Basic Analysis of a Tariff

Introductory Notes and Caveats
These notes focuses mainly on mechanics, and getting comfortable with a model that we can use to picture the effects of different kinds of import restrictions on particular markets.  We will concentrate on the policies of tariffs and quotas.  In this discussion, the question you should always be able to answer is “who benefits and who suffers from this policy?”

You may notice that when we analyze tariffs and quotas we are applying microeconomic tools, looking only at markets in individual goods and not at the big picture of overall trading patterns.  This is because in order to focus in on a few questions we have to make tons of simplifying assumptions.  One of those assumptions is the economist’s favorite ceteris paribus (“other things being equal”), which is the convenient assumption that we can look at changes in one market while assuming that everything else in our economy is not changing.  (Note for example that in Ricardian trade theory we do assume that one market affects another, when productive factors from one industry move into another industry.)  We also bring over a lot of other simplifying assumptions from neoclassical micro, such as the assumption of perfect competition in domestic industry.  So beware: these are starkly oversimplified models that are useful because they help us think about issues.  But be careful about naively using the results from a model as a guide to policy.

The core intuition of this theory, which is similar to that of the broader trade theory we examined earlier, is that restrictions on trade move the global economy farther away from an ideal international general equilibrium in which everyone buys or sells at the same set of prices.  In neoclassical theory, this one global set of prices would guide efficient use of resources.

A Tariff in a Small Country
A tariff is a fee assessed on imports.  This can be imposed in various ways but we’ll stick with the “specific tariff,” a simple per-unit charge. The tariff represents a per-unit charge that has to be paid to the government by whomever brings the good across the border and into the country.  If there is a $1,000 tariff on imported automobiles, then no new car can be imported into the United States without paying $1,000 to customs agents as it is brought in.

To do our analysis, we have to know whether the international price of the good in question will be affected by changes in our demand for it.  The easiest case is the “small country” in which the international price will not change when our demand for the good changes, so we can treat it as a given.  Suppose we are the nation of Monaco, and we are importing tubas.  Let us suppose that the standard international price of a tuba is $200.  This is a price which is not going to fall if we demand fewer tubas, or rise if we demand more, because we represent an insignificant part of the total global tuba market.

Look at this diagram.

What does it mean?  First, the assumption we just made of an unchanging international price is reflected in the horizontal foreign supply schedule.  Whether we buy one foreign made tuba or 500, foreign suppliers will always ask $200 per tuba.  (Monaco is to the world tuba market as I am to the Seattle espresso market: if I double my espresso intake, the price of espresso will not rise.)

Second, there are also domestic tuba producers, who show up as a domestic supply schedule.  What this curve says is the higher the price that domestic tuba makers can get, the larger the quantity they will be willing to supply.  We usually base this, in micro, on the assumption that producers face rising per-unit costs of making goods.  As drawn, the first tuba costs $101 to make, the second $102, the third $103, and the hundredth $200. If domestic producers made 101 tubas, the 101st tuba would cost them $201 to manufacture.  So if the price they can get is only $200 per tuba, they will make only 100 tubas, not 101 tubas.  (Remember that we assume prefect competition in this simple micro model, in which individual suppliers take the price they observe in the market as given and react accordingly.)

Finally, we have a demand schedule, the thick line which represents the quantity of tubas that consumers in Monaco will buy at each different price.  (Review the market model: Why do consumers buy larger amounts of tubas at lower prices? If there were no foreign tubas permitted, what would be the quantity of tubas produced and sold in Monaco?  At what price?  Why?)

If there are no restrictions whatever on tuba imports, what happens?  Well, it’s pretty clear that there will be imports, and that the market price will be $200.  Look at the demand schedule.  Buyers have no reason to pay more than $200, because they can always get an imported tuba for $200.  Domestic producers have no reason to sell for less than $200.  In these conditions domestic suppliers will make 100 tubas, domestic consumers will buy 400, and imports of 300 will make up the difference between domestic demand and domestic supply.

Be sure you can see this before moving on.  Think about why domestic producers, foreign producers, and domestic consumers behave as they do.

Now let us suppose that the Monagesque Tuba Maker’s Society bribes enough politicians to have a $50 tariff imposed on each imported tuba.  This means that while the international price remains $200, the price that consumers within Monaco face for an imported tuba now rises to $250.  What will the new domestic price be?  The new domestic quantities demanded and supplied?  How much will imports be?

The diagram shows the effect of this tariff on the domestic price and the quantities consumed, produced by the domestic industry, and imported.  Who gains?  Who loses?

We can deepen the analysis of gains and losses from the tariff by using a couple of ideas from microeconomics.  Think, first, about the suppliers of a good — take the example of the domestic suppliers in the example above.  Their total revenue received is quantity (150) times price ($250) or $37,500.

What of their costs?  From the above description of the supply curve, the first unit cost them $100, the second $101, and so on.  Adding up these costs to make each unit gives you the area under the supply schedule, up to Q=150, as the cost of making 150 units.  Don’t worry about the exact cost and profit numbers in the example, but see if you can make sense of the idea that the region underneath the supply curve represents total (variable) costs (there's another category called fixed costs; don't worry about that now).  The difference between total revenue and these costs is “producer surplus.”

What did the introduction of a tariff do to domestic producers’ surplus?

We can introduce an analogous concept of “consumer surplus,” though the reasoning may seem a bit less concrete.  Start with a very simple market model like this:

In this example consumers actually paid $60,000 for 300 widgets at $200 per widget.  But how much were those widgets actually worth to the consumers?  Look at the demand curve.  It tells us, for example, that had the market price been $300 rather than $200, 100 people would still have bought widgets.  If the price had been $400, 1 person would have bought one widget — there’s one person in the economy for whom a widget is actually worth $400, then another person who would buy a widget at $399, and so on.  So when widgets are actually sold for only $200, the people who would have paid a higher price, if they had been required to, actually get widgets for less.  And they are very, very happy.   So, we can add up a triangle, as shown, of what people would have paid but did not have to, and call that “consumers’ surplus.”

Now we can put our analysis together.  When the domestic price rose in our Monaco example, that reduced consumers’ surplus by the amount of the shaded area shown below.

So the first losers in our story are consumers in Monaco.  They pay more, and we can use the shaded area as a measure of how much worse off consumers are after this tariff.  The question follows, as night the day: was consumers’ loss someone else’s gain? The answer is for the most part yes.  Part of what consumers lost was gained by government, and part by domestic producers.

What of the remaining two little triangles?  Those are termed “deadweight loss,” meaning that they are a loss that is nobody else’s gain.

We now have a geometrical way to talk about who gains and who loses from a tariff.  Our answer in this case is that domestic consumers lose, but that most of that loss is made back by the protected firms and by government — another way to put it is that there is a transfer from consumers to government and protected firms.

A Tariff in a Large Country
In the case of a large country which consumes a significant part of global production of a good, it is reasonable to assume that the foreign supply schedule slopes up, rather than being a horizontal line.

For ease in exposition, we’re going to assume that this is a good that is not domestically produced in the country in question, so we don’t have to deal with a domestic supply curve.  Let’s suppose we are looking at U.S. demand for coffee.

Without restrictions, we end up at a market equilibrium of $4 a pound and 200 million pounds sold.

Now let us suppose that the U.S. government imposed a $2 tariff on every pound of coffee.  The result would be that U.S. consumers would end up paying $2 more per pound than foreign producers received.  The market would end up an equilibrium like this, with a quantity demanded and supplied at which the price paid by consumers was exactly $2 higher than the price received by the foreign suppliers.

Now we can use our analytical apparatus, developed above, to examine the winners and losers.  As in the earlier example, there has been a loss in consumers’ surplus, as shown in the green area below: coffee is more expensive than before, some people can no longer afford it, and those who still can are paying more than they used to.  So once again consumers, clearly, are losers.

Government, however, has gained quite a lot in the form of tariff revenue — $300 million, in this case (the cross-hatched area).  The government’s $300 million gain more than offsets the $175 million of lost consumer surplus.

Foreign producers, finally, lose.  the tariff forces them down their supply curve, and they end up exporting less coffee and selling it for a lower price.  So they suffer a loss in producer surplus of $175 million.

The total losses exceed the gains, but the loss in producers’ surplus is suffered by foreigners and — ha ha! — we don’t care about them.  From a purely national point of view (in this example), this tariff has produced a net gain.  You can see from this why reductions in tariffs often have to be negotiated reciprocally between countries.

©1998 Colin Danby.