Econ 455 Answers - Problem Set 4. where. ch ch ch ch ch ch ( ) ( ) us us ch ch us ch. (world price). Combining the above two equations implies: 40P

Transcription

1 Fall 011 Eon 455 Harvey Lapan Eon 455 Anwer - roblem et 4 1. Conider the ae of two large ountrie: U: emand = upply = 6 where h China: emand = ; upply = 0 h where (a) Find autarky prie: U: = = 0 = 30 h h h h h h = = = 10 China: ( ) i the prie of lothing in the U; h i the prie of lothing in China; (b) Auming free trade (no tariff), find the equilibrium prie and quantitie traded. h h h World equilibrium require: ( ) + ( ) = = 0 h w Free trade implie: = (world prie). w w Combining the above two equation implie: = 0 = 15 U import = Chinee export = ( ) = = 150 () how how a U import tariff of t affet the volume of trade, prie in China and the U, and U welfare. Who pay for the U tax? Explain. rop the ubript () for lothing; a U import tariff implie: = + t if the produt i to be old in both the U and China. Thi equation, together with the world upply = world demand equation implie: ( ) ( ) h h h h h = t = t 600 = 0 = 15 t 4 = 15 + ( 3t 4) Even though the U impoe the tax, ( 1 4 ) of the tax i paid by Chinee itizen. There i partial inidene of the tax on both U and Chinee individual. To alulate the welfare onequene for the U onider the figure below: h

2 30 15+(3/4)t A A* J F * 15-t/4 3 K L t 40-3t 40 (i)eae the tariff inreae U prie, onumer loe area (15,,*,(15+3t/4) and produer gain area (15,A,A*,15+3t/4). Calulating thee area give: ( ) ( 480 3t Δ C = 3t 4 ) = 180t + ( 9 8) t ; ( ) ( t ) 135t Δ = 3t 4 = + ( 7 16) t On the other hand government tariff revenue i tm = t ( t ), whih i area {K,L,,A}. Hene, the overall welfare impat i: * * Δ W = Area{ J, K, L, F} Area{ A, J, A } Area{, F, } = Retangle 3 Triangle 1 Triangle The lat two area are the familiar loe due to overprodution and underonumption in the U due to the import tariff. What i new i the firt area whih repreent the gain to the U beae China i reeiving a lower prie for lothing i.e., the dereaed prie time the amount imported at that prie i like a tranfer from China to the U. Thi gain to the U i a lo to China a tranfer from China to the U beae China pay part of the U tax. In term of the number given here: ( ) ( ) ( ) ( ) ( ) Δ W = Tariff Revenue +Δ C +Δ = 150t 7.5t 180t t + 135t t = 75t t The U gain from any tariff uh that Δ W > 0 0< t < 8. (ii)for t=6, U prie rie by 4.5, Chinee prie fall by 1.5, U onumer urpl dereae by , U produer urpl inreae by , U import are 105, U tariff revenue i 630 and the hange in U welfare i: Δ W = = Clearly the U gain from thi import tariff. (iii)what would happen if the import tariff of 6 were replaed by an import quota of 105 unit? With an import quota of 105, if it bind, we have:

3 h h h h U: = = 105 = 19.5 China: = = 105 = 13.5 Th, with U import limited to 105, there would be a prie gap of 6 between U and Chinee prie. Whoever had the right to import into the U (the holder of the quota liene) would make exe profit of 6. Th, the only differene between the tariff of 6 and the import quota of 105 i that the government revenue under the tariff beome exe profit for the importer under the quota. If the quota i autioned off, then the two poliie are equivalent. (iv)find the U import tariff that maximize U welfare. From part (i) above we have: Δ W = ( 75t ) ( 75 16) t Maximizing with repet to t: d( ΔW) * = t = 0 t = 4 dt 8 A tated above, free trade i not optimal for the U beae it poliie affet world prie. Th, it ha the ability to at like a monoponit on world market. ut, a with monopony, even though the monoponit an inreae (it own) welfare by retriting purhae, the lo to eller exeed the gain to the buyer there i a deadweight lo. The ame i true of the U import tariff the lo to the Chinee exeed the gain to the U, reating a deadweight lo from the tariff. (d) how how the U tariff affet Chinee welfare. For the Chinee there i no tariff revenue, o the lower world prie they fae reult in lower welfare. reaking it down by produer and onumer: t/4 A 4 3 A* 5 * t 300 5t 300 Impat on China of U import tariff 3

4 The U import tariff ae world prie (and hene Chinee prie) to fall from 15 to 15 ( t 4). Thi ae Chinee onumption to rie, prodution to fall, and export to dereae. The welfare impat on eah group i: t 5t 5t Δ = Area{ 15,, *, ( 15 ( t 4) )} = 300 = 75t { * t 15,,,( 15 ( 4) )} t Δ C = Area A A t = t 15t Δ W =Δ +Δ C = + 16 In term of the figure, the deadweight lo to China i Area{ A *, A,, * } If you ompare the figure for the U and China, you ee that area 3 i a tranfer from China to the U beae of lower export prie, while triangle 1 & for the U, and triangle 4 & 5 for China meaure the overall ineffiieny (or deadweight lo) due to the U poliy. In term of equation: ( ) ( ) ( ) ( ) ( ) ( ) Δ W +Δ W =Δ W = 75t t + 75t t = 15t 4 < 0, t > 0 (e) How doe the tariff affet world welfare? A hown in part (d), it lead to a deline in world welfare beae the volume of trade fall and a wedge i driven between prodution ot in the U and China, and the value to onumer in the two ountrie of lothing. i. Why doen t the U unilaterally eliminate it tariff? The imple point i that what i good for the world a a whole need not be good for the U without ompenation. Th, if the U unilaterally eliminate it tariff, the U loe even though China gain even more. Without ompenation of ome ort, the U will be unwilling to lower tariff. Thi i one reaon why tariff are often redued a a reult of international agreement rather than lowered unilaterally by ountrie (epeially for larger ountrie. maller ountrie, with no ability to affet world prie, do not have the ame inentive to maintain trade barrier). (f) Can China alo gain by ing an export tariff? Explain. Ye, the ame priniple that work for the U work for China a Chinee export tariff would lower prie in China but raie prie China reeive from the U for it export and ome export tariff would benefit China. i. Return to part (ii). uppoe initially the U.. ha an import tariff of t=6 and China ha no export tariff. uppoe the U.. eliminate it import tariff AN China imultaneoly impoe an export tariff of t=6. How would thi affet prodution, onumption and prie in eah ountry? How would it effet the welfare of eah ountry? rodution, onumption and prie would be the ame for eah ountry regardle of whether a U import tariff of 6 or a Chinee export tariff of 6 were ed. The only differene i who get 4

5 the tariff revenue. With the Chinee export tariff the U unambiguoly loe, while China an (and in thi ae doe) gain. From earlier alulation the hange in U welfare auming no tariff revenue i Δ W = = wherea the hange in Chinee welfare, ounting the tariff revenue, when t=6 i: ( ) Δ W =Δ +Δ C + TR= = Th, China gain but world welfare fall. ii. Ue the argument above to argue that both ountrie an gain from their own tariff (but are hurt by the other ountry tariff). I it poible to have an equilibrium where both the U and China have tariff, both are wore off than under free trade and yet neither ountry want to unilaterally eliminate it tariff? Explain (no alulation required). {If thi happen, it i alled a prioner dilemma}. ine U and Chinee tariff have the ame impat on total welfare, it i lear that when both ountrie e tariff world welfare mt fall and hene at leat one ountry mt be wore off. It i poible that one ountry gain in thi trade war but it i alo poible both ountrie loe. Regardle, neither ountry ha the inentive to inilaterally eliminate it tariff.. Free Trade Area. Conider the omputer indtry; Mexio ha following upply and emand: d d = p ; = 6000 p b Mexio an import (idential) omputer from U at p = 600 or from razil at p = 800 Mexio i mall and doe not affet world prie. Mexio i ontemplating an FTA with either the U or razil. a) Iintially, with t = 400 regardle of origin of imported omputer: mex U Mexio import from U; = = 1,000 Hene: mex = p d = 000; = 6000 p d = 4000; M d = = 000 b) Mexio form FTA with U. ine there are no taxe on U omputer, import from U ot Mexian onumer 600, thoe from razil 100. Hene, import ome from U a in (a). d = = 600; m = 100; m = 4800; M m = 3600 Mexian prodution fall, onumption inreae, import inreae. Volume trade inreae by 1600 thi i trade reation. There i no trade diverion ine import ome from U with or without the tariff. Welfare mt rie ee figure below 5

6 1000 A 600 A* H J * Conumer gain: Area {1000,*,,600} = 400*4400 =1,760,000 roduer loe Area {600,A*,A,1000} = 400*1600 =640,000 Government loe tariff revenue = 400*000 = 800,000 (Area A,,H,J) Net Gain = 30,000 Thi net gain i the gain from trade reation (triangle {A*,A,H} and {,*,J} ()If Mexio form the FTA with razil now razilian omputer in Mexio ot 800 (no tariff) while U omputer (till ubjet to the tariff) ot 1,000. Hene, Mexio will import from razil and there will be trade diverion (ee figure below) Mexian prodution fall to 1600, onumption inreae to 4400 and import are 800. Th, there i trade reation (import inreae by 800), but alo trade diverion (import from U fall from 000 to 0). The gain from trade reation are area 1 and in figure below, while the loe from trade diverion are retangle 3 due to the fat that on the 000 unit of import originally from U Mexio i paying razil 800 intead of U 600. Change in C,, tariff revenue and Mexian welfare are: { } { } { } Δ C = Area 1000,, E,800 = 00* 400 = 840, 000 Δ = Area 1000, A,,800 = 00*1800 = 360, 000 Δ Tariff Re v = Area A,, J, H = 400* 000 = 800, 000 Th, overall Mexian welfare fall by -30,000. Gain from trade reation triangle 1 and = = 00*400 / + 00*400 / = 80,000 The lo from trade diverion retangle 3 = 00*,000 = 400,000 Hene, the overall lo i 30,000 (the ame a alulated ing C, and tariff revenue) 6

7 A 1 V W 3 H J E d) If the original tariff had been 600, import from U would ot 100 and import would be 100. If FTA i formed with U, a earlier Mexio mt gain trade reation i larger than with t=400, and there i no trade diverion. If FTA were formed with razil, the loe from trade diverion will be maller than when t=400 (ine there i le trade pre-fta) and the gain from trade reation will be larger o it i poible in thi ae there are gain from forming the FTA with razil. The figure below how what happen with the tariff of 600, and the welfare gain an be alulated a: Δ C = Area{100,, E,800} = 400* 4, 000 = 1, 600, 000 Δ = Area{ 100, A,,800} = 400*, 000 = 800, 000 Δ Tar Rev = 600*100 = 70, 000 o, overall welfare inreae by 80,000 in thi ae. In term of trade reation and trade diverion: Gain trade trade reation = Area triangle 1 & = ( 1 )*400*800 + ( 1 )*400*800 = 30,000 Lo from trade diverion = Area retangle 3 = 00*100 = 40,000 Overall gain i 80,000, ame a above. 7

8 A 1 V W 3 H J E Impat FTA with razil when tariff wa 600 originally. e) General onlion: the larger i trade reation and the maller trade diverion, the more likely the FTA i to inreae welfare. Th, when tariff are initially high (on all ountrie) the FTA i more likely to raie welfare. Alo, the larger the hare of initial trade wa with the other ountrie entering the FTA, the more likely the FTA i to raie welfare (a trade diverion will be maller). 3. Thailand ha following demand and upply urve for teel: upply = = 6 ; emand = i the prie produer (eller) reeive for teel output, i the prie onumer pay for teel, and if there are no dometi taxe or ubidie, then: =. Thailand an trade (import or export) w teel at a given world prie of: = 600. ometi prodution of teel in Thailand reate pollution, whih damage the loal environment. uppoe the etimated (eonomi) ot of thi pollution i 00 per ton of teel produed. Thi mean that the marginal oial ot of produing teel exeed the marginal private ot of produing teel by 00. {ine the upply urve ome from equating marginal private ot to prie, the marginal private ot (MC) of produing teel i: = 6 MC = ( 6) }. Finally, aume the government ha no dometi poliy to redre the externality (pollution). a) The autarky prie of teel in Thailand i 500, o at a world prie of 600 Thailand will export teel. However, thi autarky prie i too low beae it doe not reflet the true oial ot of produing teel in Thailand. To make firm internalize the pollution externality, they hould be ubjet to a tax of 00 per ton of teel. If that were the ae, the upply of teel and autarky prie would be: 8

9 = 6 = 6 00 ;; emand = o autarky prie, with pollution tax, i 6( 00) = = 600 = 60. Th, Thailand hould, on effiieny ground, be importing teel not exporting teel and hene it i poible (likely) that Thailand loe from trade. upply = ( ) i. Calulate the gain (or loe) from trade in thi etting. 800 L M J K MC oial E o, prior to trade and without any pollution poliy, the autarky prie in Thailand i 500, prodution i 3000, the marginal value of another ton of teel to buyer i 500, the private marginal ot to teel firm of prodution teel i 500 UT the oial marginal ot of produing teel due to the olution i 700. Too muh teel i produed and the prie i too low. IF Thailand an buy or ell teel on world market at the prie of 600, Thailand will export teel, onumption fall to 600, prodution inreae to Conumer loe area {600,J,E,500}, produer gain area {600,K,E,500} and pollution ot inreae by 00*inreaed prodution=area {E,M,L,K}. Th the net welfare effet: Δ C = 100*800 = 80,000 Δ = 100*3300 = 330,000 Δ ollutioncot = 00*600 = 10,000 Th, not ounting the pollution ot, welfare inreae by 50,000 but ounting the pollution ot welfare atually fall by 70,000. Thi i beae teel i overprodued relative to the effiient level in autarky, o trade jt woren thi problem. In term of area, the gain to produer exeed the lo to onumer by area of triangle {E,J,K} but pollution ot inreae by trapezoid {L,M,E,K}. In theory, ountry an gain or loe from trade in thi 9

10 example it loe. ii. If the government were to e ome poliy to attak the market failure (the pollution), what poliy hould it e? e a peifi a poible. The optimal poliy would be a tax of 00 on teel prodution o that firm internalize the ot they impoe on oiety. With thi tax, the autarky prie would go to 60, Thailand would import teel and it would definitely gain from trade. iii. If only trade poliy i poible, hould the government tax or ubidize teel export? If only trade poliy i poible, the ountry want to diourage export o it hould tax teel export. Indeed, if feaible, it hould ubidize import. b) uppoe now that the world prie of teel i 400 o that, with no government poliy, the ountry will import teel. I it poible that free trade ould lower dometi welfare in thi ae? Why doe thi ae differ from part (a)? In thi ae, the ountry mt gain from trade. You have the ual gain from trade (for import, inreae in onumer urpl exeed lo in produer urpl). In addition, you have the gain from redued pollution ot. With a world prie of 400: i. Calulate the gain (or loe) from trade in thi etting. MC oial L M 500 E 400 K J ue to trade, dometi prodution fall to 400, onumption inreae to 3400, and 1000 unit are imported. Conumer gain area {500,E,J,400}, produer loe area {500,E,K,400} o the net gain exluding pollution ot i triangle EJK. In addition, ine dometi prodution fall, pollution ot 10

11 fall by area {L,M,K,E}. Numerially: Δ C =+ 100*300 = 30, 000 Δ = 100*700 = 70,000 Re dutionollutioncot = 00* Δ = 00*600 = 10,000 Hene, welfare inreae by 170,000. ii. If the government were to e ome poliy to attak the market failure (the pollution), what poliy hould it e? e a peifi a poible. If any poliy an be ed, then again taxing pollution whih i equivalent to taxing teel output i the optimal poliy (tax of 00 per ton of teel). iii. If only trade poliy i poible, the government want to redue teel prodution, o an import ubidy on teel would be the eond bet poliy. 11