Lecture 2: Factor Proportions Theory of Trade

Transcription

1 Lecture 2: Factor Proportions Theory of Trade Alfonso A. Irarrazabal University of Oslo September 25, 2007 Contents 1 Factor Proportions Model Preferences Technologies Equilibrim conditions Factor prices and good prices The e ect of a change in good prices on factor prices Resources and output The e ect of a change in factor endowments on output HO model: the e ect of trade Autarky equilibrium Trade equilibrium and the distribution of income

2 1 Factor Proportions Model In the real world, while trade is partly explained by di erences in labor productivity, it also re ects di erences in countries resources. The Heckscher-Ohlin theory: Emphasizes resource di erences as the only source of trade. Shows that comparative advantage is in uenced by: 1) Relative factor abundance (refers to countries) 2) Relative factor intensity (refers to goods). It is also referred to as the factorproportions theory Assumption of the model An economy can produce two goods, good x and y. 1.1 Preferences Suppose that the preference in each country (of the representative consumer ) are homothetics. Consumer will choose consumption to maximize subject to the budget constraint max c 1 ;c 2 U(c 1 ; c 2 ) p 1 c 1 + p 2 c 2 w n L n + r n K n where p i is the price of good i, w n is the wage in country n, r n is the interest rate, L n the country size and K n is the stock of capital. 2

3 1.2 Technologies The production of these goods requires two inputs that are in limited supply; labor (L) and capital (K). Production of food is capital-intensive and production of cloth is labor-intensive in both countries. For sector i (i = C; F ) technology is de ned by teh production function q i = F i (L i ; K i ) where f() is constant return to scale. Capital and labor are fully mobile across sectors. Therefore, endowment in each economy are L 1 + L 2 = L K 1 + K 2 = K For a country the production possibility frontier is de ned as the solution of the following problem max F 2 (L 2 ; K 2 ) st : q 1 = F 1 (L 1 ; K 1 ) L 1 + L 2 = L K 1 + K 2 = K Let the solution to this problem be q 2 = P (q 1 ; L; K) 3

4 Factor intensity Let us rewrite the production function in intensive form, ie: in terms of output per worker, as: q x = f x ( K x L x ; 1) q y = f y ( K y L y ; 1) De nition: production of a good 1 is capital intensive relative to production of 2 if for any given K/L used in that sector, the marginal product of capital is higher relative to the marginal product of labor in 1 than in 2. Graphically, this can be seen in an isoquant where is on the x axis. For a given K/L tje isoquants for X will be atter than those for Y. GDP function In a competitive economy output is choosen to maximize G(p x ; p y ; L; K) = max q x;q y p x q x + p y q y st : q y = P (q x ; L; K) The solution of this problem is p x p x x That is in a competitive economy, production in each sector is found where the relative prices equals the slope of hte production possibility frontier. As a result an increase in the relative price of x makes the economy to produce more x and less of good y. 4

5 1.3 Equilibrim conditions The rst step to determine factor prices and output is to de ne equilibrium condition for a competitive economy. Duality between technology and cost function provides a useful environment. The dual problem of technology is the following c i (w; r) = min Li;K i fwl i + rk i g st : F i (L i ; K i ) 1 which is the minimum cost to produce one unit of output. The solution to this problem can be written as c i (w; r) = wa il + ra ik where a ik (r; w) is the optimal choice for K i ; which may depend on input prices as well. (r,w) dependence will be ommitted hereafter. It can be shown i =@w = a i =@r = a ik Zero pro t conditions The ZPC are p 1 = c 1 (w; r) p 2 = c 2 (w; r) 5

6 Full employment conditions Recall i =@w = a il is hte labor used for one unit of production, so L i = q i a il is the total labor used. Similarly, for the capital sector. Therefore, the full employment conditions are a 1L q 1 + a 2L q 2 = L a 1L q 1 + a 2K q 2 = K This system of four equations must be solved for {w; r; q 1 ; q 2 } for a given value of p 1 ; p 2 : 2 Factor prices and good prices Recall the ZPC p 1 = c 1 (!; r) p 2 = c 2 (!; r) Given p 1 =p 2 we can determine!; r from above. Then, from the full employment condition we can compute a 1L ; a 2L ; a 1K ; a 2K which are functions of (!; r). Then we compute L 1 ; L 2 ; K 1 ; K 2 and nally q 1 ; q 2. It is important if we could uniquely determine!; r from ZPC. Lemma 1 As long as both goods are produced, and factor intensity reversal (FIR) do not occur, ) 8 p 1 ; p 2 we have unique factor prices (!; r). 6

7 This is a remarkable result because it establish that factor endowment does not matter for factor prices. Contrast this with a one sector economy, where factor endowment do a ect (!; r). An immediate implication is the famous factor price equalization. Theorem 2 Factor price equalization (Samuelson, 1949).Suppose two countries engage in free trade, having identical technologies but di erent factor endowments. If Lemma 1 holds, then factor prices (!; r) are equalized across countries. This result tells us that trade in goods can equalize factor prices, in this sense, trade in goods acts as a perfect substitute for trade in factors. 2.1 The e ect of a change in good prices on factor prices Total di erentiate the ZPC: Let il =!a il c i dp i = a il d! + a ik dr dp i =!a il d! p i c i! + ra ik dr c i r ; ik = ra ik ci, be cost shares. Notice that il + ik = 1. Why? Let ^! = d!=!; ^r = dr=r, then ^p i = il^! + ik ^r; i = 1; 2 7

8 Or in linear form, 0 1 A = ^p L A = 1 jj 2L 0 1K 2K 2L A 1 0 1K 1L 1 1 A ^p 2 where jj = 1L 2L = 2K 1K Assume that good 1 is labor intensive. Claim: L 1 K 1 > L 2 K 2 () 1L > 2L Since sector 1 is labor intensive, ) 1L 2L > 0 ) jj > 0 E ect on wages Now suppose that p 1 =p 2 goes up, () ^p = ^p 1 ^p 2 > 0. Then, solving for ^!; ^r, ^! = 2K ^p 1 1K ^p 2 jj 1K = ^p 1 + (^p 1 ^p 2 ) > ^p 1 2K 1K We see that wage increase by more than the price of good 1, i.e., ^! > ^p 1 > ^p 2. This implies that workers can a ord to buy more good 1 (!=p 1 has gone up), and!=p 2 " 8

9 In this case we say that the real wage has gone up. E ect on interest rate Similarly, for the real interest rate we have ^r = ^p 2 2L 1L 2L (^p 1 ^p 2 ) < ^p 2 We have r=p 2 going down, r=p 1 # So the real return of capital has fallen. Summarizing these results we have: Theorem 3 (Stolper-Samuelson) An increase in the relative price of a good will increase the real return to the factor used intensively in that good, and reduce the real return to the other factor. Stolper-Samuelson A change in product price has a magnifying e ect on factor prices. We can think of a change in p 1 =p 2 due to (1) an increase in the country export prices (if the country exports q 1 ) or (2) to a lowering of import tarri s (p 2 goes down). The SS theorem says that trade will have important distributional e ects. Even though in the previous chapter it was argued that there are gains from trade, it is true that trade has strong distributional consequences. Illustration of Stolper-Samuelson FIGURE 9

10 Suppose that the economy starts with an initial equilibrium p 2 =p 1 at point A. Notice that sector 1 is labor intensive, L 1 K 1 > L 2 K 2 ()!a 1L >!a 2L!a 1K >!a 2K a 1L a ik > a 2L a 2K A shift in p 1 will move isoquant up to equlibrium B. Clearly, wage has gone up to! 1, as well as r down to r 1. Since the unit cost functions are homogenous of degree one in factor prices, moving along the ray, an increase in p 1 implies that (!; r) rises in the same proportions to a point (! ; r ). But as seen in the gure,! 1 >! ; r 1 < r. 3 Resources and output Recall that, given p 1 =p 2, we nd (!; r) and then a il ; a ik (i = 1; 2) and therefore we can determine L 1 =K 1 ; L 2 =K 2. The allocation can be depicted in a graph. FIGURE Which sector will have a higher L=K? How do outputs change when the factor endowments change? 10

11 As before, we di erentiate the endowment equation at constant prices: a K1 dq 1 + a K2 q 2 = dk which can be expressed as K1 ^q 1 + K2 q 2 = ^K where K1 = K i =K and K1 + K2 = 1. Similarly, we have L1 ^q 1 + L2 q 2 = ^L which can be solved as ^q 1 = 1 h L2 ^K jj h ^q 2 = 1 jj i K2 ^L i L1 ^K + K1 ^L where jj = 1L 1K = 2K 2L. 3.1 The e ect of a change in factor endowments on output Recall that since industry 1 is labor intensive (L 1 =K 1 > L 2 =K 2 ) then 1L > 1K and 2K > 2L. Now suppose that ^L > 0 and ^K = 0, then we have ^q 1 = ^q 2 = 2K ( 2K 2L ) ^L > ^L > 0 1K jj ^L < 0 Therefore, the output of the labor intensive industry 1 expands, whereas the output of the capital intensoive undustry contracts. 11

12 Theorem 4 (Rybczynski) An increase in a factor endowment will increase the output of the industry using it intensively, and decrease the output of the other industry. This can be shown graphically. FIGURE An increase in K from 0 P 2 to 01 2 then since p 2=p 1 is unchanged, so is!=r. Equilibrium moves from 0 to 1. Therefore, more output is produced in sector 2 (capital intensive). Example 5 A famous example of the Rybczynski theorem is the Dutch disease.the discovery of oil led to an increase in the industry making the use of this factor.however, some other traditional export industries contracted, because resources were attracted into sectors that were intensive in oil. How did this change a ect the PPF? An increase in K or L leads to a biased expansion of the PPF towards good 2 or good 1. The gure below shows the e ect. FIGURE The lower curve represents the PPF before the change. 12

13 The outer curve represents the PPF after an increase in K. Now, for the same p 2 =p 1 the economy produces at point 1 where the outward shift is more important in the direction of good 2 (capital intensive). Corollary 6 An economy will tend to be relatively e ective at producing goods that are intensive in the factors with which the country is relatively well endowed. 4 HO model: the e ect of trade Suppose two contries H and F trade with each other. Suppose country H is labor abundant. L H K H > LF K F Furthermore, assume that the production of good 1 is labor intensive. FIGURES: two PPFs side by side showing autarky and trade equilibria. 4.1 Autarky equilibrium First, notice that given the assumption about relative factor endowments, the PPF of H is biased toward q 1. Why? IInitially the autarky price at H is lower than at F (notice the similarity with the Ricardian model here). This relation is based on the shape of the PPF s and the fact that preferences are homothetic. Free trade will equalize prices of H and F. 13

14 Therefore, we will have p H < p < p F. So now production will occur in point B, where H exports good 1 and imports good 2. Theorem 7 (HO) Each country will export the good that it has its abundant factor intensively. 4.2 Trade equilibrium and the distribution of income Trade produces a convergence of relative prices. Changes in relative prices have strong e ects on the relative earnings of labor and land in both countries: In Home, where the relative price of cloth rises:laborers are made better o and landowners are made worse o. In Foreign, where the relative price of cloth falls, the opposite happens: Laborers are made worse o and landowners are made better o. Result: Owners of a country s abundant factors gain from trade, but owners of a country s scarce factors lose. In the US we can think that it is relative abundant in skilled workers an relative scarce in unskilled workers. Therefore, our mode suggests that international trade tends to make low skileed workers in the US worse o not just temporarily but in permanent basis. Di erence between the speci c factors model and the Heckscher-Ohlin model in terms of income distribution e ects: 14

15 The speci city of factors to particular industries is often only a temporary problem. Example: Garment makers cannot become computer manufactures overnight, but given time the U.S. economy can shift its manufacturing employment from declining sectors to expanding ones. In contrast, e ects of trade on the distribution of income among land, labor, and capital are more or less permanent. 15