Answers to Problem Set #4

Tariffs

1. Here is how to go about these kinds of problems. It really helps to do these step by step.

(a)  Tariff on car imports. Step 1: figure out the impacts on relative prices in the home economy. A tariff on car imports will reduce imports, forcing up the price that domestic producers of cars receive. Further, it will provide the same higher price for car consumers, so there is no difference between consumer and producer prices. So we have:

pc = pc*(1+t), or pc pc*

Meanwhile, no policy in toys means pt = pt*. Overall, then we have p p*, where p (p*) is the relative price of cars in home (the world).

Step 2: draw a PPF diagram and first show free trade (points Qf and Cf below).

Figure 1

Step 3: work out where production and consumption must be with the tariff. Because the import tariff raises the relative price of cars, p becomes steeper than p* and production moves to a point like Qt. To determine consumption, recall that 2 things must be true: 1. Consumers face home prices p; 2. International trade must be balanced at world prices p*. So draw a line parallel to p* from point Qt; this line is the constraint along which trade must occur. Next draw a line parallel to p that is tangent to an indifference curve at a point along p*. The point I've drawn at Ct then indicates the consumption point. (Incidentally, take my word for it that it's a pain in several posterior spots to draw these diagrams in Word. This explains the arrow depicting where point Ct is.) Note that if you draw in the trade triangles the tariff on imports causes both imports and exports to fall but welfare is reduced.

(b)  Subsidization of toy exports. Again, first work out the price impacts. Because toy makers get to sell wine abroad at a fixed price, the subsidy simply raises their domestic price (and consumers must also pay this higher price). So we have

pT = pT*(1 + s) and pc = pc*, or p = (pc*/pT*(1+s) < p* . Thus, the price impacts of the export subsidy are the opposite of those of the import tariff (Note: you might want to convince yourself that an import tariff and export tax would have similar impacts on relative prices, and an import subsidy and export subsidy have similar impacts on prices, but taxes and subsidies are opposites to each other, that is taxes restrict trade and subsidies expand trade. As a result, the production point would move to Qs (see next diagram) because p is flatter than p*, and the consumption point (which must be on p* line but also tangent to p) to Cs. Note that welfare falls relative to free trade in this case also. Note also that this policy doesn't even work in terms of the objective set out because production of cars falls rather than rises.

Figure 2

T

p* p*

Qs

Qf

p

Cf

p

Cs

C

(c)  Taxation of toy production. Here there will be a difference between consumer and producer prices because consumers can buy at the given world price (no tax on imports) and so toy producers have to absorb the full price decline from the tax. In Figure 1 above, the consumer relative price remains at the world relative price: q = p*. But the producer relative price of cars is higher (because relative price of toys is lower): p p* (here we assume the tax on toys raises the relative price of cars by the same amount as the tariff on imports). Thus, production again moves to Qt and the trade constraint remains along p* through that point. However, consumers get to consume at p*, so the consumption equilibrium is at Ct'. Note that the production tax imposes lower costs on the economy than the import tariff because prices to consumers are not distorted (though producer prices are distorted).

(d) Subsidization of car production. You should convince yourselves that this policy has the same price impacts as policy (c). Thus, the effects on production, consumption, and prices are the same and final equilibrium points are Qt and Ct' in Figure 1.

The essential point of this problem is to show that a tax on imports or a subsidy to exports generates higher welfare costs than a direct intervention in production (tax toys or subsidize cars). Policies (a), (c), and (d) work to change production toward more cars, as the policy desired. However, direct production subsidies or taxes are the lower-cost policies. In terms of ranking the welfare effects of these policies, (c) and (d) are equivalent to each other and both are better than (a). Policy (b) doesn't work and is, therefore, quite stupid.

2. In the diagram below, H imports X. H's tariff raises home price and reduces imports but improves its terms of trade from p* to p1 (that is, a lower foreign price), which allows for the potential improvement in welfare. For H, the loss in "import surplus" (area below excess demand curve and above price) is -(pHp*AB). The gain in tariff revenue is +(pHp1CB). The net gain or loss is -(BDA) + (p*p1CD). Here, the first effect is the loss from reducing the VOLUME OF TRADE, so it's called the volume of trade effect. It is also the deadweight losses caused by distorting consumption and production. The second effect is the net gain from forcing down the import price; it is called the terms of trade effect. Retaliation by F would involve an export tax, shifting its excess-demand curve in the left half of the figure up (fewer exports at every price) and offsetting the initial terms of trade change, resulting in, say, price p2 somewhere near p*. The net effect is lower trade volumes (causing distortionary welfare losses) and little effect on the terms of trade, so both H and F are likely to be worse off.

p

pH

p*

B

A

D

C EH

p1 EHt = EH/(1+t)

EF

Exp. X X* Xt Xt X* Imp. X

3.  I'll show this for the case of a PPF diagram. Revenues were already shown above in question 2 for an excess-demand curve diagram.

Y

p* p

Qf

p* p

Cf

Qt

Ct

Z

V

X

The tariff on X raises domestic price of X so p > p*. This shifts production to Qt and consumption to Ct (recall our equilibrium conditions for consumption and trade). Exports of Y are the distance QtZ and total imports of X are the distance ZCt. But note that, while exports of QtZ buys imports of ZCt at world prices p*, those same exports are only worth ZV units of X at domestic prices p. Thus, the difference, VCt, gives tariff revenue in terms of good X.

A prohibitive tariff cuts off imports altogether, meaning that tariff revenues would be zero.

4.  Here is the diagram for a small country, which faces a horizontal (perfectly elastic) world supply curve S* and so can import all it wants at fixed p*.

px Sx

A B

px*(1+t) Sx*(1 + t)

px* C D E F Sx*

Q0 Q1 C1 C0 Qx

The tariff of t raises domestic price to px*(1+t), causing output to rise from Q0 to Q1 and consumption to fall from C0 to C1. The loss in consumer surplus is the area px*(1+t) px*FB. The gain in producer surplus is area px*(1+t) px*CA. The tariff revenue is ADEB. There is a net loss of - (ACD + BEF). ACD is the producer deadweight loss and BEF is the consumer deadweight loss.

5. The diagram for a large country is below. If the country is large, a tariff will drive down the world price to px*', which is a terms of trade gain for H.

px Sx

A B

px*'(1+t)

px* C D E F

px*' G H

Q0 Q1 C1 C0 Qx

In this case, domestic price rises to px*'(1+t), and consumer surplus loss is px*(1+t) px*FB. The gain in producer surplus is area px*'(1+t) px*CA. The tariff revenue is now AGHB, reflecting the reduction in world price to px*'. The net effect is -(ACD + BEF) + (DGHE). The first term is the deadweight losses ("volume of trade effect") and the second term is the net gain in tariff revenue ("terms of trade effect").

6*. A small country exporting good X would face a perfectly elastic world demand curve at fixed price px* as shown below. Because that price is fixed, the home exporters would have to absorb the tax fully in a lower price, as shown by the distorted world demand curve Dx*/(1+t).

px

Dx

Sx

A E F B

px* Dx*

px*/(1+t) C D Dx*/(1+t)

C0 C1 Q1 Q0 Qx

Because the tax drives down the domestic price, the gain in consumer surplus is

px*{ px*/(1+t)}CA and the loss in producer surplus is px*{ px*/(1+t)}DB. Note that because this is an export good there is more domestic production than consumption. The tax causes consumption to rise and production to fall. The tax revenue is ECDF. The net welfare loss is -(ACE + FDB), which consists of deadweight consumer and producer losses.

Quotas

7. Here is the diagram with excess-demand curves. Note that a small country can import the product at a fixed price p*, which is given by the perfectly elastic world supply curve EX*.

p

Z

ph B

A EX*

p* C

EXh

EXh/(1+t)

EXhQ

Exp. X X1 X* Imp. X

The tariff shifts the home excess demand curve down to EXh/(1+t). This raises domestic price to ph but has no impact on p* (because country is small). Equilibrium in home moves from A to B, with import volume falling from X* to X1. The loss in "import surplus" (which is the difference between consumer surplus loss and producer surplus gain in H) is the area php*AB. The gain in tariff revenue for H is php*CB. Net welfare loss is area BCA.

Set the quota to the same level of imports as under the tariff, X1. Then this quota has no effect on the H excess-demand curve from Z to B, at which point it becomes vertical. Thus, ZB EXhQ is the H excess-demand curve under the quota. Impacts on "import surplus" are the same as with tariff. The rectangle php*CB is now quota rents. If they go to domestic importers without any rent-seeking costs, then these rents would be considered a welfare gain for H. Thus, the welfare impacts of tariff and quota would be the same, with the only difference being who gets the revenues. However, if some portion of the rectangle is wasted as rent-seeking the welfare losses would be larger by the amount of the rent-seeking.

With a VER set at the same level of imports, X1, the H excess-demand curve is the same as with the quota. In this case, however, the rents from the trade restriction go to foreign exporters and the area php*CB is a welfare loss to Home (consider it a terms of trade loss because H has to pay a higher price to foreign exporters). In this case the total welfare loss is php*AB.

8. This problem is most easily analyzed with a partial-equilibrium diagram for good X. Suppose there is a single domestic producer and that the economy is small so it can buy the good from abroad at fixed price p*. The diagram for the import market looks like this:

px

MC

Z

pQ MR

B

pt D S*(1+t)

p* A S*

F

D

Qt

Qm Q* Ct C* Qx

In this diagram, MC is the marginal cost curve for the single home firm. Free trade is at point A, with consumption level C* and production level Q* (imports are Q*C*) Note that the monopoly home firm must act as a perfectly competitive firm and only gets price p*. The tariff distorts the world supply curve up to S*(1+t), causing home price to rise to pt. This causes consumption to fall to Ct, output to rise to Qt, and imports to fall to QtCt (= AF = DB). The quota requires that supply level AF come in from abroad but then any additional demand must be satisfied by the home firm. Thus, the home demand curve with the quota is ZFAD. This yields a marginal revenue curve for the home monopolist as shown, causing it to choose quantity Qm and set a higher price pQ. Thus, output is lower, consumption is lower (show this), price is higher, and imports are the same under the quota as the tariff. Clearly this is better for the monopolist but worse for consumers. Overall the quota is worse for the country in welfare terms.

9. See the text's discussion. Essentially the impacts on consumer and producer prices in the US are the same but with a tariff the revenue goes to the US government while with an export tax the revenue goes to the Canadian government. Any idea why the US government would agree to this?

10. Consider a small economy importing good X. With an increase in domestic supply capacity for good X, the economy's excess-demand curve will shift toward the origin (become smaller) because the economy would produce more X at home. The diagram is shown below.

p