It then gives up some capital as well and output of sector 1 falls Endowments

It then gives up some capital as well and output of

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It then, gives up some capital as well, and output of sector 1 falls Endowments appear on the axes. Note the shift in the isoquants as the en- dowment of L is increased. The isoquant of the labor intensive advances, while the isoquant of the capital intensive sector shifts backwards. 4. Generalizations This part of the notes introduce the model with home goods and intermediate factors, and more general results are then derived. Only brief "claims" are made here: 1. Rybczynski: For the case of an equilibrium with M traded goods and N en- dowments, and M = N. Suppose factor i increases and the country remains within its cone of diversification. If a subset of industries ONLY employ factor i, then at least one of these industries’ output will expand by at least 16
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in proportion to the proportional increase in the factor, and the output of other industries will not change. If the subset of industries employ MORE than one factor that increases, then it must be that one of these industries (say industry k ) expands output in greater proportion to the proportional in- crease in the factor and at least one industry (say industry j ) must contract. In this case, ˆ y k > ˆ v i > 0 > ˆ y j . (See Woodland, p. 82) 2. Stopler-Samuelson: For the case of an equilibrium with M traded goods and N endowments, and M = N. Suppose output price j increases and the country remains within its cone of diversification. At least one factor price must rise in at least proportion to the rise in output price. If one of the factors whose price rises is used in an industry other than j, then the price of some other factor, say i, must fall; this implies ˆ w k > ˆ p j > 0 > ˆ w i (See Woodland, p 88) 4 4 Consider M = N = 3 . Then ˜ w i = ξ i p 1 ˜ p 1 + ξ i p 2 ˜ p 2 + ξ i p 3 ˜ p 3 where the elasticities sum to unity. If ξ i p j < 0 , then the sum of the remaining elasticities must exceed unity. 17
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5. A specific characterization: algebra Operating on the principle that an algebraic specification strengthens the under- standing of the theory, consider the following example. Given: U = q λ 1 q (1 λ ) 2 utility L, K resource endowments at the economy level y 1 = A 1 ` α 1 k 1 α 1 : technology sector 1 y 2 = A 2 ` β 2 k 1 β 2 : technology sector 2 and hence tc 1 = α α (1 α ) α 1 w α r 1 α y 1 A 1 (5.1) tc 2 = β β (1 β ) β 1 w β r 1 β y 2 A 2 (5.2) α α (1 α ) α 1 A 1 w α r 1 α p 1 = 0 β β (1 β ) β 1 A 2 w β r 1 β p 2 = 0 . α 1 α (1 α ) α 1 A 1 w α 1 r 1 α Y 1 + β 1 β (1 β ) β 1 A 2 w β 1 r 1 β Y 2 = L α α (1 α ) α A 1 w α r α Y 1 + β β (1 β ) β A 2 w β r β Y 2 = K 18
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5.1. The factor market "rental" equations Solve the zero profit equations for w and r as functions of p 1 and p 2 to obtain w = p 1 β ( α β ) 1 p α 1 α β 2 α α (1 α ) ( α 1) A 1 !
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  • Spring '14
  • Roe,TerryLee
  • Economics, Austrian School, yj

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