Chapter 9 3) The Specific-Factors Model (SFM)

1. Chapter 9 3) The Specific-Factors Model (SFM)

2. The Heckscher-Ohlin Assumption • It is important to understand that the H-O assumption of free factor mobility between industries describes a state at which an economy can arrive in the long run. • The assumption of perfect mobility of capital implies an economy in which industries can convert one kind of capital into another. • Eg: Factory for production of good X can fully be transformed to factory for good Y.

3. The Heckscher-Ohlin Assumption • In many circumstances, this process may require a considerable time period. • the capital used to produce automobiles is much different from that required to produce wheat or textiles. • labor also maybe rigid & not easy to be transferred from one industry to another without training. • Individuals skilled in operation of textile require some re-training before becoming proficient at computer programming..

4. H-O vs Specific-Factors Model • The specific-factors model (SFM) is similar to the model Heckscher-Ohlin analysis except that one factor, capital , is assumed to be useful for the production of only one commodity. • automobiles require one kind of capital and textiles another, and in the short run the amount of capital allocated to each industry is fixed. • No substitution of capital between industries can take place, though labor is mobile. • Because capital is specific to a particular industry, the model is known as the Specific-Factors Model

5. Specific-Factors Model (SFM) • Most of the assumptions of H-O model still valid: • 2 commodities are produced • Production functions that exhibit constant returns to scale • 2 factors of production are required for both production • Tastes are assumed to be homogeneous & identical • The essential difference between the H-O model & SFM model is that in SFM: • Only labor is homogeneous and common to the two production functions. • Capital is fixed by industry in the short run. • Therefore, the production functions for (X, Y) in SFM: X = Fx (Rx, Lx) Y = Fy (Sy, Ly) (9.1) where Rx & Sy represent types of capital that are specific to sector X & Y.

6. Specific-Factors Model (SFM) • Factor-supply constraints: R = Rx S = Sy L = Lx + Ly (9.2) • The entire available stock of factor R is used to produce commodity X • The entire endowment of factor S is used to produce Y • In this model, we are assuming that all factors of production are fully employed.

7. Specific-Factors Model (SFM) • The return to labor (wage rate) is defined as w, which is the same in both industries by virtue of the free mobility of workers. • The return of R & S will be defined to be r & s. • The specificity of capital allows the returns to capital to differ across industries in the short run. • This fact points out that in the short run, the 2 capital stocks are different inputs and that the model may also be interpret as a theory with 2 goods & 3 factors.

8. Figure 9.1: Total product and Marginal product curve for labor • The Fx curves depicts the response of output in an industry to increases in a variable factor, holding constant the input of a fixed factor. • In the top panel: total product of labor in sector X rises as more labor (L) is added to the fixed stock of R, but it does so at a diminishing rate .

9. Figure 9.1: Total product and Marginal product curve for labor • In the bottom panel: • the marginal product of labor in industry X (MPLX) which is a slope of the total product curve. • Because of diminishing returns, the marginal product declines as L rises. • A similar construction applies to good Y, given the fixed stock of Sy.

10. Figure 9.1: Total product and Marginal product curve for labor • MPL ↑ (in each industry) when capital-labor ratio ↑. • Shift up in TP & MPL (Figure 9.1: FX (R’X, LX) & MP’LX).

11. Marginal Production & Capital-Labor Ratio • MPL ↑ (in both industries) when capital-labor ratio ↑. • Eg: An increase in capital usage of 10% & labor usage of 5% in industry X. • decompose into: (a)     an identical 5% rise in R & L (b)     an addition rise of 5% in R • With CRS, component (a) has no impact on the MPL. • However, component (b) raises the MPL • increase in the endowment of RX will shift up both the TP & MP curves of labor. (Figure 9.1: FX (R’X, LX) & MP’LX). • MPR ↓ when capital-labor ratio ↑. • Conclusions hold for the determination of the marginal products of capital, which are declining functions of the capital-labor ratios in each industry.

12. Marginal Production & Returns to Factor • Assumption that factor markets are perfectly competitive implying that firms pay each factor the value of its marginal product. MPLXPx = w MPKXPx = r (9.3) • The real returns to labor & capital in terms of commodity X are equivalent to their marginal products: w/Px = MPLX r/Px = MPKX • Eg: • In Figure 9.1, rise in the capital stock for a given level of employment generates a higher real wage. • MPL ↑ implies MPK ↓ (in the same sector) • If w/Px ↑, r/Px must↓. • The inter-industry labor mobility must establish a common wage in both industries, generating an equal value of marginal product of labor in equilibrium.

13. Figure 9.2: Autarky and free trade equilibria in the SFM • Employment in sector X is indicated from left to right, relative to origin 0x. • Capital stock in industry X is held fixed. • As more labor is employed in this sector, the marginal product of labor declines, causing the value of labor’s marginal product, or VMPLX, to be a downward-sloping curve.

14. Figure 9.2: Autarky and free trade equilibria in the SFM • Because equilibrium requires VMPLX = w, it is possible to interpret this schedule as the demand curve for labor in industry X. • Note: A rise in either Px or Rx would shift the VMPLX curve upward. • Demand for labor in sector Y = VMPLY schedule, which is drawn from right to left relative to origin 0Y.

15. Figure 9.2: Autarky and free trade equilibria in the SFM • Point A represents autarky equilibrium. • 0xL = employment in industry X. (in industry Y = 0YL). • Common wage, w is paid in both industries. • Total labor income paid to workers in X = w0xLA. (in Y = w0yLA). • Thus, in autarky factor R earns the area VwA. (factor S = ZwA).

16. Case 1: Commodity Prices & Factor Prices • A relative price increase of a good rises the real income of the specific factor (capital) used in that industry, reduces the real income of the other specific factor, & has an ambiguous effect on the mobile factor (labor).

17. Case 1: Commodity Prices & Factor Prices Example and explanation: • Px ↑, VMPLXVMP’LX • Actually VMPLX = MPLX Px. So a 20% rise in Px results in a 20% shift upwards in the value of MP curve throughout its length, BA. • B cannot be an equilibrium because it corresponds to a higher w in sector X than in Y. Thus labor moves from Y to X. MPLX ↓ & MPLY↑. New equilibrium at point C.

18. Case 1: Commodity Prices & Factor Prices • There’s a higher allocation of labor to good X & a higher nominal wage in both industries. • total income paid to R (specific capital stock in X) & total wages ↑.Total income for S (specific capital stock in Y) ↓. • Thus, the nominal factor price, r & w ↑ but s ↓. • Conclusion: Laborers and owners of the capital stock X enjoy higher real returns measured in terms of their ability to purchase Y (Py constant), while capital stock Y receive a lower real return.

19. Case 1: Commodity Prices & Factor Prices • Increase in labor lowers the capital-labor ratio in use in X: • raising MP of fixed capital stock R & r/Px • Thus, the specific capital stock in the expanding industry unambiguously gain real income • Px ↑  production of X ↑  demand for R ↑, but no addition R that can be supplied  r ↑. • Reduction in production of Y causes decline in MP of Sy (because assumed full-employment) • Amount of Sy is the same but smaller output of Y. • Decline in MPSy imply lower real return for Sy (s). • The fact that the K/L industry X ↓, K/L industry Y ↑ as a result of the inter-industry employment shift from A to C. • Each labor is better-off in terms of ability to consume good Y (w↑, Py fixed) but worse-off in terms of ability to consume good X (increment of ww’ < increment of Px i.e. BA). • Whether workers gain or lose welfare depends on their preferences for the 2 commodities.

20. Case 2: Factor Endowments & Factor Prices At constant commodity prices, any increase in the endowment of specific factor will increase the real returns to the mobile factor and lower the real returns to both specific factors. Example and Explanation: • Rx   excess supply of Rx  r  decline in MCx  marginal profit of X  X  excess demand of Lx  in both sector X & Y  wage  (w). • Output Y need to be reduced to release more L for Lx  means MPSy  (because amount of Sy still the same but output Y becomes smaller)  s (real return to Sy).

21. Case 3: Factor Endowments & Factor Prices Increase in the endowment of the mobile factor will reduce its own real income & increase the real income of both specific factors. Example & explanation: • In sector X: L   excess supply of Lx  real return to L (w)  MCx  marginal profit of X  X . • With the same Rx, increase in production of X means increase in MPRx r. • Similarly in sector Y: L excess supply of Ly  real return to L (w)  MCy  marginal profit of Y  Y . With the same Sy, increase in production of Y means increase in MPSys.

22. Trade & Factor Prices • In the specific-factors model, the equalization of commodity prices by international trade does not equalize factor prices. • Main reason: Specific Factor Model has 2 goods but 3 factors • Question: Is the equalization of commodity prices by international tradeequalize thefactor prices in H-O Model?

23. Factor Endowments & Outputs • An increase in one specific factor increase the output of the commodity that uses that factor and reduces the output of the other industry. • Increases in the supply of the mobile factor will expand both outputs.