Chapter 57: New Trade Theory, Firm Selection, Scale, and Geography. The Encyclopedia of Economic Principals, interactive companion

Every example here is a constructed teaching example: it uses the hypothetical numbers of the chapter's worked examples, plus a few values added for comparison and labelled as such in each panel. Nothing here measures a real market, firm or household.

Demonstration 1 of 4

Bigger market, bigger industry share

When the larger market hosts more than its share of producers, which way do goods flow?

With plant fixed costs and shipping costs, producers prefer to locate near the bigger market and ship the rest. The larger market then holds a more than proportional share of production and becomes a net exporter of the good.

$Equation, written in LaTeX: s_E=\frac{900}{900+600}=0.60.$

$Equation, written in LaTeX: s_N=\frac{8}{12}=0.6667.$

Equation, written in LaTeX: 8(125)=1{,}000

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s_E is Harbor's share of world demand and s_N its share of the 12 equal-size producers. Each producer makes 125 units. Harbor buys 900 units and Inland 600. The producer count in Harbor is an assumed equilibrium allocation, not one derived here.

Predict first. In the book's allocation, is Harbor's production share above or equal to its demand share?

Your prediction Above it Equal to it

Producers in Harbor (assumed)

Figure: Bigger market, bigger industry share. Left: Harbor's demand share 60.00 percent and producer share 66.67 percent, with Inland's shares. Right: consumption 900 and 600 against production 1,000 and 500. — Producers in Harbor (assumed): 8
Constructed example: the chapter's hypothetical Harbor and Inland (demand 900 and 600, 12 producers, 125 units each, 8 in Harbor, and the 6 of the equal-demand benchmark); allocations of 7 and 9 producers are added for comparison. Every allocation is an assumed equilibrium.

Demand share s_E: 60.00%
Producer share s_N: 66.67%
Gap s_N - s_E (points): 6.67
Harbor output: 1,000
Harbor net exports: 100

With 8 of 12 producers in Harbor (an assumed equilibrium allocation), s_N = 8 / 12 = 0.6667 against s_E = 0.60. Harbor makes 8 x 125 = 1,000 units and consumes 900, so Harbor exports a net 100 units to Inland. Harbor's producer share exceeds its demand share: the more-than-proportional home-market result.

Worked steps

s_E = 900 / (900 + 600) = 0.60
s_N = 8 / 12 = 0.6667
Harbor output = 8 x 125 = 1,000
Harbor net exports = 1,000 - 900 = 100
Inland output = 4 x 125 = 500; net exports 500 - 600 = -100

Use the idea

Compare a region's share of an industry's output with its share of the industry's demand; a production share well above the demand share, with net exports, is the home-market signature.

Where the conclusion applies

Equal-size producers, one variety per location, and an assumed allocation of producers. A full model would derive the allocation from wages, substitution, entry and zero profit.

Check your understanding: If Harbor hosted 7 producers, what are its net exports?

7 x 125 = 875 units of output against 900 consumed, so net exports are -25: a small net import.

Chapter 57 source: section "Home-market effect".

Demonstration 2 of 4

Scale economies without comparative advantage

How much do two identical countries save by trading varieties instead of duplicating plants?

With a fixed cost per plant, average cost falls as each plant makes more. Integration lets each variety be made once for both markets, so the duplicated fixed costs disappear while the product range and total output stay the same. Trade is intra-industry and balanced.

Equation, written in LaTeX: C(q)=90+2q.

Equation, written in LaTeX: C(75)=90+2(75)=240,

Equation, written in LaTeX: C(150)=90+2(150)=390.

Equation, written in LaTeX: 4(390)=1{,}560.

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C(q) = F + c q is the cost of one plant making q units, with fixed cost F and marginal cost c. Four varieties are demanded, 75 units of each in each country. Autarky needs 8 plants of 75 units; integration needs 4 plants of 150 units.

Predict first. Does the saving from integration come from a lower marginal cost?

Your prediction Yes No, from fewer fixed costs

Fixed cost per plant

Marginal cost

Figure: Scale economies without comparative advantage. Left: the average cost curve F/q + c with F = 90 and c = 2, falling from 3.20 at 75 units to 2.60 at 150 units. Right: world cost 1,920 in autarky against 1,560 integrated. — Fixed cost per plant: 90, Marginal cost: 2
Constructed example: the chapter's hypothetical East and West (F = 90, c = 2, 4 varieties, 75 units per country); fixed costs of 30 and 150 and marginal costs of 1 and 3 are added for comparison.

Autarky AC: 3.20
Integrated AC: 2.60
World cost, autarky: 1,920
World cost, integrated: 1,560
Saving: 360 (18.75%)
Gross intra-industry trade per country: 300

Integration halves the number of plants from 8 to 4, so the world saves four fixed costs: 1,920 - 1,560 = 360 = 4 x 90. Marginal cost 2 is paid on the same 600 units either way, so none of the saving comes from it. Average cost falls from 3.20 to 2.60.

Worked steps

C(75) = 90 + 2(75) = 240; AC = 240 / 75 = 3.20
C(150) = 90 + 2(150) = 390; AC = 390 / 150 = 2.60
Autarky: 8(240) = 1,920; integrated: 4(390) = 1,560
Saving = 1,920 - 1,560 = 360 = 4 x 90, or 360 / 1,920 = 18.75%
Each country exports 2(75) = 150 and imports 150: gross trade 300, net 0

Use the idea

When judging integration in a fixed-cost industry, count how many duplicate plants or product lines it removes and multiply by the fixed cost.

Where the conclusion applies

Identical countries, costless integration, fixed product set and total quantity. With free entry some of the saving could become extra varieties instead.

Check your understanding: With F = 150 and c = 2, what is the saving?

Autarky 8(150 + 150) = 2,400; integrated 4(150 + 300) = 1,800; saving 600 = 4 x 150.

Chapter 57 source: section "New-trade-theory scale mechanism".

Demonstration 3 of 4

Trade raises productivity through selection

How can average productivity rise when no firm becomes more productive?

Trade opening raises the bar for survival and lets the best firms expand abroad. The weakest firm exits and the exporter takes a bigger share of sales, so the average across the industry rises by reallocation alone.

$Equation, written in LaTeX: \bar\varphi_{s,0}=\frac{25(1.2)+30(1.8)+30(2.7)+15(4.5)}{100}=\frac{232.5}{100}=2.325.$

$Equation, written in LaTeX: \bar\varphi_{s,1}=\frac{25(1.8)+35(2.7)+40(4.5)}{100}=\frac{319.5}{100}=3.195.$

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phi is a firm's fixed productivity and the weights are its percentage of sales. The sales-weighted mean is sum(weight x phi) / 100. After opening, the survival cutoff 1.5 removes the 1.2 firm and the export cutoff 3.2 lets only the 4.5 firm export.

Predict first. Between the closed and open regimes, did any firm become more productive?

Your prediction Yes No, only the weights changed

Regime

Exporter's post-trade sales share (%)

Figure: Trade raises productivity through selection. Bars of sales weight for firms with productivity 1.2, 1.8, 2.7 and 4.5, before trade and after trade with the exporter at 40 percent. The weighted mean is 2.325 before and 3.195 in this regime. — Regime: Open (book cutoffs), Exporter's post-trade sales share (%): 40
Constructed example: the chapter's hypothetical four firms (productivities 1.2, 1.8, 2.7, 4.5; weights 25, 30, 30, 15 before and 25, 35, 40 after); exporter shares of 20 and 60 percent are added for comparison.

Mean before: 2.325
Mean in this regime: 3.195
Change: 0.870
Change (%): 37.42%

The 1.2 firm exits and the exporter takes 40 percent of sales: 25.00 x 1.8 + 35.00 x 2.7 + 40 x 4.5 = 319.50, so the mean rises from 2.325 to 3.195, a gain of 0.870 (37.42%). No firm became more productive: the rise is all reallocation.

Worked steps

Before: (25(1.2) + 30(1.8) + 30(2.7) + 15(4.5)) / 100 = 232.5 / 100 = 2.325
Exporter weight 40; the other 60 split 25:35, so 25.00 and 35.00
After: (25.00(1.8) + 35.00(2.7) + 40(4.5)) / 100 = 319.50 / 100 = 3.195
Change = 3.195 - 2.325 = 0.870, or 0.870 / 2.325 = 37.42%

Use the idea

Before crediting trade with making firms better, split an industry productivity gain into within-firm change and reallocation across firms.

Where the conclusion applies

Cutoffs and post-trade weights are assumed outcomes, not a calibration. In the constructed exporter shares the remaining weight is split between the 1.8 and 2.7 firms in the book's 25:35 ratio. The exporter share has no effect in the closed regime.

Check your understanding: How much of the rise comes from dropping the 1.2 firm alone, holding the other weights proportional?

(30(1.8) + 30(2.7) + 15(4.5)) / 75 = 202.5 / 75 = 2.70, against 2.325: about 0.375 of the 0.870 rise.

Chapter 57 source: section "Melitz selection effect".

Demonstration 4 of 4

Gravity and a cut in trade costs

How much does a bilateral trade-cost cut raise exports when everything else is held fixed?

In the gravity equation trade falls with the trade-cost factor raised to 1 - sigma. The more substitutable the varieties, the more buyers switch when costs change, so the same cost cut moves exports more.

$Equation, written in LaTeX: \frac{X'_{CD}}{X_{CD}}=(\frac{1.22}{1.30})^{1-4}=(\frac{1.30}{1.22})^3\approx1.2099.$

$Equation, written in LaTeX: X'_{CD}=160(1.2099)\approx193.58$

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X is Cedar's exports to Delta, 160 million before the reform. t is the iceberg trade-cost factor, 1.30 before and t' after. sigma is the elasticity of substitution; incomes and multilateral resistance are held fixed.

Predict first. With sigma = 4, does a 6 percent cut in the iceberg factor raise exports by about 6 percent?

Your prediction About 6 percent About 21 percent

Elasticity of substitution sigma

New iceberg factor

Export ratio: 1.2099
New exports (million): 193.58
Cost cut: 6.15%
Export rise: 20.99%

With sigma = 4 the trade-cost exponent is -3, so a 6.15% fall in the iceberg factor raises exports by 20.99%: from 160 to 160 x 1.2099030 = 193.58 million, holding incomes and resistance terms fixed.

Worked steps

X'/X = (1.22 / 1.30)^(1 - 4) = (1.30 / 1.22)^3 = 1.2099
X' = 160 x 1.2099030 = 193.58 million
Cost cut = (1.30 - 1.22) / 1.30 = 6.15%
Export rise = 1.2099 - 1 = 20.99%

Use the idea

Translate a trade-cost reform into an export response with the exponent 1 - sigma, and state what is being held fixed.

Where the conclusion applies

Constant incomes and multilateral resistance terms. General equilibrium effects, trade diversion from other partners and welfare are outside this calculation.

Check your understanding: At sigma = 6 with the book cost cut, what is the export ratio?

(1.30/1.22)^5 = 1.3737813, so exports rise to 160 x 1.3737813 = 219.81 million.

Chapter 57 source: section "Gravity equation of trade".

Bigger market, bigger industry share

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies

Scale economies without comparative advantage

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies

Trade raises productivity through selection

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies

Gravity and a cut in trade costs

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies