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Unformatted text preview: January 2001 Solutions to Problem Set 3, International Trade Question 1 a) In autarky, without intervention, the price is at ¯ (the intersection of p Supply and Demand, the two solid lines in Figure 1)) and consumption and production equal ¯ x. At that point, the social marginal value of consumption p ¯ , is less than the marginal cost of production, ¯ . The optimal level p of consumption under autarky, xa, can be achieved with either a consumption or a production tax of . In autarky, consumption = Figure 1 production, so it doesn't matter which group directly pays the tax. a a The consumer price is p and the producer price is p  , whether a production or consumption tax is used. Note that this result is merely an example of the general result that, in a closed economy, it does not matter which group (consumers or producers) directly pays the tax. The reason is that, in a closed economy, the price that the producer receives and the price that the consumer pays does not depend on which group directly pays the tax. Now consider trade, and suppose that the country is an importer, so pw is below the autarkic price (Figure 1). With trade, production
consumption. Since the "distortion" arises from consumption, it is important to target consumption rather than production. Domestic producers should face the world price, causing them to produce xp, and consumers should face a consumption tax of , so that they pay pw + . (Confirm that the policy recommendation does not change if the country is an exporter.) Note that for a small country that trades in equilibrium, the price that consumers face is independent of a tax/subsidy applied to domestic producers. When producers are taxed/subsidized, consumers pay the world price. Thus, a tax/subsidy for producers does not affect the level of consumption  which is what the policymaker wants to influence. b) Subtract the environmental cost x from the sum of consumer and producer surplus, leaving ¯ the triangle abc minus the small shaded triangle. c) If the country exports the commodity, i.e., the world price is above the autarkic price, it obtains the usual gains from trade, and also reduces the environmental cost because consumption falls. d) When the country begins to trade, domestic price falls from ¯ to pw. The change in the sum of p producer and consumer surplus is 1 and the increased environmental cost is 2, with ∆1
p ¯ mp w D( p ) S( p ) d p ¯ ∆ 2 γ D( p w ) D ( p ) For the country to be worse off from trade, we need 2 > 1. You should be able to show that 1 is a convex function of pw which (in the absence of regulation) reaches its minimum at ¯ (the p w autarkic price with no government regulation) and that 2 is a decreasing function of p , with 2(p;p) = 0. See figure 2. Therefore, for pw slightly less than ¯ , 2 > 1. ¯ ¯ p Here's another way to say the same thing: The gains from trade (including additional environmental damages) are G(pw) / 1(pw)  2(pw). Note that G(p) ¯ = 0, i.e, if the autarkic and world price are equal, there are no gains from trade. Also, dG(p)/dpw = 0 ¯ w D'(p) > 0, so when p is slightly ¯ below p, the gains are negative. ¯ (The notation dG(p)/dpw means ¯ the derivative of G with respect to the world price, evaluated where the world price equals the autarkic price.) Figure 2 Figure 3 shows a situation where 2 = bcde > abc = 1, so the net gains from trade are negative.1 Here is an answer to the question AHow can I show negative gains from trade graphically?@ One way is to show that the area that measures the loss is greater than the area that measures the gains, as in the paragraph in the text. Another method is to note that (for an
1 e) The optimal tariff must be lower than the firstbest tax, since the tariff introduces a (secondary) distortion in production. In other words, correcting the environmental distortion carries a cost. f) The gains from being able to trade (import) at price p, as we saw above, are G(p) = 1(p)  2(p), so the social marginal benefit of imports (as a function of price) is smb(p) = dG/dp = [S(p)  D(p)  D'(p)] = M(p) + D'(p) < M(p), where M(p) is the excess (import) demand function, D(p)  S(p). The reason for the negative sign in front of dG/dp is that an increase in world price decreases imports, and we want to measure how welfare changes when imports increase. So we know that the social marginal benefit curve lies below the import demand curve. Figure 3 From figure 4b we see that the optimal level of imports, M*, equates social marginal benefits and world price. This level of imports is supported by a tariff of t*. From construction of smb and figure 4a, we know that the horizontal difference between M(p) and smb is D'. Also, the slope of M(p) is 1/[D'S']. Using the "rise over run" formula for slope, we know that t* = [D'/(D'  S') < . This confirms the result we obtained from intuition in part e. importer) the gains from trade is the area below the social marginal benefit from imports, above the world price line, from quantity = 0 to the equilibrium quantity. In the absence of an externality, the social marginal benefit from imports is equal to the excess demand curve, but with the externality discussed in this problem set, the social marginal benefit of imports lies below the excess demand curve. (See figure 4.) Under autarky, imports are greater than the level that equates social marginal benefits (smb) of imports and the price of imports. So the area Aunder the smb curve, above the price line, from quantity =0 to the equilibrium quantity@ includes ‘negative area’. Figure 4 Now here is the algebra. Define W(p) as the total social gain from trade. W(p) equals the gains from trade defined above (additional consumer + producer surplus minus additional pollution damage), plus tariff revenues [which equals (p  pw)$(D  S)]: W(p) = G(p) + (ppw)$[D(p) S(p)]. The second term is tariff revenue. Here p is the import price. The world price, pw, is assumed fixed (because of the small country assumption), so p  pw / t is the unit tariff. The mathematical problem is maxp W(p). The first order condition is G'(p) = (D  S)  (p  pw)(D' S'), i.e. D'(p) + (ppw)[D'  S'] = 0. Solving this equation, using p  pw / t gives the optimal t: t = D'/[D'  S'] < . We obtained this result above using geometric arguments. (Look at figure 4b again. Using the "rise over run" relation, t*/D' = 1/(D'  S') Y t = D'/[D'  S'], which is the same formula we obtained algebraically.) g) Monopsony power increases the incentive to restrict imports and therefore leads to a larger tariff. h) This change decreases the optimal tariff, because now the tariff provides less of a "cure" for the environmental externality. Decreased domestic consumption, resulting from the tariff, causes a fall in world price and an increase in consumption abroad, which results in a domestic cost. ...
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 Fall '07
 KARP

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