# Wages and Steel Tariffs (not painfully wonkish)

Paul Krugman demonstrates just how simple models can and should be. He presented a trade model on the New York Times opinion pages. He also apologised for extreme wonkishness, but I don’t think he had to. His aim is to find an example in which Trump’s tariffs on steel cause lower wages (also for steel workers). Here the trick is to make sure that everyone has the same income “not gonna get into income distribution today”. This means that a reduction in total money metric welfare implies a reduction of each person’s welfare (including workers in the protected industry).

This “itsy-bitsy teeny-weeny model” is a major demonstration of Krugman’s extraordinary ability to make models simple.

Imagine a world of two countries, Home and Foreign. (That’s an old-fashioned trade theory convention.) In both countries, labor is the only factor of production (not gonna get into income distribution today). There are two goods, cars and steel. Cars are a final good, sold to consumers; steel is an input into car production. I’m going to assume that both countries end up producing cars.

To keep down on notation, I’m going to do some sneaky things with choice of units (another old trade theory tradition.) We assume that in each country building a car requires one unit of labor (which amounts to measuring labor in units of how much it takes to build a car.) We also assume, using the same trick, that building a car also requires one unit of steel.

This leaves us with just two parameters to specify: the amount of labor it takes to make one unit of steel in each country. Call this a in Home and a* in Foreign (stars for Foreign is traditional.) And let’s assume that a* < a. That is, Foreign has a comparative advantage in steel production. Under free trade Home will import steel from Foreign. Let w and w* be the wage rates in the two countries, in any common unit. Then the cost of producing a car in Home will be w + w*a* (because we’re importing the steel) while the cost of producing a car in Foreign is w* + w*a* Since both countries will be producing cars, these costs will have to be equal, implying w = w*: wages will be the same. Now suppose Home imposes a tariff sufficiently high to induce car producers to use domestically produced steel instead. Now Home costs of car production are w + wa = w* + w*a* because car production costs must be equal. And this implies w/w* = (1+a*)/(1+a) <1 That is, to offset the higher costs imposed by the tariff, Home’s relative wage has to fall – the opposite of what you expect from a tariff on final goods.

My points (if any) are that it is equally easy to find and example in which tariffs on final goods can be bad for everyone in the protecting country and another model in which tariffs on intermediate goods are bad for workers in the country which doesn’t protect (and do not harm or benefit people in the country which does protect).

So model 2 in both countries, 1 unit of labor is needed to make 1 unit of steel. In the home country, 1 unit of steel and a units of labor are needed to make a car and in the forgeign country 1 of steel and a* of labor are needed with a*a. So with free trade all cars are made domestically. The real wage is 1/(1+a) in both countries. With steel tariffs, foreigners start making cars. Then their wage in cars is 1/(1+a*) < 1/(1+a). So it is about equally easy to get any result one wants.