share of firms accounts for most exports.

Firms that serve a foreign market can either export or set up production there (horizontal FDI). They choose FDI when the fixed cost of a plant abroad is low relative to the trade costs saved on large sales volumes.

7. Dumping

Imperfect competition also allows firms to price discriminate between markets: charge different prices to different buyers. This is possible only if markets are segmented (buyers cannot easily resell from the cheap market to the expensive one, because of transport costs or trade barriers).

Why would a firm do this? A profit-maximizing firm sets MR = MC in each market separately. If foreign demand is more elastic than domestic demand (the firm has a small share abroad and faces many competitors, while at home it has a large share or is protected), its markup abroad is lower. So the export price is below the home price: dumping, with no predatory intent required.

Example (KOM style): a firm with MC = 10 faces a domestic price elasticity that gives an optimal home price of 20, and a more elastic foreign market where MR = 10 at a price of 14. It sells at 20 at home and 14 abroad. The foreign price is still above marginal cost, so exports are profitable.

Antidumping policy. Under WTO rules, an importing country can impose an antidumping duty (a tariff equal to the dumping margin) if a foreign firm sells below its home price or below cost and this causes material injury to the domestic industry. In the US, the Commerce Department determines dumping and the International Trade Commission determines injury. Economists are skeptical: price discrimination is normal business practice when markets differ, and selling below average cost can be rational in a downturn (when P covers MC but not the fixed cost). Antidumping cases are often a form of disguised protection. The mere threat of an antidumping case can make foreign firms raise prices. Examples include US antidumping duties on Chinese shrimp, furniture, steel and solar panels.

Reciprocal dumping (Brander and Krugman): two firms, one in each country, may each dump into the other's market, producing two-way trade in an identical product. This trade raises competition but also wastes resources on transport, so its welfare effect is ambiguous.