1. Consider a small country (Thailand) with the following demand and supply curves for steel:

Transcription

1 Fall 005 Econ 455 Econ 455 Answers - Problem Set 4 Harvey Lapan 1. Consider a small country (Thailand) with the following demand and supply curves for steel: Supply = 6( 10 ) Ps 0 ; Demand = 1800 P s (the supply curve implies output is zero if price is 100 or lower). Assume Thailand can export steel at a given world price of: P = 500. Assume that Thailand imposes an export tariff of t per unit of export. s a) Show how: domestic price, consumption and production change as t increases. Also, calculate how consumer surplus, producer surplus, and government tariff revenue change as t increases. d Given the world price, the net of tariff price a steel exporter in Thailand receives is: Ps = 500 t ; this will be the domestic price if trade occurs that is, if this price is more than the autarky price (i.e., if t 00 ). Note that for t > 00 the tariff is prohibitive, there are no exports, and the domestic price equals the autarky price of 00. Thus, assuming t < 00, we have: P d = 500 t ; D = 1800 P d = t; S = 6 P d 100 = t; X = S D = t s s s Consumption increases, production and exports fall, as t increases. From the diagram on the next page, one can see the decrease in producer surplus is given by area {500,G,H,(500-t)}, whereas the increase in consumer surplus is given by: {500,A,B,(500-t)}. Thus: Δ PS =( 1 ) t ( t ) = 400t + t ; Δ CS = ( 1 ) t ( t ) = 800t + t TR = tx = t ( t ) = 1600t 8t is tariff revenue. Thus, it is easily seen that producer surplus decreases with the tariff, and consumer surplus increases (for t < 00 ), whereas tariff revenue increases with the tariff for t < 100, and then decreases thereafter. Overall: Δ Welfare = TR +Δ PS +Δ CS =4t so that the tariff lowers overall welfare. (i)if t>00, the tariff is prohibitive, no trade occurs and domestic price is 600. b) Compare the domestic equilibrium when t=100 to the case where there is no tariff, but there is an export quota of 800 units. From part (a), with t=100, exports X = t = 800. Thus, a quota of 800 and a tariff of 100 have identical effects on domestic price, consumption, production and exports. The only possible difference is the tariff revenue (which is 80,000 under the tariff). Under the quota, exporters make 100 on each unit exported and hence will earn excess profits of 80,000, unless the quota licenses are auctioned off, in which case the two policies are identical.

2 P 500 A C K G S 500-t 00 B H t 400-6t 400 D Q Figure 1 c) Suppose the government subsidizes exports at a rate of s per unit of export. Show how this export subsidy affects: (i)domestic price domestic price for both consumers and producers increases to {500+s} (ii)consumer surplus falls - due to higher price - by area next to demand curve between two prices; s hence: Δ CS = { s} ={ 800s s } (iii)producer surplus increases due to higher price, by area next to supply between two prices: s Hence: Δ PS = { s} = { 400s + s } S D= s 400 = s (iv)government expenditures: Exports are: Hence: Cost to government = s ( s) = ( 1600s+ 8s ) (v)impact overall welfare: Δ CS +ΔPS Government Expenditures = 4s < 0, s 0. Suppose Sweden has the following supply and demand curves for shoes: f S = 4 P ; D = 400 6P ; f where P is the price firms receive and w the world price of shoes is P = 10. c c P is the price consumers pay. Sweden is a small country, and a) Under free trade, with no domestic tax or subsidies, find domestic production, consumption and imports. f c w Under free trade, with no domestic policy, P = P = P = 10. Hence:

3 Domestic Supply (or production) = 40; Domestic consumtion = = 40; Imports = 00 b) The government s goal is to increase output to 100 units. Find the tariff that will accomplish that goal and measure the welfare impacts of the policy on producers, consumers and the government. = 5 S = 100 To have domestic output of 100 requires a domestic producer price of 5:. To accomplish this with a tariff requires a tariff of 15. The tariff raises domestic production, lowers consumption and reduces imports. In terms of welfare, P f P 00/ D S 40 5 G C 10 A H E B Q Producers gain the area {10,A,G,5} = 1,050 Consumers lose the area {10,B,C,5} = 4,45 Tariff revenue is area {H,G,C,E} =,50 Deadweight loss = -1,15 = Area of AGH and area of EBC c) If the government uses a production subsidy instead, if it subsidizes output at the rate of 15, then the consumer price stays at 10, but the producer price increases to 5. Hence, consumers are unaffected (as compared to free trade), output is 100 (as under the tariff) and: Producers gain the area {10,A,G,5} = 1,050 (compared to free trade) Cost to government is area {10,H,G,5} = 1,500 Consumers - are unaffected (compared to free trade) Deadweight loss = 450 = Area AHG. Both the tariff and production subsidy result in the loss AGH, which occurs since expensive domestic production is substituted for cheaper imports. However, under the tariff there is also a deadweight loss EBC, due to lower consumption, while under the subsidy there is no such loss. Hence, if the goal is to increase output, the production subsidy - because it directly addresses production - is the better policy.

4 . Next, consider the case of two large countries: US: Demand = 400 us ; Supply us where us = o R = P is the price of oil in the US; Russia: Demand = 00 R ; Supply 6 R where is the price of oil in Russia. a) Assuming free trade (no tariffs), find the equilibrium price and quantities traded. The US import demand (M) is given by: M = D us S us = 400 4P us The Russian export supply (X) is given by: X = S R D R = 8P R 00 R us where P is the price in Russia and P is the price in the US. Note that under autarky the US price is 100, and the Russian price is 5 (see figure ), since exports (and imports) in each country will be zero R us under these prices. Under free trade we have: P = P = P f (f stands for free trade) and thus: f f f M = X 400 4P = 8P 00 P = 50 Thus, exports (imports) equal 00 under free trade. Domestic consumption and supply is found by substituting back into the demand and supply curves. For the US and Russia, under free trade: US: us f us f D = 400 P = 50; S = P = 150 ; Russia: D R = 00 P f = 100; S = 6P f = 00 b) Show how a US import tariff of 18 affects the volume of trade, prices in Russia and the US, and welfare in each country. Who pays for the US tax? Explain. Since part (c) asks you to answer this for the general case of any tariff, it is easier to start by assuming the tariff is t, rather than 18, and then substitute in for t=18. Thus, with any tariff, we have: us R P = P +t (which means when t=18, the US price is 18 units higher than the Russian price since the tax is on US imports). Equilibrium requires: M us = P R + t = X R = 8P R t = 1P R P R = 50 t, P us = 50 + t So, when t=18, the Russian price falls by 6 and the US price rises by 1. Note that, even though the US imposes the tax, Russia pays some of the tax (because the price it receives for its exports falls). Due to the tax, the trade volume falls. Substituting the equilibrium price back yields exports (imports): R () = () = 8 () 00 = = 00 8 ; for t=18, us c R M t X t P t t t X t = 18 = 15 Clearly, Russian welfare falls (they receive lower prices for exports and receive no tariff revenue), whereas the impact on the US is ambiguous. In terms of Figure, the loss to Russia is the area of the trapezoid {50,E,B,[50-(t/)]} with t=18. At t=18, this trapezoid has height 6, one base is (00), the other is 15, so the area (or loss to Russia) is 1,056. For the US, consumers lose (higher prices), producers gain (higher prices), and the government gains tariff revenue. Overall, the US private sector loses area {50,E,A,[50+(t/)]}=,11. However, the US government gains the tariff revenue, measured by area: {[50-(t/)], B,A,[50+(t/)]=18*15=,76. So, for t=18, the US gains 64, Russia loses 1056, and the overall loss is area AEB = 4. 4

5 (i)if the tariff were removed, but an import quota of 15 replaced it, then the volume of trade would be the same under the two policies. Hence, prices in each country would be the same under the quota as under the tariff (since firms are perfectly competitive). The only possible difference is that the tariff revenue now becomes profits for US importers, who buy at the Russian price (44) and sell at the U.S. price (6). If the US auctions off the quota licenses, the two policies are identical. P (t/) A Russia X 50 E F 50-(t/) B 5 US M 00-(8t/) 00 Q Figure (c)how does a US import tariff of t affect prices, trade volumes and welfare? In part (b) we saw with a US import tariff of t, the resulting price and quantities were: P R = 50 t, P us = 50 + t ; M us = X R = 00 8t (i&ii) How does the tariff affect Russia s welfare (sum of consumer and producer surplus) and US welfare (sum of consumer and producer surplus and tariff revenue)? The analysis was discussed in part (b), and the figure above illustrates these changes. Russia, due to lower export prices (and no tariff revenue) is hurt. The total loss in Russia is the area {50,E,B,[50- (t/)]}; the US private sector loses area {50,E,A,[50+(t/)]}, while the US government gains the tariff revenue, measured by area: {[50-(t/)], B,A,[50+(t/)]}. Thus: Russia loses: ( t ) ( 00 [ 4t ] ) = ( 00t ) ( 4t 9) US private sector loses: ( t ) ( 00 [ 4t ] ) = ( 400t ) ( 8t 9) t 00 8t = 00t 8t US government tariff revenue = ( ) Net US gain = ( 00 ( 8 t t ))- ( 400t ) ( 8t 9) = ( 00 ) ( t 16 t 9) 5

6 Overall welfare change = Net US gain plus Russian loss = (( 00 ) ( 16 9 )) ( 00 ) ( 4 9 ) ( 4 t t t t = t ) = Area {A,B,E} So, even if the US gains from the tariff, it gains less than Russia loses, so there is an overall inefficiency due to the tariff. In terms of the figure, the inefficiency (deadweight loss) is the triangle: {A,B,E}. Finally, the separate changes in consumer and producer surplus for Russia (and the US) can be calculated by going back to the original supply and demand curves. The calculation is similar to that of the previous examples so I will not repeat it here. Note that the US gains if 00t 16t 9 > 0 0 < t < 7.5. Also note that a tariff of 75 or higher is prohibitve. The US can gain from this tariff because it affects world price; specifically, by restricting imports the tariff lowers the world price of US imports (even though domestic price rises). This change in world price has a positive effect on the US economy (and a negative effect on the Russian economy), and thus from the US perspective the improved terms of trade may offset the inefficiency the tariff causes. However, overall world welfare (sum of US and Russian surplus) must fall, as shown above. (iii)find the tariff that maximizes US welfare. From above, the gain in US welfare is: G() t ( 00 t ) ( 16 t 9 ) =. Taking the derivative: dg 00 t =. For t small, G (US welfare) increases with the tariff; when t is large enough G dt 9 dg decreases as t increases further. The value of t that maximizes G is found by setting = 0, as the dt * second order condition is easily seen to hold. This implies: t = ( 75 4) = is the optimal tariff for the US. (iv)if the U.S. eliminates its import tariff, but Russia imposes an export tariff of the same magnitude, prices, quantities and the private sector losses are as above, but the tariff revenue is transferred to Russia. Thus, the US would lose area {50,E,A,[50+(t/)]}, while Russia would gain {50,F,A,[50+(t/)]}, while losing {B,F,E} for the same world loss of {A,B,E}. Numerically: Net Gain to Russia = Net Gain to US = ( t ) ( t ) 00t 8t 00t 4t 9 = 400t 0t 9 > 0, t < < 0 d) Suppose tariffs are banned, but the US uses a consumption tax of 18. Show how this affects prices, and US and Russian welfare. If there is no tariff, then the US price to producers is the same as the Russian price but the price to US consumers exceeds the Russian price by the tax (18). Hence: 6

7 R US: Demand 400 ( Po t) = + Supply = R where t is the consumption tax Russia: Demand = 00 R ; Supply 6 R R = where is the price of oil in Russia. Thus, equilibrium is where total demand equals total supply, or:, 600 P R t = 9P R P R = 50 t1 ; P US C = t1 o o o o Because US demand is pretty inelastic, most of the incidence of the tax is on US consumers; however, the tax does lower the world price and hence hurts Russia. Note that US producers, as well as consumers, lose from this policy (contrast to the tariff). The changes in surpluses are found, as usual, by taking the relevant area next to the demand or supply curves: t t Change in Russian consumer surplus = ; t t Change in Russian producer surplus = t t Net Change in Russian welfare = 00 < 0. At t = 18 this equals: Change in US producer surplus = t t Change in US consumer surplus = 11t 11t Tax Revenue to US government = 11t t 50 1 Change in US welfare t 5t = 00 > At t = 18 this equals: Overall loss 11t =. At t=18 this equals: Since a US tariff is like a consumption tax and a production subsidy, this is part of a tariff and hence Russian does have a right to object (and is hurt by the policy) e) Would Russian gain by taxing its own oil consumption? Would a consumption subsidy or production tax help Russia? Russia wants to drive up the world price of oil - this means it wants to reduce exports. The best way to do that is through an export tax, which lowers the domestic price. The export tax is like a consumption subsidy and production tax. Hence, a consumption tax for Russia is the opposite of what it should do. If it cannot use an export tariff, and cannot use both a consumption subsidy and production tax, then it could benefit from either a consumption subsidy or a production tax. 4. The purpose of the question is to show that, if there is a domestic distortion, then there is scope for government policy. However, this does not automatically mean trade restrictions. Almost 7

8 always trade policy is not the best policy; and even when only trade policy can be used, the appropriate policy may be to encourage, rather than restrict, trade. Thus, consider a small country (Sweden) with the following supply and demand curves for steel: D = 10,000 p c ; S = 7 p f c f where p is the price consumers pay for steel, and p is the price steel producers receive. Assume the w world price p = 400. Assume production of steel in Sweden generates pollution, which imposes costs of 100 per unit output of steel on Swedes who live near the steel mills. Currently there is no government policy that regulates the pollution emissions or makes firms bear the costs of this pollution. a. Assuming free trade and no domestic taxes or subsidies, find the equilibrium consumption, output and import levels. Is this equilibrium efficient? Explain your answer. Under free trade, with no domestic policy, domestic consumer and producer prices equal the world price, 400. Hence, domestic output is 800 (q ft in Figure ) and domestic consumption is 8800 (d ft in figure ). However, this equilibrium is not efficient since, whereas the supply curve represents the marginal private cost, marginal social cost (MSC) exceeds this by 100 units. Hence, the efficient output level would be where MSC equals the world price, which is shown as point A in figure. Since the optimal policy is to tax firms an amount equal to the pollution damage (100), the price firms receive net of tax should be 00 ( ), and hence the optimal output level is 100. P MSC S G t A B C M 100 H D q* q ft d ft Q Figure 8

9 b. As discussed above, absent government policy, domestic output is too high. In terms of figure the cost of producing the additional quantity ( qq * ft ) domestically is the area of the trapezoid { qagq * ft }, while the cost of importing that quantity would be { qabq * ft }. Hence, the overproduction domestically leads to a deadweight loss of {ABG}. The optimal policy is to tax output at rate 100; this policy would make marginal private costs (including the tax) equal to marginal social costs (which includes pollution costs). No consumption policy is needed since consumption does not create pollution. c. To calculate both the optimal policy and the second-best trade policy calculate the changes in producer surplus, consumer surplus, tax revenue and pollution costs associated with any policy. Let t 400 t. Similarly, let s denote the consumption subsidy, be the tax on output, so producers receive so consumers pay ( 400 s) {note: if s is negative, then it is actually a consumption tax}. Using the supply and demand curves (and the areas next to these curves between any two prices) we have the following: Output with tax in place: Consumption with subsidy in place: Q 400 t = 800 7t D 400 s = s Change in output due to tax: Δ Q= 7t Change in demand due to subsidy: Δ D = s 1. Change in producer surplus due to output tax: PS 7t 400.5t Δ =. Change in consumer surplus due to subsidy: Δ CS = s ( s). Net tax revenue from policies: Δ TR = t Q 400 t s D 400 s = t 800 7t s s 4. Reduction (saving) in Pollution Costs: PC ( Q) Δ = 100 Δ = 700t (note, in figure the change in producer surplus is area {400,B,H,400-t}; and since the picture shows the case where t = s, the change in consumer surplus is area {400,C,M,400-t} To get the change in welfare due to the simultaneous production tax and consumption subsidy add the terms labeled {1,,, 4} above: 5. Δ Welfare = 7t 400.5t + s s + t 800 7t s s + 700t = 700t.5t 1.5s The optimal policy is to choose ts, to maximize this expression. First, note that the term involving s can never be positive; hence, its optimal value is s = 0 - there is no reason to tax or subsidize consumption. d Maximizing equation (5) over t yields: dt proving that a tax of 100 is the optimal policy. ( ΔWelfare) * = 700 7t = 0 t = 100 Given that only trade policy can be used, this implies t = s, i.e., an import subsidy is like a tax on producers and a subsidy to consumers (note that if you want an import tariff, that is equivalent to making t = s < 0 ). Under the restriction s = t : 9

10 6. Δ = = = Welfare s t 700t.5t 1.5t 700t 5t Maximizing (6) over t yields: ( Δ ( = )) ˆ d Welfare s t dt = t = 0 t = 70 Notice that the optimal import subsidy (production tax and consumption subsidy) is less than the optimal production tax alone. This is because while the production tax creates benefits (lowering pollution), the consumption subsidy creates distortions; these side effects imply that the optimal policy will be smaller, once the marginal benefits and marginal costs of the policy are compared. EXTRA CREDIT PROBLEM 5. Same set-up as problem #: US: Demand = 400 us ; Supply = us where us P o is the price of oil in the US; Russia: Demand = 00 R ; Supply 6 R R = where is the price of oil in Russia. The US import demand (M) is given by: M = D S = 400 4P The Russian export supply (X) is given by: X = S R D R = 8P R 00 Russia has an export tariff of, us us us θ US has an import tariff of t. Hence: us R P = P + ( θ + t) a) Using earlier results (since only the sum of the two tariffs matters) you get the equilibrium price and quantity traded as a function of the combined tariff: ( θ) ( θ) M = P + t+ = X = 8P t+ = 1P us R R R R ( t+ θ) ( t+ θ) R us P = 50, P = 50 + us us ( t+ θ ) us us us 8( t+ θ ) D = 400 P = 50 ; S = P = ( t+ θ ); M = 00 R R ( t+ θ ) R R R 8( t+ θ ) D = 00 P = ; S = 6P = 00 ( t+ θ ); X = 00 θ The world price is the price outside both the US and Russia i.e., P w = P us t = P R + θ = 50 + t The US import tariff drives down the world price (helping the importing countries) and the Russian export tariff drives up the world price (helping the exporting countries). The Russian tariff has a bigger impact on the world price than the US tariff because Russian exports supply is more price responsive than US import demand. b) As earlier, US private sector loses due to higher domestic price; calculation is exactly same as earlier, except it depends on the sum of the two tariffs. Similarly, Russian private sector 10

11 loses due to decrease in domestic price; again, it is the same as earlier, except it depends on t + θ, is the sum of the two tariffs. However, the total tariff revenue, which depends on split between the two countries depending on the relative values of t, θ. Thus, from page 5: 1. Russian private loses: ([ t+ θ] ) 00 4[ t+ θ]. US private sector loses: ( [ t+ θ] ) ( 00 4[ t+ θ] ). Total tariff revenue: [ t+ θ] M = [ t+ θ] 00 ( 8[ t+ θ] ) The total tariff revenue is split as follows: 4. US tariff revenue: tm = t 00 ( 8[ t + θ ] ) 5. Russian tariff revenue: θm = θ 00 ( 8[ t+ θ] ) 6. Net Change Russian welfare = Term {5}- Term{1} = 7. Net Change in US welfare = Term {4}-Term{} = 8. Net Change in World Welfare (#6 + #7) = 4( t + θ ) t θ 8t + tθ θ 9 ( θ t) 45 ( θ + 4 tθ t ) From 8, the overall loss only depends on the sum of the tariffs, but the split between the two countries depends on their individual tariffs. Looking back at page 6, you will notice that the overall loss here is the same as in problem, given that the total tariff is the same in the two cases. c) The US chooses t to maximize its welfare (gain), given θ. From (#7): 00 d ( t + θ ) * 75 θ = = 0 t ( θ ) = dt 9 4 ( t θ ) 8 ( t + tθ θ ) Note when θ = 0 this gives you the optimal US tariff from Q#. d) Next, choose the Russian optimal export tariff, θ, given the US tariff, t. From (#6): 00 d dθ 9 ( θ t) 45 ( θ + 4tθ t ) ( θ t) = = * 0 θ = 0.4 Note that, if t=0, then Russia s optimal tariff is larger than the US s optimal tariff. This is because Russia s exports are more sensitive to price than are US imports. Recall that the optimal tariff formula says the magnitude of the optimal tariff is inversely related to the price elasticity of supply (or demand). () t t 11

12 e) Using the results from (c) and (d) and solving simultaneously: ( t θ ) 4 + = 75 10θ + 4t = 00, 5 tˆ = ; ˆ θ = 5 This is the Nash equilibrium for this tariff game. It is possible for both countries to be worse off; we know at least one must be worse off and, if the functions are fairly similar then it is likely that both countries are worse off. Russia s tariff benefits it, but inflicts more damage on the US; the US tariff benefits the US but inflicts more damage on Russia. Together, the two tariffs may (in equilibrium) hurt each country yet neither country has the incentive to unilaterally remove its tariff. f) We can use equations # and #6 above to see the net impact on each country: ( t θ ) 8 ( t tθ θ ) + + Net Change US welfare = = = Net Change Russian welfare = ( θ t) 45 ( θ 4tθ t ) 00( 7.5) + = 9 9 ( + ) since t = 1.5, θ = 5. Note that the overall net loss is = 1875, exactly as predicted by the formula 4( t + θ ). = 65 In this case, the US loses while Russia gains from the tariff since as mentioned previously the greater price sensitivity of Russian exports (compared to US imports) gives Russia more market power. g) Even though Russia gains here (there is no prisoner s dilemma per se), its gain is less than the US loss. Hence, if the two countries could coordinate policies through negotiations, for example the US could bribe Russia so that both parties eliminate tariffs and, with the bribe, both parties are better off. This bribe could be foreign aid, or a reduction in US tariffs on some other good Russia exports, etc. The key point is that without negotiations the two countries (or the many countries in the real world) are unlikely to reach the efficient outcome of free trade. 1