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Validity of Rybczynski Theorem and Magnification Effect in Indian Scenario

Contents 1. RYBCZYNSKI THEOREM …………………………………………………………………………………………………………….. 3 1. 1 Theorem: …………………………………………………………………………………………………………………………… 3 1. 1. 1 Graphical Proof ……………………………………………………………………………………………………………. 3 1. 1. 2 Mathematical Proof ……………………………………………………………………………………………………… 3 1. Magnification effect: …………………………………………………………………………………………………………… 6 1. 2. 1 Rank test: ……………………………………………………………………………………………………………………. 6 2. Summary: ……………………………………………………………………………………………………………………………….. 8 3. Description of data:………………………………………………………………………………………………………………….. 4. Research design: ……………………………………………………………………………………………………………………. 12 4. 1 Hypothesis: ……………………………………………………………………………………………………………………… 12 4. 1. 1 For Rank Test- ……………………………………………………………………………………………………………. 12 4. 1. 2 For Mathematical comparison-…………………………………………………………………………………….. 2 5. Data support for the hypothesis ………………………………………………………………………………………………. 14 5. 1 Rank Test: ………………………………………………………………………………………………………………………… 14 5. 2 Mathematical Comparison: ……………………………………………………………………………………………….. 16 6. Data Interpretations and calculations: ……………………………………………………………………………………… 17 6. Rank test: ………………………………………………………………………………………………………………………… 17 6. 2 Mathematical comparison: ………………………………………………………………………………………………… 18 7. 0 Result – Reasons for accepting the hypothesis: ………………………………………………………………………… 20 8. Bibliography: …………………………………………………………………………………………………………………………. 1 9. 0 Appendix …………………………………………………………………………………………………………………………….. 22 Exhibit 1a: Details on Gross Output, Total Capital and Total Workers for Labour Intensive Goods(X1) 22 Exhibit 1b: Details on Gross Output, Total Capital and Total Workers for Capital Intensive goods(X2) . 22 Exhibit 2: Goods production data …………………………………………………………………………………………….. 3 Exhibit 3: Factor supply data ……………………………………………………………………………………………………. 24 Exhibit 4a: Capital Intensive Goods – WITS product group classification ………………………………………. 25 Exhibit 4b: Labour Intensive Goods – ICRIER Paper (1) ………………………………………………………………… 26 Exhibit 5: Labour Force Data from CIA Factbook ………………………………………………………………………… 27 Group 2 1. RYBCZYNSKI THEOREM

The Rybczynski theorem was developed in 1955 by the Polish-born English economist Tadeusz Rybczynski (1923–1998). Tad Rybczynski was a distinguished academic economist as well as a prominent and well respected businessman. Tad also played a major role and active development in the Society of Business Economists. 1. 1 Theorem: Theorem states that in a neoclassical two sector model, if the prices are held constant an increase in a factor of production increases the output of the commodity which uses that factor more intensively and reduces the other which uses that factor less intensively.

It does not say anything about how the increased factor will be allocated. Its corollary’ states that the ‘maximum possible output’ of the commodity using the increased factor more intensively rises more than that of the commodity using the same factor less intensively. 1. 1. 1 Graphical Proof The theorem is useful in analyzing the effects of capital investment, immigration and emigration within the context of a Heckshar-Ohlin model (HO model). Consider a diagram depicting a labor constraint in red (it’s the steeper lower line) and a capital constraint in blue (the flatter line).

Suppose production occurs initially on the PPF at point A. Next, suppose there is an increase in the labor endowment. This will cause an outward parallel shift in the labor constraint. The PPF and thus production will shift to point B. Production of clothing (the labor intensive good) will rise from C1 to C2. Production of steel, the capital-intensive good, will fall from S1 to S2. If the endowment of capital increases the capital constraint would shift out causing an increase in steel production and a decrease in clothing production.

Since the labor constraint is steeper than the capital constraint, steel is capital-intensive and clothing is labor-intensive. This means that in general, an increase in a country’s endowment of a factor will cause an increase in output of the good which uses that factor intensively, and a decrease in the output of the other good. 1. 1. 2 Mathematical Proof The theorem demonstrates the effects of changes in the resource endowments on the quantities of outputs of the two goods in the context of the H-O model. One can apply the theorem anytime some change in the model causes a change in one of the endowments.

This Group 2 could occur as a country invests and thus raises its capital stock, if immigration or emigration occurs or as population growth or growth of the workforce occurs for other reasons. We use the two resource constraint conditions which must be satisfied in equilibrium. (5c) (5d) The asterisks indicate that these unit-factor requirements are the optimal levels derived from the cost minimization exercise and are functions of the wage, w, and the rental rate on capital, r. We will assume that wages and rents remain fixed which implies that output prices remain fixed as well.

Differentiating (5a) and (5d) with respect to L yields, (8a) (8b) Writing these in matrix form yields, This expression can now be solved using Cramer’s Rule to get, (9a) (9b) Group 2 Indian Institute of Foreign Trade MBA (IB) 2010-12 Whether these partial derivatives are positive or negative depends on the signs of the denominator. Assume the denominator of each expression is less than zero. Then, implies which is true if or This means that the denominator is negative if and only if production of good one is capitalintensive and production of good two is labor-intensive.

So, let’s suppose that good one is capital-intensive (good two is labor-intensive). Then, since each unit factor requirement is positive, and, This implies that if good one is capital-intensive (good two labor-intensive) and if the labor endowment rises, then the output of good one would fall and the output of good two would rise if output prices of both goods remained the same. If we conducted the same exercise for changes in the capital endowment, and we continue to assume that good one is capital-intensive and good two labor-intensive, then we would show that,

Group 2 Indian Institute of Foreign Trade MBA (IB) 2010-12 If we assumed the converse, i. e. , if good one were labor intensive and good two capital intensive, then the signs of all of the above derivatives would be reversed. These results lead to the following general statement of the Rybczynski theorem. If a factor endowment in a country rises (falls), and if prices of the outputs remain the same, then the output of the good that uses that factor intensively will rise (fall) while the output of the other good will fall (rise). 1. 2 Magnification effect:

While the Rybczynski theorem limits the changes in endowments to only one in the 2 endowment scenarios, Magnification effect takes the next leap. The magnification effect for quantities is a more general version of the Rybczynski theorem. It allows for changes in both endowments simultaneously and allows a comparison of the magnitudes of the changes in endowments and outputs. Simple Rank test can be applied to check the movement of production of goods on the basis of the theorem. The effect is initiated by changes in the endowments.

If the endowments change by some percentage, ordered as above, then the quantity of the capital-intensive good will rise by a larger percentage than the capital stock change. The size of the effect is magnified relative to the cause. The magnification effect for quantities is a generalization of the Rybczynski theorem. The effect allows for changes in both endowments simultaneously and provides information about the magnitude of the effects. The Rybczynski theorem is one special case of the magnification effect that assumes one of the endowments is held fixed.

If both endowments expand at the same rate, both commodity outputs expand at identical rates. But if factor endowments expand at different rates, the commodity intensive in the use of the fastest growing factor expands at a greater rate than either factor, and the other commodity grows (if at all) at a slower rate than either factor. 1. 2. 1 Rank test: Y2 > K* > L* > Y1 or Y2 < K* < L* < Y1 Where; L* denotes ? L/L, where ? L is an increment of L (labour) K* denotes ? K/K, where ? K is an increment of K (capital) Group 2 Indian Institute of Foreign Trade

MBA (IB) 2010-12 Y1 denotes rate of increase in Labour intensive output Y2 denotes rate of increase in Capital intensive output Expanding the model to be fit for all situations, we consider 3 set of variables m, k 1 and k2. where; m denotes the ratio of ? K/? L for a selected time duration i. e. marginal capital-labour ratio k1 denotes capital-labour ratio of the labour-intensive industry k2 denotes capital-labour ratio of the capital-intensive industry Case 1: M L* > Y1 Or Y2 < K* < L* < Y1 Where, L* denotes ? L/L, where ? L is an increment of L (labour) K* denotes ?

K/K, where ? K is an increment of K (capital) Y1 denotes rate of increase in Labour intensive output Y2 denotes rate of increase in Capital intensive output 4. 1. 2 For Mathematical comparisonCase 1 k1 Case 2 k2 Case 3 Group 2 Indian Institute of Foreign Trade MBA (IB) 2010-12 Where; m denotes the ratio of ? K/? L for a selected time duration i. e. marginal capital-labour ratio k1 denotes capital-labour ratio of the labour-intensive industry k2 denotes capital-labour ratio of the capital-intensive industry The three cases check the position of m with respect to k1 and k2.

Case 1 The production of labour intensive industry will increase and the production of capital intensive industry will decrease. Also, the rate of increase of output of labour intensive industry will be more than the rate of increase of labour endowment over the time period considered for analysis i. e. 2002 and 2007. Case 2 The production of both labour and capital intensive industry will increase as the total capital and labour endowment increases over the time period considered for analysis. Case 3 The production of capital intensive industry will increase and the production of labour intensive industry will decrease.

Also, the rate of increase of output of capital intensive industry will be more than the rate of increase of capital endowment over the time period considered for analysis. Group 2 Indian Institute of Foreign Trade MBA (IB) 2010-12 5. Data support for the hypothesis 5. 1 Rank Test: For our study, the class of industries identified as labour intensive and capital intensive, all use more than just two factors. The focus of our study would be on Labour and Capital as the two factors for application of the theorem to match the assumptions of the theorem.

Factor availability data: As can be seen from the data, supply of both the factors, labour as well as capital, displays an increasing trend during the period of our study – FY 2002 to FY 2007. Labor force (Million) Cumulative Capital 2500 2000 1500 1000 500 0 1989 1991 1993 1995 1997 Exhibit 3 1999 2001 2003 2005 2007 Labour Data: CIA World Fact book Capital Data: Penn World Table The rate of increase in the supply of capital, however, is much higher than the rate of increase in the supply of labour, even after adjusting for the scale differences.

To further validate the higher rate of growth of capital supply compared to labour supply, we calculate the capital availability per unit of labour for the same period, which is shown below: Group 2 Indian Institute of Foreign Trade MBA (IB) 2010-12 Capital supply per unit of labour 3. 2 3 2. 8 2. 6 2. 4 2. 2 2 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 Data Source: Exhibit 3 Goods production data: From the goods production data sourced from ASI (Annual Survey of Industries) reports, we can see a steep increase in the production of capital intensive goods. Capital intensive goods Production Labour intensive goods Production 00000000 150000000 100000000 50000000 0 2001 2002 2003 2004 2005 2006 2007 2008 2009 Data Source: Exhibit 2 As seen in the graph above, the increase in production of labour intensive goods has been significantly lower than the same for capital intensive goods, during our observation period of FY 2002 to FY 2007. Group 2 Indian Institute of Foreign Trade MBA (IB) 2010-12 5. 2 Mathematical Comparison: Let us now calculate ak_Cap and al_Cap for Capital Intensive Goods followed by ak_Lab, al_Lab for Labour Intensive Goods. For Capital Intensive Goods Total Capital in 2007 99500750 Gross Output in 2007 118867539 Total Workers n 2007 1503967 Capital For Production of 1 unit of Good: 0. 837072516 ak_Cap = Total Capital / Gross Output Labour For Production of 1 unit of Good 0. 012652462 al_Cap = Total Workers / Gross Output For Labour Intensive Goods Total Capital in 2007 59534988 Gross Output in 2007 79566408 Total Workers in 2007 4369393 Capital For Production of 1 unit of Good: 0. 748242751 ak_Lab = Total Capital / Gross Output Labour For Production of 1 unit of Good: 0. 054915047 al_Lab = Total Workers / Gross Output Now let us calculate the Capital Labour ratio for Capital Intensive and Labour Intensive industry. 1 = capital-labour ratio of the labour-intensive industry 13. 62545965 k2 = capital-labour ratio of the capital-intensive industry 66. 15886519 Further, as mentioned in the description in section 4. 1. 2, we compare the marginal CapitalLabour Ratio(m) with the Capital-Labour ratio of Capital(k2) and Labour Intensive industry(k1). Total Capital Availability in 2002(mn Rs) 11489. 18742 Total Capital Availability in 2007(mn Rs) 15120. 04167 Total Labour Availability in 2002(mn) Total Labour Availability in 2007(mn) 440. 00 506. 90 m = ? K/? L 54. 27285875 Hence, we observe that the final result is: k1 L* > Y1.

The data analysis has proved it to be correct. Also, through the mathematical comparison, it was observed that the data was fit for case 2. Accordingly, the data complied with the conditions for the case 2. The production of both labour and capital intensive industry increased as the total capital and labour endowment increased over the time period considered for analysis. Thus, Hypothesis was proved to be true. Thus, we can conclude that both the RYBCZYNSKI THEOREM and Magnification effect holds true in the Indian context for the time period of FY 2002 and FY 2007. Group 2 Indian Institute of Foreign Trade

MBA (IB) 2010-12 8. Bibliography: 1. “The Employment Potential of Labour Intensive Industries in India’s Organized Manufacturing” by Deb Kusum Das et. al. presented at INDIAN COUNCIL FOR RESEARCH ON INTERNATIONAL ECONOMIC RELATIONS (ICRIER) in June 2009 2. ASI reports on industry production; www. mospi. com 3. Labour force data from CIA World Factbook; www. cia. gov/library/publications/the-worldfactbook/ 4. Rybczinski theorem paper Arjit found 5. Data from penn world table; http://pwt. econ. upenn. edu/ 6. “Empirical Tests of the Factor Abundance Theory:What Do They Tell Us? by Donald R. Davis et. al. presented at EASTERN ECONOMIC REVIEW in Fall 1996 7. “The Rybczynski Theorem, Its Corollary Proposition, And An Envelope Theorem” by Frank S. T. Hsiao published in HONG KONG ECONOMIC PAPERS in October 1976 8. “Relative Factor Abundance and Trade” by Peter Debaere published in Journal of political economy in 2003 9. “Employment and Wages in Manufacturing Industries –Trends, Hypothesis and Evidence” by Nagaraj, R. published in Economic and Political Weekly in 1994 10. Journals on Indian trade; www. emeraldinsight. com 11. For search queries;www. google. om 12. For definations;www. wikipedia. com Group 2 Indian Institute of Foreign Trade MBA (IB) 2010-12 9. 0 Appendix Exhibit 1a: Details on Gross Output, Total Capital and Total Workers for Labour Intensive Goods(X1) NIC 2007 15 Description Food Prod Textiles Exhibit X: Details on Gross Output, Total Capital and Total Workers for Labour Intensive Goods Apparel Fabricated metal products Tobacco Paper Printing Furniture Hunting Wood, except furniture Total Output Gross Output – 2007 33739019 Fixed Capital 6833484 Invested Capital 13896917 Total Cap 20730401 Total Worker 1178602 7 16621606 7984055 10985613 18969668 1243265 18 28 16 21 22 36 1 20 3407730 9643972 1443074 3586386 2290752 6127938 1986710 719221 79566408 799258 2235220 231713 2189323 954328 178378 92234 491249 1538494 4178095 524438 2785353 1204048 344721 333890 1754177 Total Capital& Total Workers 2337752 6413315 756151 4974676 2158376 523099 426124 2245426 59534988 528055 405564 394869 208732 90235 173302 94384 52385 4369393

Exhibit 1b: Details on Gross Output, Total Capital and Total Workers for Capital Intensive goods(X2) NIC 2007 23 34 31 35 27 30 Description Coke Motor vehicles and trailers Electrical machinery and apparatus Other transport equipment Basic metals Computer, Electronic And Optical Products Total Output Gross Output – 2007 43665953 16329633 10378347 5592762 41726136 1174708 Fixed Capital 16633692 4574226 1645092 1219717 16633692 313071 Invested Capital 23088644 6348501 3527667 1946100 23088644 481704 Total Capital& Total Workers Total Cap 39722336 10922727 5172759 3165817 39722336 794775 Total Worker 86273 364728 245627 161259 628224 17856 18867539 99500750 1503967 Group 2 Indian Institute of Foreign Trade MBA (IB) 2010-12 Exhibit 2: Goods production data Prod. Description (in numbers) Labour Intensive Food Products Textiles Apparels Tobacco Products Paper and paper products Priniting & reproduction of recorded media Manufacture of Furniture Publishing Activities Crop & animal prodn. , hunting and related service activities Wood & Prods.

Of wood, except furniture Total Capital Intensive Coke & refined petroleum products Motor vehicles, trailers & semi-trailers Electrical machinery and apparatus Other transport equipment Pharmaceuticals, etc Basic metals Fabricated metal products, except machinery & equipments Computers, Electronics and optical products Total 27 28 23 34 31 35 14748097 5735695 3335697 2846745 NA 12257191 2513597 27 28 41726136 9643972 23 34 31 35 43665953 16329633 10378347 5592762 19 29 27 30 21 24 25 48089854 17495763 13098370 6702514 10200034 48556909 10009743 15 17 18 16 21 22 36 22 1 20 17871240 8771897 1885114 1222815 2017863 1065447 1830137 1065447 732284 294245 36756489 15 17 18 16 21 22 36 22 1 20 33739019 16621606 3407730 1443074 3586386 2290752 6127938 2290752 1986710 719221 72213188 10 13 14 12 17 18 31 58 1 16 37224408 17170010 5375706 2019260 4107717 1950897 609152 484962 1520688 849542 71312342 NIC 2002 Gross Output 2002 NIC 2007 Gross Output 2007 NIC 2008 Gross Output 2008 30 532738 41969760 30 1174708 128511511 26 3254318 157407505 Group 2 Indian Institute of Foreign Trade MBA (IB) 2010-12 Exhibit 3: Factor supply data Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 Labour force (Million) (A) 314. 751 314. 751 370 390 406 420 430 440 450 460 482. 2 496. 4 506. 9 Cumulative Capital (INR) (B) 852. 73 888. 5 927. 54 967. 36 1013. 98 1057. 57 1101. 3 1148. 92 1202. 24 1264. 16 1336. 01 1417. 38 1512 Capital supply per unit of labour supply (B/A) 2. 71 2. 82 2. 51 2. 48 2. 5 2. 52 2. 56 2. 61 2. 67 2. 5 2. 77 2. 86 2. 98 Group 2 Indian Institute of Foreign Trade MBA (IB) 2010-12 Exhibit 4a: Capital Intensive Goods – WITS product group classification Nomenclature ProductCode ProductDescription Mineral fuels, oils & product H0 27 of th H0 30 Pharmaceutical products. Photographic or H0 37 cinematographic goo H0 54 Man-made filaments. H0 55 Man-made staple fibres. Natural/cultured pearls, prec H0 71 stone H0 72 Iron and steel. H0 73 Articles of iron or steel. H0 74 Copper and articles thereof. H0 75 Nickel and articles thereof. Aluminium and articles H0 76 thereof. H0 78 Lead and articles thereof. H0 79 Zinc and articles thereof. Nuclear reactors,

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