International Trade & Economic Geography
Krugman Love-of-Variety Gain & Home-Market Effect Formula
Compute Dixit-Stiglitz-Krugman autarky varieties L / (sigma * F), frictionless trade welfare gain ((L_H + L_F)/L_H)^(1/(sigma - 1)), and iceberg Home-Market Effect firm share.
Explain intra-industry trade between identical economies and agglomeration in larger markets
Paul Krugman (1979, 1980) showed why countries with identical technology and factor endowments still trade heavily: under CES love-of-variety elasticity sigma > 1 and fixed labor setup F > 0, an autarky economy of labor L_H supports N_H = L_H / (sigma * F) differentiated varieties, whereas frictionless integration with partner L_F expands varieties to (L_H + L_F) / (sigma * F) and raises real wages by ((L_H + L_F) / L_H)^(1 / (sigma - 1))! When iceberg trade costs tau > 1 apply (trade freeness phi = tau^(1 - sigma) in (0, 1)) and Home holds demand share s_E = L_H / (L_H + L_F), Krugman’s Home-Market Effect magnifies Home’s share of manufacturing firms to s_N = MIN(1, MAX(0, ((1 + phi) * s_E - phi) / (1 - phi)))!
Verify with CES elasticity sigma = 5 (B2), Home labor L_H = 600 (B3), Foreign labor L_F = 400 (B4 -> s_E = 0.60), fixed setup F = 2 (B5), and iceberg cost tau = 1.25 (B6): Home autarky varieties are 600 / 10 = 60, frictionless real-wage multiplier is (1,000 / 600)^0.25 = 1.1362 (+13.62% welfare gain purely from variety!), trade freeness is phi = 1.25^(-4) = 0.4096, and Home’s manufacturing variety share jumps to (1.4096 * 0.60 - 0.4096) / 0.5904 = 0.7388 (60% of demand attracts 73.88% of firms!).
| Krugman New-Trade Metric (sigma=5, L_H=600, L_F=400, F=2) | Formula | Verified Output |
|---|---|---|
| Home Autarky Variety Count (N_H) | L_H / (sigma * F) | 60.00 varieties |
| Frictionless Welfare Multiplier | ((L_H + L_F) / L_H)^(1 / (sigma - 1)) | 1.1362 (+13.62% Gain) |
| Trade Freeness Index (phi) | tau^(1 - sigma) (at tau = 1.25) | 0.4096 |
| Home-Market Firm Share (s_N) | CLAMP(((1 + phi)*s_E - phi)/(1 - phi)) | 0.7388 (vs s_E = 0.6000) |
Krugman Home-Market Effect Manufacturing Share s_N Formula
Validate sigma > 1, L_H > 0, L_F > 0, F > 0, and iceberg cost tau > 1 (at tau = 1, shipping is costless so firm location is indeterminate).
=LET(sig_e, B2, l_hm, B3, l_fr, B4, f_fx, B5, tau_c, B6, IF(OR(sig_e <= 1, l_hm <= 0, l_fr <= 0, f_fx <= 0, tau_c <= 1), "Require sigma > 1 and tau > 1", LET(s_ex, l_hm / (l_hm + l_fr), phi_f, POWER(tau_c, 1 - sig_e), s_raw, ((1 + phi_f) * s_ex - phi_f) / (1 - phi_f), ROUND(MIN(1, MAX(0, s_raw)), 4))))Frictionless Love-of-Variety Real-Wage Multiplier Formula
Smaller countries (lower s_E = L_H / (L_H + L_F)) reap even larger proportional variety gains from market integration!
=LET(sig_e, B2, l_hm, B3, l_fr, B4, IF(OR(sig_e <= 1, l_hm <= 0, l_fr < 0), "Invalid Krugman Input", ROUND(POWER((l_hm + l_fr) / l_hm, 1 / (sig_e - 1)), 4)))Try the example
Use the original values or change them to test your understanding.