National accounts: value of inputs Col equals value of output Sum(BAS1)+ Sum(MARI)+ Sum(TAx1)+ Sum(laboCCIND)+ Sum( CaPItaL Sum(BasI)+Sum (BAS2)+Sum(BAS3)+Sum(BAS4)+Sum(BASS) Sum MARI+Sum (Mar2)+Sum MAR3)+Sum(MAr4)+Sum(MAR5) Sum( BASI(imp))+ Sum (BAS2(imp)) Sum (bas3(imp))+ Sum(basS(imp))l Simplifying Sum(BASI)+SumMMARI)+Sum(TAX1)+ Sum(LABOCCIND)+ Sum (CAPItAl) Sum(BAS1)+Sum(BAS2)+Sum(BAS3)+Sum (BAS4)+ Sum (BASS) SumMMARI)+Sum(MAR2)+Sum(MAR3)+Sum(MAR4)+Sum(MAR5 Sum( BaSI(imp))+ Sum(Base(imp)) Sum(baS3(imp))+ Sum(BasS(imp)
6 National accounts: value of inputs CoPS equals value of output Sum(BAS1) + Sum(MAR1) + Sum(TAX1) + Sum(LABOCCIND) + Sum(CAPITAL) = Sum(BAS1)+Sum(BAS2)+Sum(BAS3)+Sum(BAS4)+Sum(BAS5) + Sum(MAR1)+Sum(MAR2)+Sum(MAR3)+Sum(MAR4)+Sum(MAR5) - [Sum( BAS1(imp)) + Sum(BAS2(imp)) + Sum(BAS3(imp)) + Sum(BAS5(imp))] Sum(BAS1) + Sum(MAR1) + Sum(TAX1) + Sum(LABOCCIND) + Sum(CAPITAL) = Sum(BAS1)+Sum(BAS2)+Sum(BAS3)+Sum(BAS4)+Sum(BAS5) + Sum(MAR1)+Sum(MAR2)+Sum(MAR3)+Sum(MAR4)+Sum(MAR5) - [Sum( BAS1(imp)) + Sum(BAS2(imp)) + Sum(BAS3(imp)) + Sum(BAS5(imp))] Simplifying:
Income and expenditure measures of GDP CoPS Sum(LABOCCIND)+ Sum(CAPITAL)+ Sum TAXl) Sum(tarIFF)+ ∑ Sum(TAXo Sum(BaS2)+ Sum (MAR2)+ Sum(TAX2) Sum(baS3)+ Sum MAR3)+ Sum(TAX3) Sum(baS4)+ Sum (MAR4)+ Sum(TAX4) Sum(Bass)+ Sum(MAr5)+ Sum(TAX5) [2 Sum(BASO(imp))-Sum(TARIFF)I 7
7 CoPS Income and expenditure measures of GDP Sum(LABOCCIND) + Sum(CAPITAL) + Sum(TAX1) + Sum(TARIFF)+ 5 =2 Sum(TAX) = Sum(BAS2) + Sum(MAR2) + Sum (TAX2) + Sum(BAS3) + Sum(MAR3) + Sum(TAX3) + Sum(BAS4) + Sum(MAR4) + Sum(TAX4) + Sum(BAS5) + Sum(MAR5) + Sum(TAX5) - [ = 3,5 1 Sum(BAS(imp)) - Sum(TARIFF)]
One-country input-output model CoPs ∑ Output ofi= intermediate demand final demand A*X t Y XXX where B=(I-A) Properties of B Biji is the amount of i that must be produced to supply final demand with an extra unit of i, holding all other final demands constant B:≥0,B:≥ for all i and j 8
8 One CoPS -country input-output model 1 2 i ij j i j X a X Y , i , ,...,n = + = Output of i = intermediate demand + final demand X A* X Y = + ( ) 1 X I A * Y − = − X B*Y = where 1 B (I A)− = − Properties of B Bij is the amount of i that must be produced to supply final demand with an extra unit of j, holding all other final demands constant 0 1 B , B for all i and j ij ii
Leontief paradox CoP Labor content in U.S. exports LiE=l′*B*E Capital content in U.S. exports: KinE=kbe Labor content in U.S. imports LinM=1′兴BM Capital content in U.S. imports: KinM=kB*M where I and k' show labor and capital input per unit of output in each U.S. industry LinE P arado. for the us in 1947 Kine Kin Leontief, wassily(1953),"Domestic Production and Foreign Trade; The american Capital Position Re-Examined", Proceedings of the American Philosophical Society, 97(4): 332-49
9 CoPS Leontief paradox Labor content in U.S. exports: L E *B*E in = l Capital content in U.S. exports: K E B*E in k * = Labor content in U.S. imports: L M *B*M in = l Capital content in U.S. imports: K M B*M in k * = where l and k show labor and capital input per unit of output in each U.S. industry Paradox: L E L M K E K M in in in in Leontief, Wassily (1953), “Domestic Production and Foreign Trade; The American Capital Position Re-Examined”, Proceedings of the American Philosophical Society, 97 (4): 332–49. for the US in 1947
Corden's effective rates of protection (CoPs ∑nP,j=12m Value added per Pric Cost of intermediate unit output in j inputs Set quantity units so that 1+t: for all j where t, is the rate of tariff on imports of ∑a“(1+t),j=1,2,n Effective rate of protection for commodity j (ER indicates by how much Vi is inflated by tariffs ER ∑n1“(t),j=1,…m Corden, WM.(1966), "The structure of a tariff system and the effective protective rate Journal of political Economy 743), June, pp. 221-37
10 Corden’s CoPS effective rates of protection 1 2 j j ij i i V P a * P , j , ,...n = − = Value added per = Price − Cost of intermediate unit output in j inputs Set quantity units so that: 1 P t for all j j j = + where j t is the rate of tariff on imports of j j j ij i (1 1 1 2 ) ( ) i V t a * t , j , ,...n = + − + = Effective rate of protection for commodity j (ERj ) indicates by how much Vj is inflated by tariffs. ( ) ( ) 1 2 j j ij i i ER t a * t , j , ,...n = − = Corden, W.M. (1966), “The structure of a tariff system and the effective protective rate”, Journal of Political Economy 74(3), June, pp. 221-37