Spring 000 Eon 455 Harvey Lapan Eon 455 Answers - Problem Set 4 1. Consider a small ountry (Belgium) with the following demand and supply urves for loth: Supply = 3P ; Demand = 60 3P Assume Belgium an import loth at a given world prie of: P = 5. Further, assume that Belgium imposes a tariff of t per unit of import. a) Show how: domesti prie, onsumption and prodution hange as t inreases. Also, alulate how onsumer surpl, produer surpl, and government tariff revenue hange as t inreases. d Given the world prie, domesti prie in Belgian is given by: P = 5+ t, if t 5. Note that for t > 5 the tariff is prohibitive, there are no imports, and the domesti prie equals the autarky prie of 10. Th, assuming t < 5, we have: P d = 5 + t ; D= 60 3P d = 45 3; t S= 3P d = 15+ 3; t M = D S = 30 6t ( ) Clearly, onsumption and imports fall, and prodution rises, as t inreases. The hanges in onsumer and produer surpl an be seen from the diagram on the next page. The hange in produer surpl is given by the area {5,A*,A,(5+t)}, whereas the hange in onsumer surpl is given by: {5,B*,B,(5+t)}. Th: 1 3 1 3 TR= tm = t 30 6t = 30t 6t is tariff revenue. PS = t ( 15+ 15+ ) = 15 t+ t ; CS= t ( 45+ 45 ) = 45t+ t ( ) Th, it is easily seen that produer surpl inreases with the tariff, and onsumer surpl dereases (for 5 t 5 ), where tariff revenue inreases with the tariff for t, and then dereases thereafter. Overall: Welfare= TR+ PS+ CS= so that the tariff lowers overall welfare. b) Compare the domesti equilibrium when t= to the ase where there is no tariff, but there is an import quota of 18 units. From part (a), with t=, imports M = 30 6t = 18. Th, a quota of 18 and a tariff of have idential effets on domesti prie, onsumption, prodution and imports. The only possible differene is the tariff revenue (whih is 36 under the tariff). Under the quota, importers make on eah unit imported and hene will earn exess profits of 36, unless the quota lienses are autioned off, in whih ase the two poliies are (an be) idential.
P S 10 5+t A B 5 A* E F B* D 15 15+ 45-45 Q Figure 1. Next, onsider the ase of two large ountries: US: Demand = 90 ; Supply = P China: Demand = 30 ; Supply = where P P P where P is the prie of loth in US; P is the prie of loth in Korea; (Note that I have hanged the demand and supply for China from the problem set so that the export supply is unhanged. The problem with the original funtions: D= 30 P, S= P is that it implied negative onsumption under free trade, whih is not sensible. The mehanis of the problem do not hange at all. Sorry!!) a) Assuming free trade (no tariffs), find the equilibrium prie and quantities traded. The US import demand (M) is given by: M = D S = 90 3P The Chinese export supply is given by: X = S D = 3P 30 where P is the prie in China and P is the prie in the US. Note that under autarky the US prie is 30, and the Chinese prie is 10 (see the following figure), sine imports (and exports) will be zero under these f pries. Under free trade we have: P = P = P (f stands for free trade) and th: f f f M = X 90 3P = 3P 30 P = 0 Th, exports (imports) equal 30 under free trade. Domesti onsumption and supply is found by substituting bak into the demand and supply urves. For the US and China, under free trade:
f f US: D = 90 P = 50; S = P = 0 ; China: D = 30 P f = 10; S= P f = 40 b) Show how a US import tariff of $t affets equilibrium pries. The equilibrium onditions above are modified by: P = P + t. Th, equilibrium requires: t t M = 90 3( P + t) = X = 3P 30 10 = 6P P = 0, P = 0 + Th, as the tariff inreases, US pries inrease and Chinese pries fall (see the figure). P 30 0+.5t A China X 0 E F 0-.5t B 10 US M 30-(1.5)t 30 Q Figure (i) How does the tariff affet China s welfare (sum of onsumer and produer surpl)? Clearly China, due to lower export pries (and no tariff revenue) is hurt. The total loss in China is the area {0,E,B,[0-.5t]}; the US private setor loses area {0,E,A,[0+.5t]}, while the US government gains the tariff revenue, measured by area: {[0-.5t, B,A,[0+.5t]}. Th: China loses: 15t US private setor loses: 15t 3
US government tariff revenue = Net US gain = 30t 30t 15t = 15t > 0 if t < 3 9t 40 9 3 3 Overall welfare hange = Net US gain pl Chinese loss = 15t t 15t t = t < 0 4 So, even if the US gains from the tariff, it gains less than China loses, so there is an overall ineffiieny due to the tariff. In terms of the figure, the ineffiieny (deadweight loss) is the triangle: {A,B,E}. Finally, to alulate the hanges in onsumer and produer surpl for China (and the US) you mt go bak to the demand and supply urves (not jt the export supply or import demand urves). While the figures are not drawn, the method of finding the surpl is the same as above. Hene: For China: 1 ( )( 0 1) 1 t 10 10 t CS P D D 5t t = + = + + = + 1 1 t t PS= ( P)( S0+ S1 ) = ( 40+ [ 40 t] ) = 0t + 4 Net Change in Chinese welfare= PS+ CS= 15t (ii)the impat on US welfare, summarized above is given by: 1 1 t t CS= ( P)( D0+ D1 ) = ( 50+ [ 50 t] ) = 5t 4 1 ( )( 0 1) 1 t 0 0 t PS P S S 10t t = + = + + = + Change Private Setor Welfare (US) = Tariff Revenue = Net US gain = 30t CS+ PS= 15t, as above 30t 15t = 15t > 0 if t < 3 9t 40 The US an gain from this tariff beae it affets world prie; speifially, by restriting imports the tariff lowers the world prie of US imports (even though domesti prie rises). This hange in world prie has a positive effet on the US eonomy (and a negative effet on the Chinese eonomy), and th 4
from the US perspetive the improved terms of trade may offset the ineffiieny the tariff aes. However, overall world welfare (sum of US and Chinese surpl) mt fall. Th: Net US gain + Net Chinese gain = 9 3 3 15t t 15t t = t < 0, as explained earlier. 4 (iii)if the U.S. eliminates its import tariff, but China imposes an export tariff of the same magnitude, the private setor losses are as above, but the tariff revenue is transferred to China. Th, the US would lose area {0,E,A,[0+.5t]}, while China would gain {0,F,A,[0+.5t]}, while losing {B,F,E} for the same world loss of {A,B,E}. Numerially: Net Gain to China = Net Gain to US = 9t 15t + 30t = 15t 15t < 0 3. The purpose of the question is to show that, if the goal is to inrease domesti prodution, prodution subsidies are more effetive (less ostly) than tariffs. To illtrate this, e the model of problem 1, and assume the government s goal is to inrease prodution to 4 units.. a) To inrease domesti prodution to 4 with a tariff requires a domesti prie of 8, hene a tariff of 3. Using the results from Problem 1, domesti onsumption falls to 36. The welfare impat (t=3) are: 3 117 3 43 PS= 15 t+ t = ; CS= 45t+ t = ; TR= 30t 6t = 36 Net Welfare Change = -7 b) With a prodution subsidy of 3, the onsumer prie remains at 5 (the world prie) and onsumers are unaffeted. The prie reeived by produers inreases to 8, so the hange in produer surpl is the same as (a). However, instead of tariff revenue there is the ost to taxpayers of the subsidy. Hene, with a prodution subsidy: 3 117 PS= 15 t+ t = ; Tax Revenue = ( ) 3 4 = 7 ; Net Welfare Change = 7 ) Clearly, the prodution subsidy is more effiient sine it does not involve a loss to onsumers (in terms of Figure 1, the inrease in produer surpl is area {5,A*,A,[5+t]}, and the ost of the subsidy is {5,E,A,[5+t]}, so the deadweight loss is area {A*,E,A}. With the tariff there is the additional deadweight loss of {B,B*,F}, due to the hange in onsumption. 5
4. Consider a small ountry in whih domesti prodution aes an externality (pollution) that damages soiety. Without appropriate government poliy (a pollution, or prodution, tax), the firm produes too muh (sine it does not ount these pollution damages in its deision proess). We look at different poliies in that setting. Domesti demand and supply for steel are given by: S= 15 P; D= 00 5P w The (onstant) world prie is P = 0. The pollution from domesti steel prodution entails a marginal soial ost of 5 per unit. Foreign produed steel does no (pollution) damage to the domesti eonomy. (a) First, find the free trade equilibrium pries, prodution, onsumption, exports, onsumer and produer surpl, and the pollution damages. d w Under free trade, the domesti prie equals the world prie: P = P = 0. Th, domesti onsumption is 100, domesti prodution is 300, and exports are 00 (see figure below). From the figure, onsumer surpl is the area next to the demand urve (the triangle {40,A,0} and produer surpl is the area next to the supply urve (triangle {0,B,0}). However, the produer surpl does not ount the pollution damages due to steel prodution. Th, these measures are: 1 0100 1,000 Pollution Costs = 5 300= 1,500 Total Surpl = 1,000+ 3,000 1,500=,500 1 0300 3,000 = Consumer Surpl = ( ) = ; Produer Surpl = ( ) P 40 D MSC 0 A C B S 15 G E 0 100 15 5 300 Q Figure 3 6
(b) A tax (t) on domesti prodution of 5 ( t = 5 ) will not affet onsumers but will affet domesti prodution, and hene exports. In terms of the figure above, the tax lowers the net of tax prie produers reeive to 15, and hene lowers output to 5 (see point E in figure). Another way to view this is as shifting the tax-inlive supply urve up by 5 (to the dotted line labelled MSC, marginal soial ost). The overall impat: Output = 5, Consumption = 100 (unhanged), Exports = 15 Total Consumer Surpl (unhanged) = 1,000 Total Produer Surpl = Area {0,E,15} = 1,687.5 (dereases by: 1,31.5) Pollution Cost = 5*(5)=1,15 (pollution redution, or saving, of 375) Tax Revenue=5*(5)=1,15 (inrease of 1,15) Total Surpl=CS+PS+TR-Pollution Cost =,687.5 (inrease of 187.5) Th, the pollution tax raises welfare by foring firms to reognize the ost of their pollution (hene, reduing output and pollution). () If only a tariff an be ed, then this export tariff will redue domesti prodution (as for the prodution tax), but it will also hange (inrease) onsumption. This reates a welfare loss ompared to the prodution tax (th, the tariff is not as effetive as the prodution/pollution tax and, if you have to e a tariff, the optimal tariff would be less than 5). With the export tariff of 5, the domesti prie (for both produers and onsumers) is 15. Also: Output = 5; Consumption = 15 (inreased ompared to b); Exports = 100 (dereased ompared to b). Total Consumer Surpl=Area {40,G,15} = 1,56.5 (inreased ompared to b) Total Produer Surpl = 1,687.5 (same as b) Pollution ost (PC) = 1,15 (same as b beae prodution is same) Tariff Revenue (TR) = 500 (5*100) Total Surpl = CS+PS+TR-PC =,65 Notie that total welfare is higher here than in part (a), but lower than in part (b), indiating that beae of the domesti market failure (pollution), an export tariff is better than doing nothing, but the better (best) poliy is to tax pollution (prodution), rather than ing an export tariff. As I said earlier, if you have to e an export tariff, the optimal tariff would be less than 5. 7