ECON6023 · International Trade
Krugman's Monopolistic-Competition Model
Week 7 moves to new trade theory: monopolistic competition with love of variety and increasing returns from a fixed cost. The full Krugman (1980) solve — CES demand, the constant markup, free entry, equilibrium firm size and the number of varieties, and the market-size gains from trade — is the flagship ~25-mark exam theory question (Q2 in recent years).
What this chapter covers
- 01Monopolistic competition: many firms, each a unique variety, free entry, zero long-run profit
- 02Love of variety and increasing returns from a fixed cost: labour l = α + βy
- 03CES preferences U = (Σ cᵢ^ρ)^(1/ρ) with ρ = (σ−1)/σ; demand cᵢ = (I/P)(pᵢ/P)^(−σ)
- 04Firm output yᵢ = L·cᵢ and profit π = pᵢyᵢ − w(α + βyᵢ)
- 05Constant markup p = wβ·σ/(σ−1) over marginal cost wβ
- 06Free-entry / zero-profit condition and equilibrium firm size y = α(σ−1)/β (independent of L)
- 07Number of varieties N = L/(σα) from labour-market clearing; N proportional to market size
- 08Gains from trade through variety; the pro-competitive (markup-lowering) gains only under non-CES demand
Krugman (1980): markup, firm size and number of varieties
- +1Demand and firm output. CES demand gives cᵢ = (I/P)(pᵢ/P)^(−σ) with constant perceived elasticity σ; aggregating over L consumers, a firm sells yᵢ = L·cᵢ. This is the demand the firm faces.
- +1Constant markup. Maximising π = pᵢyᵢ − w(α + βyᵢ) with constant elasticity σ gives p = wβ·σ/(σ−1). With w = 1, β = 1, σ = 3: p = 1·1·(3/2) = 1.5, a 50% markup over marginal cost wβ = 1.
- +1Free entry pins firm size. Zero profit p·y = w(α + βy) together with the markup gives y = α(σ−1)/β = 6·(3−1)/1 = 12. Output per firm does not depend on market size.
- +1Number of varieties. Full employment L = N(α + βy) with α + βy = 6 + 12 = 18 gives N = L/(α + βy) = 1800/18 = 100 (equivalently N = L/(σα) = 1800/(3·6) = 100).
Key terms
- Monopolistic competition
- A market of many firms each making a unique differentiated variety, with free entry driving long-run profit to zero even though each firm has some market power. The structure behind intra-industry trade.
- Love of variety
- The preference for spreading spending across more varieties: with concave sub-utility, N varieties are worth more than the same income spent on fewer. The source of the gains from trade in Krugman's model.
- CES markup
- Under CES demand each firm sets a constant price p = wβ·σ/(σ−1), a fixed markup σ/(σ−1) over marginal cost wβ. It does not vary with market size, so pure-CES gains run through variety, not price.
- Free-entry / zero-profit condition
- Entry continues until π = 0, i.e. p·y = w(α + βy). Combined with the markup it pins the equilibrium firm size y = α(σ−1)/β.
- Equilibrium firm size
- y = α(σ−1)/β, the output per firm, which is independent of the size of the market — a key Krugman result. Larger markets add firms, not scale per firm (under CES).
- Number of varieties (N)
- N = L/(σα) from labour-market clearing L = N(α + βy). Proportional to market size L, so opening to trade (a larger effective market) raises the varieties available to each consumer.
Krugman's Monopolistic-Competition Model FAQ
Why does opening to trade raise welfare in the Krugman model?
Trade enlarges the effective market to L + L*. Since equilibrium firm size and (under CES) the markup are fixed, the extra market supports more firms and hence more varieties available to every consumer. Love of variety then raises real income — consumers can buy from more differentiated producers even though each variety is made in only one place. That variety gain is the gains-from-trade channel.
Does firm size grow when the market gets bigger?
No — this is the signature result. Equilibrium output per firm is y = α(σ−1)/β, which contains no L. A larger market raises the number of firms N = L/(σα), not the scale of each firm. Writing output per firm as increasing in L is a common and costly error.
Can AI help me with the Krugman derivation?
Yes. Sia can take you through the whole chain — CES demand, firm output yᵢ = Lcᵢ, the profit-maximising markup, the free-entry firm size, and the number of varieties — one line at a time, and check your algebra and your welfare conclusion. It explains the method and never does graded assessment for you; USyd academic-integrity rules apply.
When do markets deliver pro-competitive (lower-markup) gains rather than only variety gains?
Only when demand is non-CES (variable elasticity). Under pure CES the elasticity, and hence the markup, is constant, so a larger market cannot lower the price — the gain is purely more variety. With variable-elasticity demand a bigger market makes each firm face more elastic demand, lowering the markup and price and raising output per firm. The unit is explicit about this caveat.
Exam move
Rehearse the six-step Krugman (1980) cookbook until you can reproduce it on a blank page: demand → firm output → markup → free-entry firm size → number of firms → welfare in L. This is the flagship 25-mark exam question, so practise it with fresh α, β, σ, L and always normalise w if instructed. Lock in the two examinable results — firm size independent of L, and CES gains running through variety not price — and be ready to explain the non-CES pro-competitive caveat. Work the Week 7 tutorial and past-exam Krugman questions rather than only reading. Confirm exam timing on Canvas.
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