MTA-ECON3901 Fall 2009 Heckscher-Ohlin-Samuelson or Model

Transcription

1 MTA-ECON3901 Fall 2009 Heckscher-Ohlin-Samuelson or Model From left to right: Eli Heckscher, Bertil Ohlin, Paul Samuelson 1

2 Reference and goals International Economics Theory and Policy, Krugman & Obstfeld, Chapter-4 This model provides an explanation for the pattern of trade based on the two countries difference in their input-endowments. Initially developed by Heckscher and Ohlin, and later Samuelson, the model it is also called for 2-inputs and 2- outputs and 2-countries. 2

3 HOS Model: A Preview Two countries are different in their factor (input) endowments. The combination of inputs embodied in each output is also different leading to difference in Opportunity Costs in the two countries. Hence, Comparative Advantage in this model stems from on factorendowment (as opposed to productivity in Ricardian model). This model has important conclusions for income distribution: we will be able to say how owners of different factors of production will be affected after free-trade. 3

4 Assumptions Inputs (factors of production): Land and Labour available at limited amount. Outputs: Food and Cloth differing in their use of inputs. Technology is identical in the two countries. Markets for both inputs and outputs are competitive before and after trade. Factor Mobility: Capital and labour are immobile between countries but mobile between sectors. 4

5 Production process Home is endowed with L units of labour (subscript L) and T units of land (subscript T) as factors of production (input). Home produces two goods Food (subscript F) and Cloth (subscript C). Definitions a TC = acres of land used to produce one unit of cloth a LC =hours of labour used to produce one unit of cloth a TF = acres of land used to produce one unit of food a LF =hours of labour used to produce one unit of food 5

6 Relative Factor Intensity Cloth is said to be Labour-Intensive (compared to Food) if: a LC / a TC > a LF / a TF It says that labour-land ratio (L C /T C ) used in producing one unit of cloth is greater that the one used in producing one unit of food (L F /T F ). If Cloth is Labour-Intensive then Food is Land-intensive: a TF /a LF > a TC / a LC Note: factor intensity is defined based on the comparison of the inputs ratios; hence if one output is land-intensive then the other is necessarily labour-intensive. 6

7 Production Possibility Frontier Recall that HOS model comparative advantage stems from differences in factor endowment. The same way as in Ricardian model, PPF indicates opportunity costs hence the comparison of PPFs will reveal each countries comparative advantage. Le t s relate the shape of PPF to the input-endowments of the country and see how relative input-endowment affect the shape of PPF. 7

8 On Endowments (Resources Constraints) The quantity of land and labour used in the production of the two goods cannot exceed the country's endowment. (i) (ii) Q F a TF + Q C a TC (smaller or equal) Land available (T) Q F a LF + Q C a LC Labour available (L) The above two conditions must be simultaneously satisfied. When one is satisfied with = and the other with < we have some unemployed resources. 8

9 PPF and Endowments (Resources Constraints)-1 Food Labour/a LF Labour constraint Land/a TF PPF Possible combinations of outputs Land constraint Labour/a LC Land/a TC Cloth 9

10 PPF and Endowments (Resources Constraints)-2 Food Labour/a LF All the land employed, labour left => with less land-intensive good we can get a lot more labour intensive good Land /a TF All the labour employed, land left => with less labour intensive good we can get a lot more land intensive good Labour/a LC land/a TC Cloth 10

11 Smooth PPF with two inputs-1 In reality some degree of substitution between inputs are possible. That is why we can approximate the PPF by a Smooth curve. PPF is Concave to the origin. This represents the disparity in the factor intensities of the two goods. As we increase the production of one output we have to use more and more resources that are poorly suited to produce it. Hence the Opportunity cost is not constant. 11

12 Smooth PPF and two inputs-2 Food PPF The shape of this PPF implies that opportunity costs of a good in not constant along PPF. +Food -10 cloth Conventions: Cloth, labour-intensive on the x-axis; Food, Land intensive, on the Y-axis Relative Price is P C /P F. +Food -10 cloth Cloth 12

13 Introducing relative prices In HOS model there are two sets of relative prices : Outputs relative price, in this case price of cloth (P C ) to price of food (P F ): P C /P F Inputs relative price, in this case price of labour (wage: w) and price of land (return to physical capital: r) and w/r Question: How many market have we already introduced? 13

14 PPF and RP of outputs-1 Food Higher Iso-value lines The equation for a given iso-value is: V=P C Q C +P F Q F Q F = V - P C /P F Q C Producer s choice Cloth 14

15 PPF and RP of outputs-2 Food Rise in elative Price of Cloth (P C /P F ) leads to increase in the Quantity of Cloth produced and a fall in the Quantity of Food produced. Producer s old choice Producer s New choice Cloth 15

16 Relating Relative Prices Recall that HOS is a General Equilibrium model. It implies that it is important to find out how prices relate to each other for being able to use the implications of freetrade. (For instance how free-trade affects wage...) We have to sets of relative prices: Inputs RP (labour and capital: w/r) and Outputs RP (cloth and food: P C /P F ). This is what we will see next! 16

17 Relationship between RPs-1 (i) Prefect competition and mobility in input markets (labour and land) implies that wage rate (w) and land rental rate (r) are the same in both sectors. So we get a relationship between w/r and PPF. (ii) Perfect competition in output market implies that profits are maximized (at zero). So we get a relationship between P C /P F and PPF. These two conditions (of efficiency) together imply that P C /P F and w/r should also satisfy a specific relationship. 17

18 Relationship between RPs-2 If Relative Price of Cloth (P C /P F ) rises then profit-seeking firms will be willing to produce more Cloth and less Food. Increasing Cloth and decreasing Food cause an excess demand (ED) of labour (factor intensively used in cloth) and an excess supply (ES) of land (factor intensively used in food). 18

19 Relationship between RPs-3 Since the quantity of resources in the economy are fixed ED for labour leads to a rise in wage (w) and ES of land leads to a fall in rental rate (r). Hence the rise of P C /P F leads to a rise in w/r: an upward sloping curve. The Figure in the next page represent it. 19

20 Relationship between RPs-2 The relationship is direct between the relative price of Cloth and the relative price of the its factor intensively used in its production. SS is the curve the relates the two relative prices. w/r SS P C /P F 20

21 SS-Application Samuelson-Stolper result and the resulting figure (SS curve in the space of the two RPs) is important in: Allowing us to predict how the price of inputs (inherently related to an economy s input-endowment) relates to relative price of outputs (inherently affected by free-trade). Recall that free-trade impacts relative price of goods and this is how its impact is modelled in Economic Theory. 21

22 Stolper-Samuelson Result This relationship illustrated in the previous slide is known as Stolper- Samuleson theorem. It states that (under some economic assumptions: constant returns, perfect competition): A rise in the relative price of a good will lead to a rise in the return to that factor which is used most intensively in the production of the good, and conversely, to a fall in the return to the other factor. SS, the title of the curve, is for Stolper-Samuelson. 22

23 Question for you: How one must characterise the Autarkic Equilibrium? You now know after Ricardian Model... 23

24 Autarkic Equilibrium Autarkic equilibrium (RP and quantities) is determined by the highest IC lattainable given (PPF). Food Q F IC Slope:- P C / P F Cloth Q C 24

25 Trade Equilibrium: Preview Reminder: Driving force of Trade: Difference in Relative Prices before Trade; Which means difference in Opportunity Costs; Which means the existence of Ricardian Comparative Advantage. Since we want to explain the pattern of trade as a function of difference in Factor Endowments we need to know how difference in factor endowment affect autarkic RP (OCs) therefore CA. 25

26 Definition: Factor-abundance Home is said to be Labour-Abundant compared to Foreign if: Total Labour at Home/ Total Land at Home is greater than Total Labour in Foreign/ Total Land in Foreign It is not a Single Comparison between total land endowments or total labour endowments, it is the comparisons of the ratios eg. Hence if Home is Labour-abundant then Foreign is automatically Land-abundant in comparison. 26

27 Shape of PPF and Factor-abundance Since in HOS model, comparative advantage stems from factor endowment; And that PPF summarises information about comparative advantage; It is important to see How factor(input) endowment affects the shape of PPF. This is what is done in the next slides. 27

28 We want to answer the questing below: How does factor-abundance affects the shape of PPF and from there autarkic relative price (and comparative advantage)? 28

29 Increase in labour Food Labour constraint L/a LF Labour Endowment Increased => Shape of PPF changed. T/a TF Land constraint L/a LC T/a TC Cloth 29

30 Impact of RP Food Labour Endowment Increased=> The Land/Labour Decreased => Autarkic Relative Price of Cloth Decreased. Cloth 30

31 Endowments and PPF We can think of the change is endowments as the case of two different countries. The country in the second scenario is Labour-Abundant compared to the country in the first scenario. We see that if this country produces more of Food (land-intensive good) the quantity of unemployed resource (here labour) will be relatively high compared to producing more of cloth (labour-intensive good) where the quantity of unemployed resource (land) will be much less. That is why it is more efficient for this country to produce more cloth. This is the fact behind difference is OCs (and RP) and from there CA and gains from trade. 31

32 Increase in land Food Labour constraint Land Endowment Increased=> Shape of PPF changed. L/a LF T/a TF Land constraint L/a LC T/a TC Cloth 32

33 Impact of RP Food Land Endowment increased=> The Land/labour ratio increased => Relative Price of Cloth increased. Cloth 33

34 Factor Endowment, Autarkic RP, OC, CA So all else equal: The Relative Price of the good intensive in a country s relatively abundant factor is lower than the other country. The opportunity cost of the good intensive in a country s relatively abundant factor is higher than the other country. (Why: the country s proportion of resource is more suited to produce this good.) A country has comparative advantage in the good intensive in its abundant factor. 34

35 HOS Summary-1 We assumed that goods can be identified by their relative use of inputs. In two goods world Food is land-intensive and Cloth is labour-intensive as soon as (L/T) Cloth > (L/T) Food We assumed that countries can be identified based on their relative endowments of inputs. In a two countries world Home is labour abundant and Foreign is land abundant as soon as: (L/T) Home > (L/T) Foreign We saw that the relative abundance of factors of production determine the opportunity costs of the goods hence the shape of PPF. 35

36 HOS Summary-2 We saw that all else equal the autarkic relative price of cloth will be lower in a labour-abundant country. The reason is the proportion of factors in this country is better suited to produced cloth than food. Another way of looking at it is the (i) remember that price is an expression of relative scarcity; (ii) each good embodies a given proportion of the two inputs; hence the country s relative scarcity of inputs is expressed in goods relative-price. This allows us to expect the implications of Comparative Advantage to be valid. 36

37 HOS-Summary-3 We saw that there is a unique relationship between each level of relative price of outputs (P C /P F ) and the relative price of inputs w/r. The result, Stolper-Samuelson theorem, helps us to later infer the impact of trade of the two groups of producers (labourers and land owners) in the country. The next step is to find the World Relative Supply curve. So that we have a better idea about the consequences of Trade. 37

38 RP of inputs and input-ratios w/r CC Profit-maximization implies that the higher the wage rate relative to land rental rate the higher the share of Land (relatively cheaper input) to labour (relatively more expensive input). FF Food is land intensive and Cloth is Labour intensive. Why? Land/Labour in Cloth Land/Labour in Food Land/Labour 38

39 RPs and input-ratios The relationships between our four markets (Cloth, Food, Land, Labour) are represented below. SS w/r CC FF P Cloth /P Food P C /P F T C /L C T F /L F Land/Labour (T/L) 39

40 Rise in RP of outputs and inputs ratio Understanding these unique relationships are helpful in understanding how we can derive Relative Supply Curves. SS w/r CC FF P Cloth /P Food (P (P C /P F ) 1 C /P F ) 2 T C /L C T F /L F Land/Labour (T/L) 40

41 Invisible Hand s Story-1 In the next two slides you will learn what happens behind the scenes of slide 19. Suppose an increase in RP of cloth then several adjustments are necessary in the economy: (i)production pattern (ii) RP of inputs (iii) Proportion of inputs employed 41

42 Invisible Hand s Story-2 (1) If price of cloth relative to food (P C /P F ) rises Quantity of Cloth produced increases and Quantity of Food produced declines. (2) Excess Demand for the factor intensively used in cloth, labour => (wage) rises => w/r rise as well. (3) As w/r increases the relative use of inputs in production changes: land-labour ratio increases in the production of both goods. Why? 42

43 Invisible Hand s Story-3 Let us look at each output individually: Cloth market: (i) P C rises then Q C rises then: L C rises and T C rises. (ii) But as w rises relative to r: L C falls. Combining (i) and (ii) we conclude that T C /L C rises. Food market: (i) P C rises so Q F falls so: L F falls and T F falls. (ii) And as w rises relative to r: L F falls. Combining (i) and (ii) I we conclude that T F /L F rises. 43

44 World Relative Supply To find the world equilibrium se need to have world relative supply: World Relative Supply=RS W = Total quantity of Cloth/Total Quantity of Food To have an idea how the RS differ from RS Foreign we use what is called HOS box. Suppose Home is Labour-Abundant and Foreign is Land- Abundant. 44

45 HOS Box Preliminaries We are looking for RS for both Home and Foreign. Hence we need to know how, at a given price, relative quantities differ as a function of factor-endowment. Suppose relative price is fixed at given number. We know that there exist a unique land to labour ratio for every given RP (Curves CC and FF). Adding the total labour & land endowments we have HOS box. 45

46 HOS Box Labour used in food production L F O F Land used in cloth production T C Labour/Land ratio Land /Labour ratio FF CC T F Land used in food production O C Labour used in cloth production L C 46

47 HOS Box Interpretation HOS is For a given Relative Price HOS shows the equilibrium amount of Labour and Land employed by each sector therefore the quantity produced of each output therefore Relative quantity supplied. It also lets us compare, facing the same relative price, how the Endowment of Land/Endowment of Labour affects the amount of Labour and Land employed by each sector therefore the quantities produced of each good output therefore Relative quantity supplied. 47

48 Increase in land P C /P F, demand and RFI remained constant. Land used in cloth production T 1 C T 2 C Less land FF 2 Labour used in Food production L 2 F Less labour FF 1 L 1 F C O 2 F O 1 F T F Land used in food production O C L 2 C Labour used in Cloth production L 1 C 48

49 HOS BOX Interpretation-2 HOS is For a given Relative Price Land Increased=> (i) Labour employed in cloth (food) decreased (increased); (ii) Land employed in cloth (food) decreased (increased). (i) &(ii) => Quantity of Cloth (Food) produced should decrease (increase). Pattern: The production of good whose intensively used input increased will increase at the expense of the other good. 49

50 HOS box and Relative supply Suppose these two scenarios are two different countries hence the second is land-abundant and the first labour abundant. We deduced that for any given price the higher the T/L the lower the quantity of Cloth/Food. Or the relative supply (Cloth/Food) of a labour-abundant country is higher than a land-abundant country. At constant relative goods prices, a rise in the endowment of one factor will lead to a more than proportionate expansion of the output in the sector which uses that factor intensively, and an absolute decline of the output of the other good. This is known as Rybczynski theorem. 50

51 Factor Endowments and Autarkic RS-1 Home: Labour-Abundant; Foreign: Land-Abundant: T/L H < T/L F We saw that Relative Supply of Cloth will be higher in a Labour-abundant country than in a Land-abundant country. Relative Price of Cloth RS F RS H P C /P F Cloth to Food 51

52 Factor Endowments and Autarkic RS-2 Home: Labour-abundant; Foreign: Land-abundant: T/L H < T/L F We also saw before (slides 28-34) that all else equal Relative Price of Cloth will be higher in a Labour-abundant country than in a Land abundant country. Relative Price of Cloth (P C /P F ) F RS F RS H (P C /P F ) H Cloth to Food 52 A given Cloth to Food Qunatity

53 Trade and its impact-3 P C /P F For simplicity we assume that the demand-side of the market is identical in the two countries. World relative price lies in between the two autarkic prices. RS F RS H RD W Cloth to Food 53

54 Trade: Flow of goods Since RP of outputs differs in these two countries after trade profit-seeking firms of each country will produce more of the products that temporarily have the higher price and less of the other. Thus the land-abundant country will export the land-intensive good since the price will be initially higher in the other country. Likewise the labor-abundant country will export the labor-intensive good. Excess supply of Cloth in foreign will bring the relative price of cloth down in foreign and Excess supply of Food will bring the relative price of cloth up at Home Trade flows will rise until relative price of goods is equalized in the two markets as result of import-exports. 54

55 Gains from Trade-1 After trade the relative price of the output using a country s scarce factor tend to fall (land at Home and labour in Foreign). Intuition: Since the two country are now integrated it is the world relative scarcity that counts and for a labour-abundant country the scarcity of land falls. After trade the relative price of the output using a country s abundant factor tend to rise (labour at Home and land in Foreign). Intuition: Since the two country are now integrated it is the world relative scarcity that counts and for a labour-abundant country the scarcity of labour rises. 55

56 Gains from trade-2 After trade consumption will be on the budget constraint instead of PPF. Budget constraint is defined based on World Equilibrium Relative Price and a country s PPF. The Production and Consumption need not coincide as countries engage in Import and Export. We are sure that if the old choice is still available then the utility (satisfaction) cannot be lower. Moreover we see that it is possible to reach higher Indifference Curves so the country gains from trade. 56

57 Gains from trade-home (Labour Abundant) Food After trade budget constraint Slope: world P C /P F (Higher) Consumption choice Old Q F Production Choice Cloth Old Q C Exports 57

58 Gains from trade-foreign (Land Abundant) Food After trade budget constraint Slope: world P C /P F (Lower) Production Choice Consumption choice Old Q F Imports Cloth 58

59 Impact of Trade At Home World Relative Price will be between the two autarkic prices: Since Home is Labour-abundant World P C /P F > Home Autarkic P C /P F. Hence After trade P C /P F increases at Home. The adjustments that follow are: (i) Quantity of Cloth produced increases and quantity of food decreases. Home exports cloth and imports food. (ii) w/r increases. (iii) Land/Labour increases. 59

60 Impact of Trade in Foreign World Relative Price will be between the two autarkic prices: Since Foreign is Land-abundant: World P C /P F <Foreign Autarkic P C /P F. Hence After trade P C /P F decreases in Foreign. The adjustments that follow are: (i) Quantity of Food produced increases and quantity of Cloth decreases. Foreign imports cloth and exports food. (ii) w/r decreases. (iii) Land/Labour decreases. 60

61 Distribution of Gains from Trade-2 World P C /P F > Home Autarkic P C /P F. Hence After trade P C /P F increases at Home. By S-S we know that w increase and r decrease. So all else equal purchasing power of land-owners declines relative to labourers at Home. World P C /P F < Foreign Autarkic P C /P F. Hence After trade P C /P F decreases in Foreign. By S-S we know that w decrease and r increase. So all else equal purchasing power of labourers declines relative to land owners in Foreign. So Trade makes the owners of a country s scarce-factor worse off. 61

62 HOS and Ricardian Model A Labour-abundant Country has Comparative Advantage in Cloth (labour intensive good). A Land Intensive Country has Comparative Advantage in Food. It is so because their endowment proportions are more suited for that type of goods. Land-abundant country will export the land-intensive good and the labor-abundant country will export the labor-intensive good. 62

63 Concluding Remarks According to this model since both countries gain from trade Global gains from trade are positive as well. HOS goes far in examining the implications of international trade: the distribution of gains from trade among different groups of producers. HOS explains the situations in which a country exports the product(s) for whose production it is well endowed and it will import the other(s). Do you think this is always the case? If not then what is missing in HOS? 63