Econ 455 Answers - Problem Set 4. P is the price of oil in the US; = where is the price of oil in Saudi Arabia.

Transcription

1 Fall 010 Econ 455 Harvey Lapan Econ 455 Answers - Problem et 4 1. Consier the case of two large countries: U: eman = ; upply 7 where P o = P o o P is the price of oil in the U; A: eman = A ; upply 1 A A = where is the price of oil in aui Arabia. P o P o P o (a) Fin autarky prices: U: = 10Po 000 = 0 Po = 00 A A A A A A 1 aui Arabia: = 1P o ( 500 3P o ) = 15Po 500 Po = 33 3 (b) Assuming free trae (no tariffs), fin the equilibrium price an quantities trae. A A A + = P + P = Worl equilibrium requires: ( ) ( ) A w o P o Free trae implies: Po = P (worl price). w w Combining the above two equations implies: 5Po 500 = 0 Po = 100 U imports = aui Arabian exports = A A = P A = o ( ) (c) how how a U import tariff of t affects the volume of trae, prices in aui Arabia an the U, an U welfare. Who pays for the U import tax? Explain. rop the subscript (o) for oil, for simplicity; the U import tariff implies: P = P + t if the prouct is to be sol in both the U an aui Arabia. This equation, together with the worl supply = worl eman equation implies: ( ) 10 10P + 15P A 500 = 10 P A + t + 15P A 500 = 0 P A = 100 t = 100 t 5 5 P = ( 3t 5) Th, even though the U imposes the tax, only ( 35 ) is pai by U citizens while ( 5 ) is pai by aui Arabian citizens. There is partial incience of the tax. To calculate the welfare consequences for the U consier the figure below: o o A

2 P (3/5)t A B (/5)t 1 4 A* J B* 3 K E F t t 1700 Q Impact of Tariff on U (i)becae the tariff increases U price, consumers lose area {100,B*,B,( t)} an proucers gain area (100,A*,A, t). Calculating these areas gives: ( ) ( t ) Δ C =.6t = ( 100 t.54t ); ( ) ( t ) Δ P = 3t 5 = ( 40t + 1.6t ) On the other han government tariff revenue is tm = t ( t ), which is area {E,A,B,F}. Hence, the overall welfare impact is: * * Δ W = Area{ E, J, K, F} Area{ A, J, A } Area{ B, K, B } = Rectangle 3 Triangle 1 Triangle The last two areas are the familiar losses ue to unerconsumption an overprouction in the U ue to the import tariff. What is new is the first area which represents the gains to the U becae aui Arabia is receiving a lower price from the U for oil i.e., the ecrease price times the amount importe at that price. This gain to the U is a loss to aui Arabia a transfer from aui Arabia to the U becae aui Arabia pays part of the U tax. In terms of the numbers given here: ( ) ( ) ( ) Δ W = Tariff Revenue +Δ C +Δ P = t t + 40t + 1.6t 100 t.54t = 400t 4.t The U gains from any tariff such that W t ( ) Δ > 0 0 < < 400 / (ii)for t=40, U price rises by 4, aui Arabian price falls by 16, U consumer surpl ecreases by 39,906, U proucer surpl increases by 18,816, U imports are 760, U tariff revenue is 30,400 an the change in U welfare is: Δ W = 30,400 39, ,816 = 9,80. Clearly the U gains from the import tariff.

3 (iii)what woul happen if the import tariff of 40 were replace by an import quota of 760 units? With an import quota of 760, since it bins (free trae imports are 1000), we have: U: = P = 760 P = 14; aui Arabia: A A = 15P A 500 = 760 P A = 84 Th, with U imports limite, there woul be a price gap of 40 between U an aui Arabian prices. Whoever ha the right to import into the U (the holers of the quota licenses) woul make excess profits of 40. Th, the only ifference between the tariff of 40 an the import quota of 760 is that the government revenue uner the tariff becomes excess profits for the importers uner the quota. If the quotas are auctione off, then the two policies are equivalent. (iv)fin the U import tariff that maximizes U welfare. From part (i) above we have: Δ W = 400t 4.t Maximizing with respect to t: ( ΔW) * 400 = t = 0 t = 47.6 t 8.4 As state above, free trae is not optimal for the U becae its policies affect worl price. Th, it has the ability to act like a monopsonist on worl markets. But, as with monopsony, even though the monopsonist can increase (its own) profits by restricting purchases, the loss to sellers (i.e., aui Arabia) excees the gains to the firm there is a eaweight loss. The same is true of the U import tariff the loss to the auis excees the gains to the U, creating a eaweight loss from the tariff. () how how the U tariff affects aui Arabian welfare, The U import tariff caes worl price (an hence aui price) to ecrease from 100 to 100 ( 5) t. This caes aui consumption to rise, prouction to fall, an exports to ecrease. The welfare impact is (see figure below) { 100,, *, ( )} { } 100,, *, ( ) 80.4 Δ P = Area B B t = t t { } { } Δ C = Area A A t = t + t A Δ W =Δ P +Δ C = 400t+ 1.t * * In terms of the figure below, the eaweight loss to aui Arabia is {,,, } triangle 4 + triangle 5. Area A A B B = Rectangle 3 + If you compare the figures for the U an aui Arabia, you see that area 3 is a transfer from aui Arabia to the U becae of lower export prices, while triangles 1 & for the U, an triangles 4 & 5 for aui Arabia measure the overall inefficiency (or eaweight loss) ue to the U policy. In terms of equations: A ( ) ( ) Δ W +Δ W =Δ W = 400t 4.t + 400t+ 1.t = 3t < 0, t 0 3

4 t A L A* M B* B 33 1/ t t 100 Impact on aui Arabia of U import tariff i. A aui export tariff, by lowering omestic prices in aui Arabia, woul reuce the supply of exports an th raise the worl price of oil. Th, jt as the U gains from an import tariff, aui Arabia can gain from an export tariff. But note that, in each case, the benefits to the winner are smaller than the losses to the loser. Hence, it is possible that each country tries to act as a monopolist (a monopsonist in the case of the U.., since it is a buyer), but by oing so both countries are worse off. However, neither country has the incentive to unilaterally en its tariff. (e) How oes the tariff affect worl welfare? As shown in part (), it leas to a ecline in worl welfare becae the volume of trae falls an a wege is riven between prouction costs in the two countries, an also a wege is riven between the value of oil to consumers in the two countries. i. Why oesn t the U unilaterally eliminate its tariff? The simple point is that what is goo for the worl as a whole nee not be goo for the U without compensation. Th, if the U unilaterally eliminates its tariff, the U loses even though aui Arabia gains even more. Without compensation of some sort, the U will be unwilling to lower tariffs. This is one reason why tariffs are often reuce as a result of international agreements rather than lowere unilaterally by countries (especially for larger countries. maller countries, with no ability to affect worl prices, o not have the same incentive to maintain trae barriers).. Free Trae Area. Consier the computer intry; Mexico has following upply an eman: = p ; = p J Mexico can import (ientical) computers from the U at p = 1000 or from Japan at p = 800 4

5 Mexico is small an oes not affect worl prices. a) Iintially, with t = 300 regarless of origin of importe computers: mex J Mexico imports from Japan; P = P = 1,100 mex Hence: Q = p = 1100; = p = 3700; M = = 600 b) Mexico forms FTA with U. ince there are no taxes on U computers, imports from U cost Mexican consumer 1000, those from Japan Hence, imports come from U. P = P = 1000; m = 1000; m = 4000; M m = 3000 Mexican prouction falls, consumption increases, imports increase. The volume of trae increases by 400 (from 600 to 3000) this is trae creation; but all imports come from U rather than Japan this is trae iversion. To see the welfare impact, consier this figure: P 1100 A B 1000 A* V W B* 800 H J Q Consumers gain: Area {1000,B*,B,1100} = 100*3850 =385,000 Proucers lose Area {1000,A*,A,1100} = 100*1050 =105,000 Government loses tariff revenue = 300*600 = 780,000 (Area ABHJ) Net Loss = 500,000 This net loss is the gain from trae creation (triangles {A*,A,V} an {B,B*,W}) min the loss ue to trae iversion (area {V,W,H,J}) - which reflects the higher costs pai for the original level of imports (600 units) from the U rather than from Japan. (c)if the tariff were originally $600 per unit (instea of $300 per unit), then before the FTA the price of Japanese imports in Mexico woul be $1400, an all imports woul come from Japan. o: 5

6 mex Pre-FTA: P = 1400; Q = 1400; = 800 ; Imports =1400 ; Tariff revenue = 840,000 (see figure below) After the FTA, the tariff on U goos is eliminate an imports come from U. The post-fta situation is the same as in (b): mex Post-FTA P = 1000; Q = 1000; = 4000 ; Imports = 3000 Th, the amount of trae creation is larger than in (b), an the amount of trae iversion is smaller. Hence, the net loss shoul be smaller (or the net gain larger). To measure it, see figure below: Consumers gain: Area {1000,B*,T,1400} = 1,360,000 Proucers lose: Area {1000,A*,,1400} = 480,000 Government loses tariff revenue = 840,000 (Area TLM) Net welfare gain = 40,000 This welfare gain equals the gains from trae creation (the triangles {A*,,J} an {K,T,B*}) less the loss from trae iversion (area {J,K,M,L}) ue to the fact higher price imports from the U replace imports from Japan. P 1400 T 1000 A* J K B* 800 L M Q o, joining the FTA benefits Mexico in case (c), but not in (b). Explanation: trae creation in (c) is larger as imports increase from 1400 to 3000, whereas in (b) imports increase only by 400. In both cases trae iversion occurs, as imports from Japan that previoly cost $800 to the country (remember the tariff revenue goes to the Mexican government) are iverte to imports from the U, which cost $1000. This trae iversion is larger in (b), where imports are originally,600 becae of the lower tariffs, than in (c), where imports are only Moral: even if lowering all tariffs is goo, it oes not automatically follow that lowering some tariffs will improve welfare. 6

7 3. Consier a small country (Thailan) with the following eman an supply curves for steel: s s upply = Q = 6P s ; eman = P c s s c Note that P s is the price proucers (sellers) receive for steel output, P s is the price consumers pay for c s steel, an if there are no omestic taxes or subsiies, then: Ps = Ps. Assume Thailan can import steel at a given worl price of: P s = 00 per ton of steel. uppose that the omestic prouction of steel in Thailan creates pollution, which amages the environment. uppose the estimate (economic) cost of this pollution is 100 per ton of steel prouce. This means that the marginal social cost of proucing steel excees the marginal private cost of proucing steel by 100. {ince the supply curve comes from equating marginal private cost to price, the s s s marginal private cost (MPC) of proucing steel is: Q = 6P s MPC = ( Q 6) }. Finally, assume the government has no omestic policy to reress the externality (pollution). a) uppose worl price is 00. ince this is below the omestic autarky price, that means the country will import steel. There are the ual gains from trae (increase consumption becae, starting from autarky, the value of steel excees the worl price; the gains from ecrease prouction, becae private prouction costs excee worl price) an, in aition, there is the gain from the fact that the presence of pollution for which there was no government policy means that steel is overprouce omestically in autarky, an that reuce prouction reuces pollution amages. Th, in this case, trae will be beneficial. i. Calculate the gains or losses from trae in this setting. P 600 G MC R 500 E A 1 00 A H K Q 7

8 The figure above shows the eman curve, the supply curve (marginal private cost) an the marginal social cost curve (MC), which lies 100 units above the supply curve becae of the pollution costs. The autarky equilibrium is at E, with a price of 500, an output/consumption of This is not efficient becae, at that output level, marginal social cost (point G) lies above the marginal value of the aitional unit of output. Uner autarky, the efficient equilibrium is at R, with a higher price an lower prouction/consumption. tarting from E (no pollution tax), the movement from autarky to free trae at a price of 00 reuces omestic price an prouction, while increasing consumption. Consumers gain area: {500,E,K,00} Proucers lose area: {500,E,A,00} o, ignoring pollution, the gains by moving to free trae is the triangular area AEK, compose of the smaller triangles labele 1 an. This is the ual argument of the gains from trae. However, becae of pollution, the lower output reuces pollution costs by 100*reuce output; this reuction in pollution costs is given by area of parellelogram {A,A,G,E}. Hence, the total gains from free trae are area {EHK} or triangle the gain ue to increase consumption; pl area {A,A,G,H} the gains ue to reuce prouction (i.e., it is the savings in social cost the area uner the MC curve between 100 an 3000, less the cost of importing this quantity area of rectangle {100,A,H,3000}. The gains from trae are larger than in the case where there are no externalities. Calculating the gains: Δ C = ( 1 ) i300i[ ] = 1, 080, 000 Δ P = ( 1 ) i300i[ ] = 630, 000 Reuction in pollution costs: 100* ( Δ Q) = 100*1800 = 180,000 Total Welfare Gain= 1,080, , ,000=630,000 ii. iii. The best policy to attack the market failure is to internalize the externality i.e., make firms take in to account the costs they impose on others. This means taxing their output base on pollution emissions (an amages one), or for this specific case a 100 tax on steel output. What to o if only trae policy can be e? In this case, since the problem is firms prouce too much (even at the lower worl price, the marginal social cost of proucing steel is above the cost of getting steel from the worl market), then the optimal policy is to subsiize imports, reucing omestic price, th omestic output an pollution. {You o not have to o a calculation here but I will}. If the subsiy is s, then omestic price is (00-s), omestic prouction is 6P =100-6s; omestic consumtion is P = 400+4s, an imports are s. The changes in surpl are an in pollution costs ue to the subsiy (as compare to free trae) 1 Δ P = ( s) + + ( s) = s + s ( ) ( ) ( ) Δ C = s s = 400s + s 8

9 ( ) ( )( ) ( ) ( ) TR = s M = s + s = s s ReuctionPollutionCost = 100 Δ Q = 100 6s = 600s Th, the overall welfare change is: is tariff revenue (which is negative) Δ W =Δ C +Δ P + TR ReuctionPollutionCost = 5s + 600s W * s 0 s 60 s = = = o, the secon best policy is an import subsiy that reuces omestic price to 140 an lowers omestic output. The best solution is a tax of 100 on steel output (or pollution). b) If the worl price is 550, above the autarky price (without a pollution tax), the country will export, rather than import, steel an th trae will increase omestic prouction an pollution. Hence, it is quite possible that for this case trae reuces welfare. First, note that while the autarky price is 500, the efficient autarky price (point R in the figure) is foun from imposing a tax of 100 on prouction c c c c s c = 6 P 100 = P 10P = 560 P = 560; P = P 100 = 460 so: ( ) Th, if a pollution tax were impose on firms, the country shoul import, rather than export, steel. P MC J K R A E B 100 Q i. ue to trae, omestic price increases from 500 to 550, omestic consumption falls from 3000 to 800, an omestic prouction increases from 3000 to The welfare effects are as follows: 9

10 Δ C = area{500, E, A,550} = 145, 000 Δ P =+ area{500, E, B,550} =+ 157,500 Increase Pollution Costs = 100*300 =+ 30,000 Δ Welfare = 145, ,500 30, 000 = 17,500 Th, trae lowers welfare. Overall, the gain is area {A,E,B} less area {E,J,K,B} ii. iii. As in part (a), since the market failure is that marginal private prouction costs are lower than marginal social costs, the optimal policy is to tax pollution, which in this case is synonymo with a tax of 100 on prouction of steel. If that were one the autarky price woul be 560, an the country woul uner free trae impoprt steel rather than export steel. If only trae policy is possible, then the goal of the policy woul be to reuce omestic prouction below that which woul occur uner free trae. ince, uner free trae without pollution taxes, the country woul export steel while uner the optimal policy it woul import steel clearly banning steel exports is esirable. Furthermore, if feasible, it is actually optimal to import some steel, which woul of course require significant import subsiies. You are not expecte to calculate that subsiy, but you coul in the following way. We can express proucer surpl, consumer surpl an pollution costs as a function of the omestic price. ince we can also calculate prouction an eman, we can etermine imports as a function of the omestic price. Having one that, we can calculate the government tax revenue or cost as a function of the omestic price, an ing all these terms we can calculate the optimal omestic price. From the eman an supply curves: (C) Consumer urpl = (P) Proucer urpl = ( ) ( P ) 150 P 3 Pollution Costs = 6P z; Imports = P z = 100 (exports, if negative) (GR) Govt. Revenue (costs, if negative) P P Q = P P Welfare = C +P Pollution Cost + GR: W = 150 W P = ( P ) + 3 ( P ) + ( )( ) ( w )( ) ( )( ) P P 6zP ( ) + 6 ( ) ( ) ( P P + P 10 P 550 6z = P 6z Note if z = 0 (no pollution) free trae is optimal i.e., P = P = 550. For z=100 w ) 10

11 W P = P = 0 P = 490. Th, for this case, the optimal trae policy given that ( w ) no other policy is feasible is a ban on exports AN an import subsiy of 60 = P 490. Note that you mt have the export ban otherwise people will buy at 490 on the omestic market an resell internationally. If you can t have an import subsiy, then you shoul jt ban exports. 11