International Trade & Customs Analytics
Samuelson Iceberg Trade Cost & CIF/FOB Wedge Formula
Convert customs CIF and FOB prices into Paul Samuelson’s (1954) iceberg factor tau = P_CIF / P_FOB >= 1, melting loss share (tau - 1) / tau, and Eaton-Kortum trade attenuation tau^(-theta).
Avoid confusing the ad-valorem freight markup (tau - 1) with the iceberg melting fraction (tau - 1)/tau!
Paul Samuelson (1954) eliminated the need for a separate global shipping-sector general equilibrium by modeling transport friction as a melting iceberg: to deliver 1 intact unit at Destination CIF (Cost, Insurance, and Freight) price P_CIF, an exporter must ship tau >= 1 units from Origin FOB (Free on Board) price P_FOB, so zero-arbitrage requires P_CIF = tau * P_FOB -> Iceberg Multiplier tau = P_CIF / P_FOB! Analysts routinely confuse Ad-Valorem Freight Markup f_adv = tau - 1 = (P_CIF - P_FOB) / P_FOB with the Melting Loss Fraction s_melt = 1 - (1 / tau) = (tau - 1) / tau = (P_CIF - P_FOB) / P_CIF! Under Krugman / Eaton-Kortum trade elasticity theta > 0, bilateral trade value shrinks relative to frictionless trade by exact attenuation factor tau^(-theta)!
Verify on Exporter_FOB P_FOB = 80.00 (B2), Importer_CIF P_CIF = 100.00 (B3), and Trade_Elasticity theta = 4.0 (B4): Iceberg Multiplier is tau = 100 / 80 = 1.2500 (ship 1.25 units so 1.00 arrives!), Ad-Valorem Freight Rate is 1.25 - 1 = 0.2500 (25.00% over FOB), Iceberg Melting Fraction is (1.25 - 1) / 1.25 = 0.2000 (20.00% of shipped cargo "melts" in transit: 0.20 * 1.25 = 0.25 -> 1.00 arrives!), and Bilateral Gravity Trade Attenuation is 1.25^(-4) = 0.4096 (a seemingly modest 25% freight wedge slashes bilateral trade volume by 59.04%!)!
| Iceberg Trade Metric (P_FOB = 80, P_CIF = 100, theta = 4) | Formula | Verified Output |
|---|---|---|
| Samuelson Iceberg Multiplier (tau) | P_CIF / P_FOB = 100 / 80 | 1.2500 units shipped / unit |
| Ad-Valorem Freight Wedge (tau - 1) | (P_CIF - P_FOB) / P_FOB | 0.2500 (25.00% over FOB) |
| In-Transit Melting Share (1 - 1/tau) | (tau - 1) / tau | 0.2000 (20.00% Melts En Route) |
| Bilateral Trade Attenuation (tau^-theta) | 1.25^(-4) | 0.4096 (-59.04% Trade Volume!) |
Samuelson Iceberg Factor tau & Melting Share Formula
Validate P_FOB > 0 and P_CIF >= P_FOB (tau >= 1; CIF below FOB flags customs mirror-data misreporting or currency mismatch!).
=LET(p_fb, B2, p_cf, B3, IF(OR(p_fb <= 0, p_cf < p_fb), "Invalid CIF/FOB Wedge", LET(t_ic, p_cf / p_fb, ROUND((t_ic - 1) / t_ic, 4))))Gravity / Eaton-Kortum Bilateral Trade Volume Attenuation Formula
Validate trade elasticity theta > 0 (typical empirical range 3.5 to 8.0 in Eaton & Kortum 2002).
=LET(p_fb, B2, p_cf, B3, th_el, B4, IF(OR(p_fb <= 0, p_cf < p_fb, th_el <= 0), "Invalid CIF/FOB Wedge", ROUND((p_cf / p_fb) ^ (-th_el), 4)))Try the example
Use the original values or change them to test your understanding.