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PS9_Solutions
Course: AEM 4150, Fall 2008School: Cornell
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4150 AEM PRICE ANALYSIS Fall 2008 Problem Set #9 Suggested Solutions 1. Least cost method transfer cost (per unit of product) air truck rail 0 (a) the least cost method: blue lines. Distance (b) No. Because at any distance, air is more expensive than truck or rail. 2. Market boundary. (a) Net price A = 6 - .5Y Net price B = 4 - .6(6 - Y) Equate and solve for Y: 6 - .5Y = 4 - .6(6-Y) 1.1Y = 5.6 Y* = 5.09 Net...
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4150 AEM PRICE ANALYSIS Fall 2008 Problem Set #9 Suggested Solutions 1. Least cost method transfer cost (per unit of product) air
truck rail
0 (a) the least cost method: blue lines.
Distance
(b) No. Because at any distance, air is more expensive than truck or rail. 2. Market boundary. (a) Net price A = 6 - .5Y Net price B = 4 - .6(6 - Y) Equate and solve for Y: 6 - .5Y = 4 - .6(6-Y) 1.1Y = 5.6 Y* = 5.09 Net price at the boundary = 6 - .5 Y* = 4 - .6 (6-Y*) = 6-.5*5.09 = $3.45 New market boundary = 509 miles from A, and P = $3.45 (b)
1
Market A new market boundary
Market B
$6 $4 $2 $.4 A 600 100 500 200 400
old market boundary
$6 $5 $3
300 300
400 200
500 100
600 B
Distance from market
(c) See the yellow curve above. 3. Spatial equilibrium model and international trade Under free trade, algebraic solution for the initial trade equilibrium: United States Qsus = 50P Qdus = 3000 200P EDus = Qdus Qsus = 3000 200P 50P = 3000 250P Initial trade equilibrium: EDus = 3000 250P = 4500 = Pw = Qt = US supply: Qsus = 50(Pw) = 50(10) = 500 Conclusion: EScn 200P - 1500 450P 10 500 US demand: Qdus = 3000 200(10) = 1000 China Qscn = 100P Qdcn = 1500 100P EScn = Qscn - Qdcn = 100P (1500 100P) = 200P - 1500
World Free Market
Quantity trade 500 World Price 10
United States
Domestic Price 10 Qs 500 Qd 1000
2
And US will import 500 units of toys from China. i) Export subsidy>subsidy on seller, ES shifts down by the subsidy. New ES: P = 7.5 + Q/200 - 1 = 6.5+Q/200 ED: P = 12-Q/250 Let ED=ES, then Q*=611.1 This is the quantity of trade P* = 6.5+611.1/200=9.556 This is the buyers price Seller receive P* plus the subsidy. Sellers price = 10.556 China: Qs= 100*seller P=100*10.556=1055.6 Qd=1500-100*seller P = 1500-100*10.556=444.4 EXP=Qs-Qd=1056-444=611.1. EXP increased compared with the free trade case. U.S. : Qs= 50*buyer P=50*9.556=477.8 Qd=3000-200*buyer P=3000-200*9.556=1088.8 IMP=Qd-Qs=1088.8-477.8=611.1
ii) Export tax>tax on seller, ES shifts up by the tax. New ES: P = 7.5 + Q/200 + 1 = 8.5+Q/200 ED: P = 12-Q/250 Let ED=ES, then Q*=388.9 This is the quantity of trade P* = 8.5+388.9/200=10.44 This is the buyers price Seller receive P* net of the $1 tax. Sellers price = 9.44 China: Qs= 100*seller P=100*9.44=944 Qd=1500-100*seller P = 1500-100*9.44=556 EXP=Qs-Qd=944-556=388.9 EXP decreased compared with the free trade case. U.S. : Qs= 50*buyer P=50*10.44=522 Qd=3000-200*buyer P=3000-200*10.44=912 IMP=Qd-Qs=912-522=388.9
3
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