Trade Under Increasing Returns and Imperfect Competition

ECON 171 · Spring 2026 · Week 7

Sasha Petrov

Today’s Agenda

  1. The Krugman model: structure of the economy
  2. Consumers — love of variety, demand for a variety
  3. Firms — cost, optimal price, free entry
  4. Equilibrium — PP and CC curves, \(n^{*}\), \(Q^{*}\), \(P^{*}\)
  5. Pro-competitive and love-of-variety gains from trade
  6. The home market effect
  7. Case study: intra-industry trade

What We Aim to Learn

Who actually trades with whom?

  • Ricardo and H-O predict trade between dissimilar countries (different tech, different endowments).
  • Data say the opposite: rich-rich pairs account for ~50% of world trade — and that share has grown since the 1960s.
  • Half of that flow is intra-industry: the same HS-6 product crossing the same border in both directions.

What drives trade between similar countries — and why does it produce gains?

Fouquin & Hugot / CEPII, via OWID. Methodology: Brülhart, Account of Global Intra-industry Trade (WB PRWP 5066, 2009).

BMW round-trips the Atlantic

BMW X5 (G05) SUV, the Spartanburg-built model that the US exports.
X3 / X5 / X7 → world
⇄
BMW 3-series sedan, the German-built model that the US imports.
3 / 5 / 7 series → US
BMW US Manufacturing facility in Greer, South Carolina.
Plant Spartanburg, SC
BMW Plant Munich, Germany.
Plant Munich, Germany
  • 2022: BMW shipped 227,029 X-models worth $9.6 B from South Carolina to 120+ countries.
  • Largest destination: Germany (15.5%), ahead of China (13.5%) and South Korea (12.8%).
  • That same year, the US imported BMW 3 / 5 / 7-series from Munich, Dingolfing, Leipzig.
  • Spartanburg = #1 US auto exporter by value 9 yrs running; $113 B cumulative 2014–25.

Same firm. Same broad product. Same year. Both directions across the Atlantic. H-O cannot explain this.

Source: BMW Group US, Feb 2024 & Feb 2025 press releases. Photos via Wikimedia Commons: X5 (OWS Photography, CC BY 4.0) · 330i (Vauxford, CC BY-SA 4.0) · Plant Spartanburg (Ken Lund, CC BY-SA 2.0) · Plant Munich (Diego Delso, CC BY-SA 3.0).

The Krugman model

Structure of the economy

Consumers

  • A representative consumer with love of variety — utility rises in the number of varieties consumed, not just in total quantity.
  • Spends total income \(S\) across \(n\) differentiated varieties of one good.

Firms

  • \(n\) symmetric firms, one variety each.
  • Cost: fixed \(F\) + variable \(c\) per unit.
  • Choose price \(P_i\) given a downward-sloping residual demand.

Why this needs imperfect competition

  • Fixed cost \(F\) ⇒ \(AC(Q) = F/Q + c > c = MC\) for any finite \(Q\).
  • Under perfect competition \(P = MC\) ⇒ firms lose \(F\) on every variety.
  • \(P > MC\) is required to break even ⇒ monopolistic competition with free entry to \(\pi = 0\).

A model where consumers value variety and firms have IRS generates two-way trade between identical countries — exactly what H-O could not.

Consumers

Love of variety

  • Two cars at $5K each beat one car at $10K — at the same total spend, more varieties raises utility.
  • Captured by CES utility over varieties: \[U = \left( \sum_{i=1}^{n} q_i^{\,(\sigma-1)/\sigma} \right)^{\sigma/(\sigma-1)}\]
  • \(\sigma > 1\): elasticity of substitution. Small \(\sigma\) = very different (Toyota / Tesla); large \(\sigma\) = near-substitutes.

More \(n\) raises welfare even at fixed \(P\) and fixed total spend. This is what H-O misses.

TODO: love-of-variety illustration

Demand for a single variety

  • Industry sales \(S\) are split across \(n\) symmetric varieties.
  • The CES first-order condition gives a linear approximation (KMO §8.2): \[Q_i = S \cdot \left[\tfrac{1}{n} - b \cdot (P_i - \bar{P})\right]\]
  • \(b\) measures substitutability: smaller \(b\) ⇒ more differentiation ⇒ less elastic firm-level demand.
  • At common prices \(P_i = \bar{P}\) each firm sells \(Q = S/n\) — a fair share of the market.

TODO: residual demand chart

Firms

Cost function

  • Total cost: \(TC(Q) = F + c \cdot Q\).
  • Marginal cost: \(MC = c\) (constant).
  • Average cost: \(AC(Q) = F/Q + c\) — falls with scale (IRS).
  • The vertical gap \(AC - MC = F/Q\) is the per-unit “fixed-cost burden” the firm must cover via markup.
  • This is the simplest cost structure that produces internal economies of scale and a non-degenerate scale-vs-variety trade-off.

TODO: AC vs MC chart

Optimal price-setting

  • Each firm faces residual demand \(\;Q_i = S\,[\,1/n - b(P_i - \bar P)\,]\) given \(n\) competitors and their average price \(\bar P\).
  • Profit: \(\pi_i = (P_i - c)\,Q_i - F\). Firm chooses \(Q_i\) to maximize.
  • FOC: marginal revenue equals marginal cost, \(MR_i = MC = c\). This intersection pins down \(Q_i^{*}\); the price \(P_i^{*}\) is read off the demand curve at \(Q_i^{*}\).
  • Each firm has market power (residual demand slopes down) ⇒ \(P_i^{*} > c\).
  • Best response depends on \(\bar P\) — strategic interaction. Equilibrium pins this down once we impose symmetric Nash.

Entry decision

  • \(\pi_i > 0\) ⇒ new firms enter; \(\pi_i < 0\) ⇒ firms exit.
  • Free entry pins down \(n\) where economic profits are exactly zero: \[\pi_i = (P_i - c)\,Q_i - F = 0\]
  • This is a break-even condition every operating firm must satisfy: the markup over marginal cost, multiplied by output, must cover the fixed cost.
  • Equivalently: \(P_i = AC(Q_i) = c + F/Q_i\) — the firm operates at a price equal to its average cost.
  • It doesn’t pin down \((n, P, Q)\) on its own — but combined with the pricing FOC and symmetry, it will.

Equilibrium

Symmetric assumption

Symmetric Nash equilibrium. Identical firms, identical conditions ⇒ no firm deviates from the average: \[P_i = \bar{P} = P^{*}, \quad Q_i = Q^{*} = S/n.\]

Cost: silent on which firms enter, who is most productive, who survives.

Next week (Melitz 2003): drop symmetry — firms differ in productivity; trade reallocates output to the most productive.

  • Pricing FOC (\(Q_i = bS(P_i - c)\)) + symmetry collapses into one equation in \((n, P)\) — the PP curve.
  • Zero-profit (\(\pi_i = 0\), \(Q_i = S/n\)) + symmetry collapses into one equation in \((n, P)\) — the CC curve.
  • We derive each in the next two slides, then intersect.

PP curve: derivation

  • Pricing FOC for any firm: \(Q_i = b S (P_i - c)\).
  • At the symmetric Nash equilibrium \(P_i = \bar P = P\) — so each firm’s residual demand is just its share of the market: \(Q_i = S/n\).
  • Substitute \(Q_i = S/n\) into the FOC: \[\frac{S}{n} = b S (P - c) \;\;\Longleftrightarrow\;\; P = c + \frac{1}{bn}\]
  • The PP curve: \(P\) as a function of \(n\), holding firm behavior fixed.
  • Downward-sloping in \(n\): more competitors ⇒ lower price.
  • Asymptotic to \(P = c\) as \(n \to \infty\). Independent of \(S\) and \(F\).

CC curve: derivation

  • Zero-profit condition: \(P_i = AC(Q_i) = c + F/Q_i\).
  • At symmetric quantities \(Q_i = S/n\), so each firm’s average cost is \(c + nF/S\).
  • Substitute: \[P = c + \frac{n F}{S}\]
  • The CC curve: the price at which each firm just breaks even, as a function of \(n\).
  • Upward-sloping in \(n\): more firms ⇒ smaller scale ⇒ higher AC ⇒ higher break-even price.
  • Pivots flatter as \(S\) rises (bigger market lowers AC at every \(n\)); steeper when \(F\) rises.

Equilibrium: PP meets CC

  • Equilibrium \((n^{*}, P^{*})\): PP = CC, \(\;c + 1/(b n^{*}) = c + n^{*} F / S\).
  • Solving: \[n^{*} = \sqrt{\tfrac{S}{b F}}, \;\; P^{*} = c + \sqrt{\tfrac{F}{b S}}, \;\; Q^{*} = \sqrt{b F S}\]
  • Both more firms and bigger firms with a larger market: \(n^{*}, Q^{*} \propto \sqrt{S}\).
  • Markup falls with \(S\): \(P^{*} - c \propto 1/\sqrt{S}\).

Same logic applies to trade: opening borders raises effective market size to \(S + S^{*}\).

What are the gains from trade?

Trade as a larger integrated market

  • Consider two countries, Home and Foreign, with the same technology, tastes, and factor endowments — H-O predicts no trade.
  • Open the borders: the integrated market has size \(S_W = S + S^{*}\), larger than either country alone.
  • Krugman model says the integrated market supports \[n^{*}_W = \sqrt{S_W/(bF)} > \max(n^{*}_H, n^{*}_F)\]
  • Two distinct gains follow: lower prices (pro-competitive) and more varieties (love-of-variety).

Pro-competitive gains: lower markups, lower prices

  • Larger market \(S_W \Rightarrow\) more firms \(n^{*}_W\) enter \(\Rightarrow\) each firm faces tougher competition.
  • Markup falls: \(P^{*}_W - c = 1/(b \cdot n^{*}_W) < 1/(b \cdot n^{*}_H)\).
  • Each firm produces more (\(Q^{*}_W = \sqrt{b F S_W} > Q^{*}_H\)): exploits scale economies — moves down the AC curve.
  • Lower prices benefit consumers in both countries.

Gains here come from market size, not factor endowments — H-O is silent on both.

Love-of-variety gains: more varieties

  • Even if prices stayed constant, opening to trade would still raise welfare.
  • Each consumer now buys from \(n^{*}_W = \sqrt{S_W/(bF)}\) varieties — strictly more than \(n^{*}_H\) alone (though \(n^{*}_W < n^{*}_H + n^{*}_F\) due to consolidation).
  • Welfare gain follows from CES preferences (Dixit–Stiglitz aggregator): utility rises in the number of available varieties.
  • A gain unique to monopolistic competition — neither Ricardian nor H-O captures it.

What is the home market effect?

Home market effect: statement

  • With iceberg trade costs \(\tau > 1\) (a fraction of every shipment “melts in transit”), firms prefer to locate where demand is large.
  • Result (Helpman-Krugman 1985): the country with the larger market hosts a disproportionately larger share of firms — and is a net exporter of the differentiated good.
  • “Disproportionate” \(=\) if Home has a 60% share of world demand, Home hosts > 60% of firms (often much more).
  • Trade pattern is determined not by comparative advantage but by market size + scale economies + trade costs.

TODO: schematic / cartoon of HME mechanism (no equation here)

How does the mechanism work?

  • A firm based in Home pays no trade cost on Home sales but pays \(\tau\) on Foreign sales (and vice versa).
  • If demand is symmetric across countries, location is indifferent — but if Home demand is larger, operating profit is higher for a Home-based firm.
  • Free entry until profits = 0 ⇒ Home hosts more firms; the price index falls more in Home than in Foreign.
  • Home becomes a net exporter of varieties; Foreign imports them at the iceberg-inflated price \(\tau \cdot P^{*}\).

Case study: intra-industry trade

What does the data say?

Grubel-Lloyd index

  • Measures the share of two-way (intra-industry) trade in total trade.
  • \(GL = 1 - |X - M| / (X + M)\), ranging from 0 (pure inter-industry) to 1 (pure intra-industry).
  • High between rich, similar economies (US-Canada, France-Germany, Japan-Korea).
  • Lower between dissimilar pairs (US-Bangladesh, Germany-Vietnam).

TODO: GL index chart or table.

Options: - WITS bilateral GL by country pair - BACI / CEPII intra-industry trade share - Static table from KMO Ch. 8 reproduced

If a hosted chart is available, use the OWID-style iframe pattern with data-external="1" to bypass embed-resources inlining.

Further reading:

Where does the simple Krugman model fall short?

1. Firm heterogeneity (Melitz 2003)

  • The simple Krugman model assumes all firms are identical.
  • In reality, only a small fraction of firms export, and exporters are larger and more productive than non-exporters (Bernard et al. 2007).
  • Trade reallocates resources from low- to high-productivity firms — an additional source of gains the symmetric model misses.

2. Multinational production and global value chains

  • A firm may serve Foreign demand by exporting or by setting up a subsidiary abroad — a choice the Krugman model rules out.
  • Modern trade increasingly happens within multinational firms via fragmented production stages.
  • Next week: multinationals, FDI, and global supply chains (KMO Ch. 9).