Liberation Day was a monumental day for exposing the mathematical skills of the Trump administration. Matt Parker and others already made videos that explain the ludicrous maths. I would like to go a step further and try to work out the last bits of ambiguity of what the Trump administration actually did with the numbers.
They showed a complicated formula:
$$\Delta \tau_i=\frac{x_i-m_i}{\epsilon*\varphi *m_i}$$
This formula is clearly Mathiness, an approach to make their calculations look more complex and trustworthy than they really are. The actual calculation comes down to:
$$t=\frac{\text{exports-imports}}{\text{imports}}$$
We now have the starting point for calculating the tariffs (t). We only need imports and exports per country. The US Census provides this information, and you can download its data. Trump only posted the poster boards with some numbers, but the Guardian published the full list. I downloaded the list from here, but it contained an error for Reunion.
We now have to make some slight modifications since imports and exports can be considered from the perspective of the USA or the foreign country. Moreover, we need to have the deficit expressed as a positive percentage number. So for the data from the US Census, this comes to:
$$t=\frac{\text{exports-imports}}{\text{imports}} \times -100$$
There are a few more rules we have to consider:
- All trade surpluses are ignored, resulting in a default of 10%.
- The reciprocal tariff is set to the rounded half of the trade deficit percentage, but no lower than 10%.
- If the trade deficit percentage is an uneven number, then one is added before it is halved.
This results in the following table that you can also download as a CSV file. There are a couple of odd choices that I still cannot explain. For this purpose I calculated the deltaTarif column to show the difference between my calculations and the official data.
Afghanistan, for example, has a trade deficit of 49%. This should result in a reciprocal tarif of 25%, but they only get 10%. Some countries are off by one, such as Vietnam. They should have 45% but got 46%. Same problem with Japan (24% vs 23%).
Lying in the chart of what the numbers mean and then presenting a misleading formula is just terrible. If you want to be evil, be at least good at it.
| Country | New US tariffs | Tariffs charged to the USA | IYR | EYR | deficitFraction | calcTariff | deltaTariff |
|---|---|---|---|---|---|---|---|
| Afghanistan | 10 | 49 | 22.588359 | 11.446788 | 49.32439315 | 49 | -15 |
| Albania | 10 | 10 | 128.280409 | 141.727893 | -10.48288207 | 10 | 0 |
| Algeria | 30 | 59 | 2461.611142 | 1014.504109 | 58.78698745 | 59 | 0 |
| Andorra | 10 | 10 | 3.369249 | 4.911141 | -45.76367018 | 10 | 0 |
| Angola | 32 | 63 | 1869.239166 | 682.352869 | 63.49568951 | 63 | 0 |
| Anguilla | 10 | 10 | 1.190598 | 72.488329 | -5988.396671 | 10 | 0 |
| Antigua and Barbuda | 10 | 10 | 23.75155 | 573.765998 | -2315.699178 | 10 | 0 |
| Argentina | 10 | 10 | 7092.161169 | 9170.997286 | -29.31174387 | 10 | 0 |
| Armenia | 10 | 10 | 121.583116 | 160.78363 | -32.24174153 | 10 | 0 |
| Aruba | 10 | 10 | 10.704668 | 725.539495 | -6677.786056 | 10 | 0 |
| Australia | 10 | 10 | 16685.50984 | 34593.34854 | -107.3256908 | 10 | 0 |
| Azerbaijan | 10 | 10 | 157.776472 | 255.07449 | -61.66826826 | 10 | 0 |
| Bahamas | 10 | 10 | 1792.373019 | 5639.742401 | -214.6522705 | 10 | 0 |
| Bahrain | 10 | 10 | 1204.340922 | 1646.230202 | -36.69137799 | 10 | 0 |
| Bangladesh | 37 | 74 | 8365.766327 | 2213.964142 | 73.53542933 | 74 | 0 |
| Barbados | 10 | 10 | 48.564639 | 772.603153 | -1490.875931 | 10 | 0 |
| Belize | 10 | 10 | 81.128498 | 590.448355 | -627.7940176 | 10 | 0 |
| Benin | 10 | 10 | 48.623404 | 216.446069 | -345.1479148 | 10 | 0 |
| Bermuda | 10 | 10 | 23.328268 | 540.382525 | -2216.427971 | 10 | 0 |
| Bhutan | 10 | 10 | 3.281048 | 3.427734 | -4.470705701 | 10 | 0 |
| Bolivia | 10 | 20 | 504.146695 | 401.036421 | 20.45243478 | 20 | 0 |
| Bosnia and Herzegovina | 35 | 70 | 179.089584 | 52.988456 | 70.41231834 | 70 | 0 |
| Botswana | 37 | 74 | 405.123674 | 104.327456 | 74.24799816 | 74 | 0 |
| Brazil | 10 | 10 | 42316.32362 | 49666.97632 | -17.37072617 | 10 | 0 |
| British Virgin Islands | 10 | 10 | 60.246807 | 312.909554 | -419.3794818 | 10 | 0 |
| Brunei | 24 | 47 | 238.849306 | 127.213271 | 46.73910796 | 47 | 0 |
| Burundi | 10 | 10 | 3.736684 | 6.61399 | -77.0015875 | 10 | 0 |
| Cabo Verde | 10 | 10 | 4.482999 | 12.246976 | -173.1871232 | 10 | 0 |
| Cambodia | 49 | 97 | 12661.80682 | 321.629583 | 97.45984449 | 97 | 0 |
| Cameroon | 11 | 22 | 248.80528 | 193.064344 | 22.40343774 | 22 | 0 |
| Cayman Islands | 10 | 10 | 49.39955 | 1286.490024 | -2504.254541 | 10 | 0 |
| Central African Republic | 10 | 10 | 1.422027 | 35.070359 | -2366.223145 | 10 | 0 |
| Chad | 13 | 26 | 80.814038 | 59.939855 | 25.82989728 | 26 | 0 |
| Chile | 10 | 10 | 16469.47996 | 18167.7934 | -10.31188262 | 10 | 0 |
| China | 34 | 67 | 438947.3861 | 143545.7395 | 67.29773453 | 67 | 0 |
| Christmas Island | 10 | 10 | 1.747242 | 2.11479 | -21.03589543 | 10 | 0 |
| Cocos (Keeling) Islands | 10 | 10 | 1.100644 | 2.58047 | -134.4509215 | 10 | 0 |
| Colombia | 10 | 10 | 17690.34896 | 19037.61341 | -7.615816097 | 10 | 0 |
| Comoros | 10 | 10 | 1.848391 | 4.738928 | -156.3812527 | 10 | 0 |
| Cook Islands | 10 | 10 | 0.892119 | 6.861175 | -669.08742 | 10 | 0 |
| Costa Rica | 10 | 17 | 11634.90533 | 9676.788152 | 16.82967866 | 10 | 0 |
| Djibouti | 10 | 10 | 40.11125 | 144.982858 | -261.451857 | 10 | 0 |
| Dominica | 10 | 10 | 2.306195 | 58.79899 | -2449.610506 | 10 | 0 |
| Dominican Republic | 10 | 10 | 7505.430838 | 13081.66107 | -74.29593789 | 10 | 0 |
| Ecuador | 10 | 12 | 8524.306263 | 7531.653753 | 11.64496534 | 10 | 0 |
| Egypt | 10 | 10 | 2546.000141 | 6092.022475 | -139.2781672 | 10 | 0 |
| El Salvador | 10 | 10 | 2311.212791 | 4556.353458 | -97.14123579 | 10 | 0 |
| Equatorial Guinea | 13 | 25 | 127.640788 | 95.379691 | 25.27491212 | 25 | 0 |
| Eritrea | 10 | 10 | 0.852918 | 37.475441 | -4293.791783 | 10 | 0 |
| Eswatini | 10 | 10 | 22.588609 | 46.113517 | -104.1450051 | 10 | 0 |
| Ethiopia | 10 | 10 | 465.844335 | 1017.706562 | -118.4649432 | 10 | 0 |
| European Union | 20 | 39 | 605760.3933 | 370189.2304 | 38.88850535 | 39 | 0 |
| Fiji | 32 | 63 | 259.272473 | 94.679571 | 63.48259809 | 63 | 0 |
| French Guiana | 10 | 10 | 1.821129 | 28.999681 | -1492.401252 | 10 | 0 |
| French Polynesia | 10 | 10 | 40.42327 | 145.19757 | -259.1930341 | 10 | 0 |
| Gabon | 10 | 10 | 171.666854 | 171.065105 | 0.350533016 | 10 | 0 |
| Gambia | 10 | 10 | 1.969897 | 80.563522 | -3989.732712 | 10 | 0 |
| Georgia | 10 | 10 | 165.414171 | 1736.461692 | -949.7659792 | 10 | 0 |
| Ghana | 10 | 17 | 1171.728486 | 967.304543 | 17.44635771 | 10 | 0 |
| Gibraltar | 10 | 10 | 0.431179 | 650.596519 | -150787.8027 | 10 | 0 |
| Grenada | 10 | 10 | 14.074818 | 165.335817 | -1074.692397 | 10 | 0 |
| Guadeloupe | 10 | 10 | 3.427661 | 470.637794 | -13630.5817 | 10 | 0 |
| Guatemala | 10 | 10 | 5019.892412 | 9714.801951 | -93.52609884 | 10 | 0 |
| Guinea | 10 | 10 | 6.179835 | 138.336186 | -2138.509378 | 10 | 0 |
| Guinea-Bissau | 10 | 10 | 0.122848 | 3.394912 | -2663.506121 | 10 | 0 |
| Guyana | 38 | 76 | 5375.48866 | 1314.93053 | 75.53840008 | 76 | 0 |
| Haiti | 10 | 10 | 616.770785 | 1214.423999 | -96.90037669 | 10 | 0 |
| Heard and McDonald Islands | 10 | 10 | 0.013589 | 0.058879 | -333.284274 | 10 | 0 |
| Honduras | 10 | 10 | 5532.561721 | 7057.473677 | -27.56249334 | 10 | 0 |
| Iceland | 10 | 10 | 1072.626837 | 985.844921 | 8.090597122 | 10 | 0 |
| India | 26 | 52 | 87416.44858 | 41752.66797 | 52.23705762 | 52 | 0 |
| Indonesia | 32 | 64 | 28084.73788 | 10202.09572 | 63.67387952 | 64 | 0 |
| Iran | 10 | 10 | 6.218491 | 90.84743 | -1360.924041 | 10 | 0 |
| Iraq | 39 | 78 | 7422.275381 | 1660.554212 | 77.62742385 | 78 | 0 |
| Israel | 17 | 33 | 22217.48485 | 14792.03496 | 33.42164939 | 33 | 0 |
| Jamaica | 10 | 10 | 361.372579 | 2644.127532 | -631.6901408 | 10 | 0 |
| Japan | 24 | 46 | 148208.5666 | 79740.84555 | 46.1968715 | 46 | 1 |
| Jordan | 20 | 40 | 3364.877293 | 2030.78495 | 39.64757781 | 40 | 0 |
| Kazakhstan | 27 | 54 | 2330.74942 | 1077.097171 | 53.78751736 | 54 | 0 |
| Kenya | 10 | 10 | 737.305128 | 782.524079 | -6.13300373 | 10 | 0 |
| Kiribati | 10 | 10 | 0.808162 | 4.220009 | -422.1736484 | 10 | 0 |
| Kosovo | 10 | 10 | 34.015946 | 49.388369 | -45.19181386 | 10 | 0 |
| Kuwait | 10 | 10 | 1643.60575 | 2411.831329 | -46.74025867 | 10 | 0 |
| Kyrgyzstan | 10 | 10 | 16.66837 | 133.144912 | -698.7878359 | 10 | 0 |
| Laos | 48 | 95 | 803.320155 | 40.385293 | 94.97270263 | 95 | 0 |
| Lebanon | 10 | 10 | 257.571987 | 541.421719 | -110.2020974 | 10 | 0 |
| Lesotho | 50 | 99 | 237.257685 | 2.794513 | 98.82216123 | 99 | 0 |
| Liberia | 10 | 10 | 72.529569 | 220.400195 | -203.8763335 | 10 | 0 |
| Libya | 31 | 61 | 1465.562558 | 567.220437 | 61.29674343 | 61 | 0 |
| Liechtenstein | 37 | 73 | 243.72052 | 66.04089 | 72.90302433 | 73 | 0 |
| Madagascar | 47 | 93 | 733.215493 | 53.407211 | 92.71602803 | 93 | 0 |
| Malawi | 17 | 34 | 41.05461 | 26.940731 | 34.3783049 | 34 | 0 |
| Malaysia | 24 | 47 | 52534.84796 | 27704.75083 | 47.26405062 | 47 | 0 |
| Maldives | 10 | 10 | 4.765289 | 92.612024 | -1843.471298 | 10 | 0 |
| Mali | 10 | 10 | 5.500278 | 51.496789 | -836.257931 | 10 | 0 |
| Marshall Islands | 10 | 10 | 20.448963 | 127.426248 | -523.1428361 | 10 | 0 |
| Martinique | 10 | 10 | 2.807758 | 199.161662 | -6993.263095 | 10 | 0 |
| Mauritania | 10 | 10 | 2.854898 | 139.755555 | -4795.290655 | 10 | 0 |
| Mauritius | 40 | 80 | 234.519911 | 47.99104 | 79.53647526 | 80 | 0 |
| Mayotte | 10 | 10 | 1.88971 | 1.817609 | 3.815453165 | 10 | 0 |
| Micronesia | 10 | 10 | 2.44009 | 50.489582 | -1969.168842 | 10 | 0 |
| Moldova | 31 | 61 | 136.495167 | 53.629683 | 60.7094638 | 61 | 0 |
| Monaco | 10 | 10 | 47.589664 | 162.798791 | -242.0885489 | 10 | 0 |
| Mongolia | 10 | 10 | 26.97744 | 396.615463 | -1370.174572 | 10 | 0 |
| Montenegro | 10 | 10 | 15.382306 | 27.681345 | -79.95575566 | 10 | 0 |
| Montserrat | 10 | 10 | 5.631794 | 12.071251 | -114.3411318 | 10 | 0 |
| Morocco | 10 | 10 | 1904.884441 | 5268.646115 | -176.5861278 | 10 | 0 |
| Mozambique | 16 | 31 | 216.070589 | 149.698447 | 30.71780491 | 31 | 0 |
| Namibia | 21 | 42 | 275.225098 | 160.506498 | 41.68173645 | 42 | 0 |
| Nauru | 30 | 59 | 2.238924 | 0.916696 | 59.05640388 | 59 | 0 |
| Nepal | 10 | 10 | 120.461589 | 120.890203 | -0.355809685 | 10 | 0 |
| New Zealand | 10 | 20 | 5617.042562 | 4499.423962 | 19.89692241 | 10 | 0 |
| Nicaragua | 18 | 36 | 4622.325539 | 2940.985161 | 36.37433936 | 36 | 0 |
| Niger | 10 | 10 | 8.306694 | 43.252222 | -420.6911679 | 10 | 0 |
| Nigeria | 14 | 27 | 5699.175959 | 4174.298267 | 26.7561083 | 27 | 0 |
| Norfolk Island | 29 | 58 | 0.191165 | 0.080944 | 57.65752099 | 58 | 0 |
| Norway | 15 | 30 | 6583.33417 | 4592.039618 | 30.24750834 | 30 | 0 |
| Oman | 10 | 10 | 1319.991529 | 1954.270075 | -48.05171337 | 10 | 0 |
| Pakistan | 29 | 58 | 5123.65616 | 2135.147106 | 58.32766604 | 58 | 0 |
| Panama | 10 | 10 | 555.820472 | 10702.13406 | -1825.465973 | 10 | 0 |
| Papua New Guinea | 10 | 15 | 79.150698 | 67.20022 | 15.09838612 | 10 | 0 |
| Paraguay | 10 | 10 | 356.152957 | 3158.414426 | -786.8140398 | 10 | 0 |
| Peru | 10 | 10 | 9363.192761 | 11223.8033 | -19.87153942 | 10 | 0 |
| Philippines | 17 | 34 | 14177.62812 | 9297.313129 | 34.42264776 | 34 | 0 |
| Qatar | 10 | 10 | 1834.185727 | 3804.248139 | -107.4080113 | 10 | 0 |
| Reunion | 10 | 10 | 44.066856 | 11.883522 | 73.03297063 | 73 | -27 |
| Rwanda | 10 | 10 | 30.238416 | 44.757797 | -48.0163412 | 10 | 0 |
| Samoa | 10 | 10 | 5.717674 | 54.397476 | -851.3917023 | 10 | 0 |
| San Marino | 10 | 10 | 25.233029 | 80.023469 | -217.137784 | 10 | 0 |
| Saudi Arabia | 10 | 10 | 12733.72516 | 13177.01009 | -3.481188132 | 10 | 0 |
| Senegal | 10 | 10 | 235.125168 | 350.866605 | -49.22545638 | 10 | 0 |
| Serbia | 37 | 74 | 814.350544 | 209.85911 | 74.2298803 | 74 | 0 |
| Sierra Leone | 10 | 10 | 28.74785 | 119.859059 | -316.9322541 | 10 | 0 |
| Singapore | 10 | 10 | 43203.7229 | 46032.64597 | -6.547868746 | 10 | 0 |
| Sint Maarten | 10 | 10 | 101.535218 | 753.934338 | -642.5348099 | 10 | 0 |
| Solomon Islands | 10 | 10 | 1.345899 | 13.147232 | -876.8364491 | 10 | 0 |
| South Africa | 30 | 60 | 14655.78659 | 5818.998932 | 60.29555359 | 60 | 0 |
| South Sudan | 10 | 10 | 0.805202 | 59.276702 | -7261.718178 | 10 | 0 |
| Sri Lanka | 44 | 88 | 3015.585462 | 368.214575 | 87.78961566 | 88 | 0 |
| Sudan | 10 | 10 | 13.133891 | 56.610929 | -331.0293804 | 10 | 0 |
| Suriname | 10 | 10 | 90.91341 | 383.542932 | -321.8771818 | 10 | 0 |
| Switzerland | 31 | 61 | 63425.3186 | 24961.98692 | 60.64349779 | 61 | 0 |
| Syria | 41 | 81 | 10.651468 | 2.020826 | 81.02772313 | 81 | 0 |
| Taiwan | 32 | 64 | 116264.0269 | 42336.86142 | 63.58558829 | 64 | 0 |
| Tajikistan | 10 | 10 | 4.633938 | 56.83741 | -1126.546622 | 10 | 0 |
| Tanzania | 10 | 10 | 204.714855 | 573.380041 | -180.0871686 | 10 | 0 |
| Thailand | 36 | 72 | 63328.18022 | 17719.24949 | 72.01996106 | 72 | 0 |
| Togo | 10 | 10 | 89.996365 | 283.59244 | -215.1154383 | 10 | 0 |
| Tokelau | 10 | 10 | 0.177585 | 0.295764 | -66.54785033 | 10 | 0 |
| Tonga | 10 | 10 | 2.845246 | 19.909723 | -599.7540107 | 10 | 0 |
| Trinidad and Tobago | 10 | 12 | 3325.877971 | 2939.684738 | 11.61176797 | 10 | 0 |
| Tunisia | 28 | 55 | 1123.215612 | 503.588215 | 55.16549008 | 55 | 0 |
| Turkey | 10 | 10 | 16745.66406 | 15292.97969 | 8.674988135 | 10 | 0 |
| Turkmenistan | 10 | 10 | 14.590585 | 82.234419 | -463.6128983 | 10 | 0 |
| Turks and Caicos Islands | 10 | 10 | 10.983629 | 713.57661 | -6396.728995 | 10 | 0 |
| Tuvalu | 10 | 10 | 0.224447 | 0.570424 | -154.1464132 | 10 | 0 |
| Uganda | 10 | 20 | 132.618139 | 106.29285 | 19.85044369 | 10 | 0 |
| Ukraine | 10 | 10 | 1186.498293 | 1683.510839 | -41.88902327 | 10 | 0 |
| United Arab Emirates | 10 | 10 | 7474.432624 | 26969.30898 | -260.8208186 | 10 | 0 |
| United Kingdom | 10 | 10 | 68084.46833 | 79941.34275 | -17.41494751 | 10 | 0 |
| Uruguay | 10 | 10 | 1228.834152 | 1649.000113 | -34.19224314 | 10 | 0 |
| Uzbekistan | 10 | 10 | 42.437585 | 380.795484 | -797.3071488 | 10 | 0 |
| Vanuatu | 22 | 44 | 13.667021 | 7.601059 | 44.38393707 | 44 | 0 |
| Venezuela | 15 | 29 | 5987.862777 | 4232.021935 | 29.32333134 | 29 | 0 |
| Vietnam | 46 | 90 | 136561.1558 | 13098.15512 | 90.40857919 | 90 | 1 |
| Zambia | 17 | 33 | 169.112021 | 113.762941 | 32.72924046 | 33 | 0 |
| Zimbabwe | 18 | 35 | 67.833118 | 43.782746 | 35.45520641 | 35 | 0 |
