Econ452 Learning Unit 08
- 1. Learning Unit 8 Resources and Trade in Long Run ECON452 International Economics
- 2. Objectives 1. Describe the concepts of factor abundance and factor intensity 2. Derive the relative factor demand 3. Explain a relationship between factor price and good price – Stolper-Samuelson theorem 4. Explain how resources affect a shape of production possibilities frontier – Rybczynski theorem
- 3. Introduction • Trade occurs due to differences in resources across countries. – differences in labor, labor skills, physical capital, capital, land, and entrepreneurship across countries. • Two aspects of resources – Countries may have different quantities of resources: Factor abundance. U.S. has many capital and skilled labor, while Bangladesh has many unskilled labor. – Each product may require different combinations of resources: Factor intensity. Production of car requires capital (assembly line), while production of apparels require labor (operating sawing machine).
- 4. Factor Abundance • Factor abundance: A nation is abundant in one factor if the ratio of the price of the factor to the other factor in lower in the nation than that in the other nation. – Based on both supply and demand condition of factor market • Factor prices: costs of each unit of factor of production – wage (w) for labor and rental cost (r) for capital. – If supply of one factor is high or demand for the factor is low, then the factor is abundant and its market price is low. Alternatively, if supply of one factor is low or demand for the factor is high, then the factor is scarce and its market price is high. • Because one country may have lower factor prices on all resources, a relative factor price (ratio of the price of one factor to the other factor) is compared across countries.
- 5. Factor Abundance - Example • Wage-rental ratio (w/r): a ratio of wage rate of labor to rental cost of capital. • Wag-rental ratios are 1 ($10/$10) in Home and 1.5 ($30/$20) in Foreign. – Because the wage-rental ratio (w/r) is lower in Home than Foreign, Home is labor-abundant. – Because the wage-rental ratio (w/r) is higher in Foreign than Home, the rental-wage ratio (r/w) is lower in Foreign than Home, so Foreign is capital-abundant. Home Foreign Wage Rate of Labor (w) $10 $30 Rental Rate of Capital (r) $10 $20
- 6. Factor Abundance - Caveats • A country cannot be abundant in all factors. – Factor abundance is relative concept like relative price and comparative advantage. When two countries are compared, each country is abundant in at least one factor. • A country can be abundant in one factor relative to one country, but abundant in other factor relative to other country. – China is labor-abundant relative to the U.S., but capital-abundant relative to Bangladesh. • Having more factors than other countries does not necessarily make factor abundance. – U.S. (330 million in 2019) has more population than Bangladesh (160 million in 2019), but Bangladesh is considered as labor-abundant. • Lower factor price does not necessarily make the country abundant in the factor. – Both wage rate and rental rate are lower in Home than Foreign, but Home is NOT capital- abundant.
- 7. Factor Intensity • Factor intensity: A good can be produced cheaply by using more of one factor than the other. • Labor-Capital ratio (L/K): a ratio of quantity of labor to quantity of capital in production. • Labor-Capital ratios are 1 (100/100) for cloth production and 0.5 (20/40) for food production. – Cloth is labor-intensive because its labor-capital ratio is greater (using relatively more labor and less capital) than food – Food is capita-intensive because its labor-capital ratio is less (using relatively less labor and more capital) than cloth Cloth Food Quantity of Labor (L) 100 20 Quantity of Capital (K) 100 40
- 8. Factor Intensity - Caveats • The minim cost combination of inputs is compared for all products, when producers are facing the same input prices. – Input combinations vary as input prices change (input substitution) • A product cannot be intensive in all factors. – Factor intensity is relative concept. When two products are compared, each product is intensive in at least one factor. • A product can be intensive in one factor relative to one product, but intensive in other factor relative to other product. – Food production is capital-intensive as compared with apparel production, but labor-intensive as compared with airplane production. • Factor intensity reversal: A product can be intensive in one factor at one relative input price, but intensive in other factor at other relative input price.
- 9. Factor Abundance and Factor Intensity • Factor abundance is determined when two countries are compared in terms of resource supply and demand. – Example: Comparing U.S. and China, which country has relatively abundant in labor resource? • Factor intensity is determined when two products are compared in terms of cheapest input combinations. – Example: Comparing production of apparels and production of airplane, which product uses capital more intensively? • Difference in factor abundance among countries and difference in factor intensity among products will determine which country should produce which product. – If China is labor-abundant, should China produce labor-intensive apparels or capital-intensive airplanes?
- 10. Minimum Cost Combination of Input • There are many combinations of two inputs to produce a fixed number of output. • Given input prices, there is one combination of two inputs which is lowest in total cost. • To find the minimum cost combination of inputs, we use isoquant- isocost diagram.
- 11. Isoquant • Isoquant: A curve showing all the combinations of two inputs that will produce the same level of output. – Example: All three combinations of labor and capital (A, B, C) can produce 100 units of output. • One isoquant for each level of output. – Example: Isoquant corresponding to 200 units of output lies above the isoquant corresponding 100 units of output. Quantity of Labor (L) Quantity of Capital (K) Isoquant (at Q = 100) A B C Isoquant (at Q = 200) 10 10 207 5 15
- 12. Marginal rate of Technical Substitution • Marginal rate of technical substitution (MRTS): a rate at which a firm can substitute one input for another, while keeping the level of output constant. • MRTS is the slope of an isoquant. MRTS = ΔK/ΔL – Example: At B, MRTS = 1 • MRTS is a ratio of marginal product. MRTS = MPL/MPK = (ΔQ/ΔL)/(ΔQ/ΔK) = ΔK/ΔL Quantity of Capital (K) B 10 Isoquant (at Q = 100) Quantity of Labor (L) 10 5 15
- 13. Slope of Isoquant • Isoquant becomes steeper as it uses more capital (moving toward upper left) and flatter as it uses more labor (moving toward lower right). – As K increases, MPK decreases and MPL increases due to diminishing marginal return, so MRTS increases. – With more capital is used, it requires more and more capital to replace labor to maintain the output. Quantity of Labor (L) Quantity of Capital (K) Isoquant (at Q = 100) A B C 10 10
- 14. Isocost Line • Isocost line: All the combinations of two inputs that have the same total cost. – Example: All three combinations of labor and capital (a, b, c) cost $2000 in total. • One isocost line for each total cost. – Example: Isocost line corresponding to $2000 total cost lies above the isocost line corresponding $1000 of total cost. Quantity of Labor (L) Quantity of Capital (K) Isocost (at TC = $1000) a b c Isocost (at TC = $2000)10 10 205 5 15 15 20
- 15. Slope of Isocost Line • Slope of isocost line is equal to wage- rental ratio (w/r). TC = w*L + r*K K = (TC/r) – (w/r)L • Example: At w = $100 and r = $100, if L = 100 and K = 100, TC = $2000. w/r = $100/$100 = 1 Quantity of Labor (L) Quantity of Capital (K) b Isocost (at TC = $2000)10 10 20 20
- 16. Minimum Cost Combination • There are many combinations of two inputs to produce a fixed number of output. • Given input prices, there is one combination of two inputs which is lowest in total cost. – Example: All three combinations (A. B, C) can produce 100 units of output. – At A and C, it costs $3000, while at B it costs $2000. – At D, it costs $1000, but it cannot produce 100 units of output. Quantity of Labor (L) Quantity of Capital (K) Isoquant (at Q = 100) B 10 10 A C D Isocost (at TC = $2000) Isocost (at TC = $3000) Isocost (at TC = $1000)
- 17. Condition of Optimal Combination of Inputs • At the optimal (minimum) combination of inputs, the isocost line is tangent to the isoquant. • A slope of isocost line is equal to a slope of isoquant. w/r = MRTS = MPL/MPK Quantity of Labor (L) Quantity of Capital (K) Isoquant (at Q = 100) B 10 10 Isocost (at TC = $2000)
- 18. Factor Price and Factor Substitution • As one factor becomes more expensive relative to another factor, a cost-minimizing firm substitutes relatively-cheap factor for relatively-expensive factor. • A rise in wage-rental ratio (w/r) shifts the lowest-cost input choice from point B to point A; that is, it leads to the choice of a lower labor-capital ratio (L/K). – As capital becomes relatively cheaper to labor, more capital and less labor are used to produce at the lowest total cost. – An inverse relationship between w/r and L/K. Slope = w/r = 1 Slope = w/r = 2 Quantity of Labor (L) Quantity of Capital (K) Isoquant (at Q = 100) A B 10 10
- 19. Relative Factor Demand • Relative Factor Demand: A relationship between a relative input price (wage- rental ratio) and a relative input quantity demanded (Labor-capital ratio). – Relative factor demand curve is downward- sloping. – As labor becomes relative more expensive to capital (w/r rises), more capital and less labor are used to produce the same quantity of output (L/K falls).
- 20. Factor Intensity and Isoquant • Given the same wage-rental ratio (w/r), the isoquant of Cloth production (CC) requires more labor and less capital, while the isoquant of Food production (FF) requires more capital and less labor to produce at the lowest costs. – Example: L/K of Food = 1/6 (5/30), and L/K of Cloth = 2 (20/10). • Food is capital-intensive, while Cloth is labor-intensive. 5 10 30 20
- 21. Factor Intensity and Relative Factor Demand • Relative factor demand curve of labor- intensive good (CC) lies right to relative factor demand curve of capital-intensive good (FF). – At any given wage-rental ratio, cloth production uses a higher labor-capital ratio than food production. w/r L/KCCL/KFF
- 22. Factor Prices and Good Prices • In competitive markets, the price of a good should equal its cost of production, which depends on the factor prices. • How changes in the wage and rent affect the cost of producing a good depends on the mix of factors used. – An increase in the wage rate of labor should affect the price of cloth more than the price of food since cloth is labor-intensive. • The higher the relative cost of labor, the higher must be the relative price of the labor-intensive good.
- 23. Stolper-Samuelson Theorem • Stolper-Samuelson theorem: If the relative price of a good increases, then the real wage or rental rate of the factor used intensively in the production of that good increases, while the real wage or rental rate of the other factor decreases. – When the relative price of labor-intensive Cloth (PC/PF) increases, profit-maximizing firms increase the production of Cloth. – To produce more cloth, they demand more labor relative to capital because Cloth is labor- intensive. – Given full employment of resources, labor must be released from Food industry. Because Food industry is capital-intensive, as Food industry reduce its production, it makes labor and even more capital available. However, capital is not demanded much from Cloth industry. – Then, the wage rate increases relative to rental rate (w/r) as demand for labor high and demand for capital low.
- 24. Relative Price of Good and Relative Factor Demand • When the relative price of labor- intensive cloth rises – from PC/PF 1 to PC/PF 2 • the wage-rental ratio must rise – from w/r1 to w/r2 • the labor-capital ratio used in the production of both goods must decrease – from LF/KF 1 to LF/KF 2 in food industry – from LC/KC 1 to LC/KC 2 in cloth industry
- 25. Relative Price and Income Distribution • An increase in the relative price of labor-intensive cloth (PC/PF) raise income of workers relative to that of capital owners (w/r). • It raises the real income (purchasing power) of workers and lowers the real income of capital owners.
- 26. Factor Abundance and Factor Intensity • Because of a difference in factor abundance between two countries, the isocost lines in two countries have different slopes (w/r). – A labor-abundant Home has flatter isocost line (lower wage-rental ratio) than a capital-abundant Foreign. • Assuming the same technology, both countries face the same isoquants. – Home uses more labor and less capital at H, while Foreign uses more capital and less labor at F. – Labor-capital ratio is higher in Home than Foreign. Slope = w/rH Slope = w/rF Quantity of Labor (L) Quantity of Capital (K) Isoquant F H LHLF KF KH
- 27. Factor Abundance and Relative Factor Demand • In each country Cloth is labor-intensive and Food is capital-intensive. – Assuming the same technology across countries, the relative factor demands are identical among the countries. • Labor-abundant country produces all goods at higher labor-capital ratio. – Home is labor-abundant and its wage-rental ratio is low. – Home uses more labor to produce both goods as compared with Foreign. LF/KF H > LF/KF F for production of food LC/KC H > LC/KC F for production of cloth HH H FF F
- 28. Factor Abundance and Production Possibilities • An economy with a high ratio of labor to capital produces a high output of cloth relative to food. • Comparing two countries, a labor-abundant country can produce relatively more labor-intensive goods and its PPF is skewed more toward labor-intensive goods production. • Example: Home is relatively abundant in labor and Foreign in capital. – Home will be relatively efficient at producing cloth because cloth is labor-intensive and labor is relatively cheap in Home. – Home can produce relatively more of Cloth than Foreign and its production possibilities frontier is skewed toward the horizontal axis (measuring quantity of labor-intensive cloth).
- 29. Factor Abundance and Output • Comparing two countries, facing the same relative price, a labor-abundant country chooses to produce more labor-intensive goods. • Given a relative price at PC/PF, – Labor-abundant Home will produce QC H of Cloth and QF H of Food. – Capital-abundant Foreign will produce QC F of Cloth and QF F of Food. QC H QF F QF H QC F Slope = PC/PF
- 30. Rybczynski Theorem • When resources increase, a resulting expansion of production possibilities is biased toward goods whose production requires intensive use of increased resources. – When the U.S. increases its skilled-labor, its production of skilled-labor-intensive goods will increase more than proportional, while its production of unskilled-labor-intensive goods will decrease. • Rybczynski theorem: Holding output prices constant, as the amount of a factor of production increases, then the supply of the good that uses this factor intensively increases and the supply of the other good decreases. – Constant relative price means constant wage-rental ratio, and constant labor-capital ratio in each industry.
- 31. Rybczynski Theorem - Formula • Changes in resources affect the allocation of factors across sectors, holding the prices of outputs constant. • L/K = (LC/KC)(KC/K) + (LF/KF)(KF/K) – Where LC/KC >LF/KF (labor-capital ratio in Cloth and Food industries) are constant. – KC/K and KF/K are proportions of capital allocated in Cloth and Food industry, respectively. • When labor resource increases, – Labor-capital ratio increases (L/K) – Capital will be allocated more in labor-intensive cloth industry and less in capital-intensive food industry (KC and KF↓) – Labor will also be allocated more in labor-intensive cloth industry and less in capital-intensive food industry (LC and LF↓)
- 32. Rybczynski Theorem - Diagram • An increase in the quantity of labor resource shifts the economy’s production possibility frontier outward disproportionately in the direction of labor-intensive cloth production. • At an unchanged relative price of cloth, labor- intensive cloth production increases and capital- intensive food production declines. – Before expansion at TT1, at PC/PF a country produces QC 1 of Cloth and QF 1 of Food. – After expansion to TT2 due to an increase in labor resources, at PC/PF a country will produces QC 2 of Cloth and QF 2 of Food. Decrease Increase
- 33. Rybczynski Theorem – Numerical Example • Originally, with 6 units of capital and 6 units of labor, a country produces 2 units of cloth and 2 units of food. – Labor-capital ratios are ½ in Cloth industry and 2 in Food industry. • When labor resources increase by 50% from 6 units to 9 units, at constant relative price (constant labor-capital ratios) under constant returns to scale. – the country increases its output of cloth by 100% from 2 units to 4 units – its output of food decreases by 50% from 2 units to 1 unit Labor Capital L/K Output Cloth 2 4 2/4 = ½ 2 Food 4 2 4/2 = 2 2 Total 6 6 Labor Capital L/K Output Cloth 4 8 4/8 = ½ 4 Food 2 1 2/1 = 2 1 Total 6 9
- 34. Disclaimer Please do not copy, modify, or distribute this presentation without author’s consent. This presentation was created and owned by Dr. Ryoichi Sakano North Carolina A&T State University Disclaimer Please do not copy, modify, or distribute this presentation without author’s consent. This presentation was created and owned by Dr. Ryoichi Sakano North Carolina A&T State University