ho_14_class - HECKSCHER-OHLIN-SAMUELSON MODEL T.Roe AP8701 Contents 1 References 2 Motivation 2.1 Graphic of the H-O model 2.2 Points to discuss 3 Analy

ho_14_class - HECKSCHER-OHLIN-SAMUELSON MODEL T.Roe AP8701...

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HECKSCHER-OHLIN-SAMUELSON MODEL T.Roe AP8701 September 10, 2014 Contents 1 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1 Graphic of the H-O model . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Points to discuss . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 Analytical Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.1 Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.2 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.3 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.4 Characterization of equilibrium . . . . . . . . . . . . . . . . . . . 7 3.4.1 Solve for factor rental rates . . . . . . . . . . . . . . . . . 7 3.4.2 Solve for supply: . . . . . . . . . . . . . . . . . . . . . . . 8 3.4.3 Excess demand Walras’ law . . . . . . . . . . . . . . . . . 9 3.4.4 Utility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.5 Points to discuss . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.6 Comparative static analysis . . . . . . . . . . . . . . . . . . . . . 11 3.6.1 Relative factor intensity . . . . . . . . . . . . . . . . . . . 11 3.7 The Stolper-Samuelson Theorem: Applied to the C-D case; . . . . 12 3.8 Rybczynski Theorem: the CD case . . . . . . . . . . . . . . . . . . 14 4 Generalizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 5 A specific characterization: algebra . . . . . . . . . . . . . . . . . . . . 18 5.1 The factor market "rental" equations . . . . . . . . . . . . . . . . 19 5.2 The supply functions . . . . . . . . . . . . . . . . . . . . . . . . . 19 6 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 6.1 Marginal physical products & competition for labor . . . . . . . . 21
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6.2 Exogenous technological change . . . . . . . . . . . . . . . . . . . 23 6.2.1 Factor price equalization and technological change . . . . . 23 6.2.2 E § ect of technological change on supply . . . . . . . . . . 24 6.3 More General statement of Stopler-Samuelson and Rybscynski. . . 25 2
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HECKSCHER-OHLIN-SAMUELSON MODEL A point of departure 1. References Roe, Smith & Sirin, Chapter 2 Woodland, Chapter 1 through 5 2. Motivation 2.1. Graphic of the H-O model 2.2. Points to discuss 1. The line p 2 /p 1 ; at the point of tangency to the ppf, we have Gross Domestic Product ( GDP ) p 1 Y 1 + p 2 Y 2 3
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2. Recall that if production functions y 1 = f 1 ( ` 1 , k 1 ) are homogeneous of de- gree one, Euler’s theorem: f 1 ` 1 ( · ) ` 1 + f 1 k 1 ( · ) k 1 = y 1 and profit max implies, e.g., w = p 1 f 1 ` 1 ( · ) . So, therefore w ` 1 + rk 1 = p 1 y 1 Generalizing, we have p 1 Y 1 + p 2 Y 2 = wL + rK Implication is that the tangency line is GDP = p 1 Y 1 + p 2 Y 2 = wL + rK 3. Households’ income is GDP = wL + rK They spend this income on goods Q 1 and Q 2 GDP = wL + rK = p 1 Q 1 + p 2 Q 2 Thus we have p 1 Y 1 + p 2 Y 2 = p 1 Q 1 + p 2 Q 2 or (Walra’s Law) p 1 ( Y 1 Q 1 ) + p 2 ( Y 2 Q 2 ) the value of exports equal the value of imports and the current account is balanced. 4. Notice: NO savings 5. The problem is "separable" in the sense that: 1. We solve for production to determine GDP = p 1 Y 1 + p 2 Y 2 , 2. Then we use wL + rK = p 1 Q 1 + p 2 Q 2 as a budget constraint for house- holds to maximize utility 6. Can be viewed as a model of the individual "farm" household 4
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7. Drawing the ppf; suppose f 1 ( ` 1 , k 1 ) is capital "intensive" f 2 ( ` 2 , k 2 ) is labor "intensive" what does this imply about the ppf?? 8. Comparative advantage 3. Analytical Specification The key steps are: 1. A statement about the environment of the modeled economy 2. Specification of model primitives, i.e., utility, household behavior, technol- ogy, firm behavior 3. Characterization of equilibrium (define endogenous variables and equations to express them as functions of exogenous variables 4. Comparative statics: the relationship of endogenous variable to exogenous variables. Here we have two theorems. 5
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3.1. Environment A small open and competitive economy that produces and consumes two goods y 1 , y 2 , and c 1 , c 2 , respectively and given prices p 1 , p 2 . Goods are produced from a constant returns to scale technology that employs the services of the country’s endowments, labor L and capital K.
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  • Spring '14
  • Roe,TerryLee
  • Economics, Austrian School, yj

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