Topics in Trade: Slides

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1 Topics in Trade: Slides Alexander Tarasov University of Munich Summer 20 Alexander Tarasov (University of Munich) Topics in Trade Summer 20 / 2

2 : Rybczynski Theorem (955) How factor endowments affect product outputs? Theorem An increase in a factor endowment will increase the output of the industry using it intensively, and decrease the output of the other industry. Proof. In the class! NOTE: The factor-intensive industry not only absorb the entire amount of the extra factor endowment, it also absorbs further labor and capital from the other industry! As a result, the output of the other industry falls. Example: Dutch Decease, industries making use of oil expanded, other industries contracted. Alexander Tarasov (University of Munich) Topics in Trade Summer 20 2 / 2

3 : Factor Price Equalization Revisited Before (for two countries): if both countries produce both goods and FIRs do not occur, then (w, r) are equalized across the countries. Now: for any allocation of labor and capital (of both countries) within the cones of diversication =) both goods are produced!! =) Factor price equalization Moreover, the equilibrium is the same as in the integrated world. Alexander Tarasov (University of Munich) Topics in Trade Summer 20 3 / 2

4 The goal of the model is to predict the pattern of trade in goods between the two countries, based on their differences in factor endowments. Assumptions: identical technologies identical and homothetic preferences different factor endowments trade in goods (factors are not mobile across the countries) no FIRs (factor intensity reversals) Alexander Tarasov (University of Munich) Topics in Trade Summer 20 4 / 2

5 Assumptions: FPE: endowments are in the "cone of diversication" home country is labor abundant: good is labor intensive: a L a K L K > L K : L = L, K < K > a 2L a 2K Alexander Tarasov (University of Munich) Topics in Trade Summer 20 5 / 2

6 The Heckscher-Ohlin Theorem: Each country will export the good that uses the abundant factor intensively. That is: the home country will export good, while the foreign country will export good 2. Intuition: Since the home country is labor abundant and good is labor intensive, the home country has a comparative advantage in producing good. That is, the autarky relative price of good in the home country is lower than that in the foreign country. As a result, the home country will export "cheaper" good and import good 2, which is "cheaper" abroad. Alexander Tarasov (University of Munich) Topics in Trade Summer 20 6 / 2

7 More formal: a representative consumer with homothetic preferences. Let us denote p a as the relative price of good at home in the autarky equilibrium (no trade equilibrium): p a = pa p2 a. In the same manner, p a is the relative price abroad. Then (see the picture drawn in the class), p a < p a. Let us also denote z(p) as the excess demand for good in the home country (given the relative price p), z (p) is the excess demand abroad. Then, in the trade equilibrium: z (p w ) + z(p w ) = 0. Alexander Tarasov (University of Munich) Topics in Trade Summer 20 7 / 2

8 As we can infer from the picture: z(p a ) = 0 z (p a ) > 0 =) z (p a ) + z(p a ) > 0. Given p a, there is world excess demand for good. By analogy, z (p a ) = 0 z(p a ) < 0 =) z (p a ) + z(p a ) < 0. Therefore, p a > p w > p a. Alexander Tarasov (University of Munich) Topics in Trade Summer 20 8 / 2

9 Gains from trade: as it can be seen from the pictures (trade triangles), both economies gain from trade. In fact, trade "improves" the consumer budget constraints and agents in both countries receive higher utility. However!!!! Not everybody gains. Consider the home country. In the trade equilibrium, the relative price of good goes up compare to the autarky price. Then, according to the Stolper-Samuelson Theorem, this will increase the real return to labor (the factor used intensively in the production good ) and will decrease the real return to capital. Workers gain, but holders of capital lose. Inequality rises. Trade is good, but can increase inequality. Alexander Tarasov (University of Munich) Topics in Trade Summer 20 9 / 2

10 Equilibrium conditions (general equilibrium): Assume that consumers spend the share α of their income on good and the share ( α) on good 2. The example is the Cobb-Douglas utility function: U(y, y 2 ) = (y ) α (y 2 ) α. Then, the world demand for goods and 2 is given by D = αy w p and D 2 = ( α)y w p 2, where Y w is the world income. Alexander Tarasov (University of Munich) Topics in Trade Summer 20 0 / 2

11 Equilibrium conditions (continue): In the equilibrium, world demand is equal to world supply. Therefore, the world production of good is equal to αy w ( α)y w p, while the production of good 2 is p. 2 Given the factor price equalization, we have a L αy w p + a 2L ( α)y w p 2 = L + L () a K αy w p + a 2K ( α)y w p 2 = K + K. (2) Alexander Tarasov (University of Munich) Topics in Trade Summer 20 / 2

12 Equilibrium conditions (continue): In addition, Y w = w(l + L ) + r(k + K ) a il = a il (w, r) a ik = a ik (w, r) p i = c i (w, r). We have two equations (() and (2)) and two unknowns: w and r. So, it is possible to solve for w and r. Alexander Tarasov (University of Munich) Topics in Trade Summer 20 2 / 2

13 An Example: Production (the Cobb-Douglas production function), f i (L i, K i ) = (L i ) β i (K i ) β i, where i =, 2 is the industry index and > β > β 2 > 0 (good is labor intensive). We need to nd c i (w, r) and a il and a ik, c i (w, r) = min L i,k i fwl i + rk i jf i (L i, K i ) = g. Alexander Tarasov (University of Munich) Topics in Trade Summer 20 3 / 2

14 An Example (continue): This minimization problem implies (see the details in the class notes) that a il = a ik = β i β i βi βi βi w r w r βi c i (w, r) = ( β i )β i (β i ) β w β i r β i. i a il and a ik depend only on the ratio w r, c i(w, r) has the same functional form (Cobb-Douglas), as the production function. No FIRs: a L a K > a 2L a 2K () β > β 2. Alexander Tarasov (University of Munich) Topics in Trade Summer 20 4 / 2

15 An Example (continue): Autarky Consider rst the autarky equilibrium. The equilibrium conditions are given by where Y = wl + rk plus a L αy p + a 2L ( α)y p 2 = L, a K αy p + a 2K ( α)y p 2 = K, p i = c i (w, r). Alexander Tarasov (University of Munich) Topics in Trade Summer 20 5 / 2

16 An Example (continue): Autarky Some algebra: α (wl + rk ) ( α) (wl + rk ) β + β w 2 = L () w L + r w K (β α + β 2 ( α)) = L () r w = L K β α + β 2 ( α). Higher L K increases r w. More labor in the economy means that capital is now relatively scarce resources. This in turn means that rent on capital is relatively higher. Alexander Tarasov (University of Munich) Topics in Trade Summer 20 6 / 2

17 An Example (continue): Autarky Finally, p a = pa p2 a = c (w, r) w c 2 (w, r) = β β 2 ( β ) β (β 2 ) β 2 r (β ) β ( β 2 ) β 2 β β K 2 β2 β ( β = ) β (β 2 ) β 2 L β α + β 2 ( α) (β ) β ( β 2 ) β 2. If β β 2 > 0, then higher K L increases pa. Therefore, since K > K and L = L, p a > p a (see previous considerations). Alexander Tarasov (University of Munich) Topics in Trade Summer 20 7 / 2

18 An Example (continue): Autarky Finally, p a = pa p2 a = c (w, r) w c 2 (w, r) = β β 2 ( β ) β (β 2 ) β 2 r (β ) β ( β 2 ) β 2 β β K 2 β2 β ( β = ) β (β 2 ) β 2 L β α + β 2 ( α) (β ) β ( β 2 ) β 2. If β β 2 > 0, then higher K L increases pa. Therefore, since K > K and L = L, p a > p a (see previous considerations). Alexander Tarasov (University of Munich) Topics in Trade Summer 20 8 / 2

19 An Example (continue): Some comments Notice that we cannot nd nominal values of w and r, only w p i and r p i. In particular, w p i = r p i = w w c i (w, r) = βi (β i ) β i r ( β i ) β i. r βi (β i ) β i w ( β i ) β i. Then, we can substitute for the expression for r w. Alexander Tarasov (University of Munich) Topics in Trade Summer 20 9 / 2

20 An Example (continue): The trade equilibrium In the trade equilibrium, the equilibrium equations are almost the same. The only difference is that instead of Y we have Y w plus the factor endowments are equal to the world endowments. The equilibrium is equivalent to the autarky equilibrium with the world endowments of labor and capital (FPE matters a lot). Then, r w = L + L K + K, β α + β 2 ( α) K + K p w β β 2 β2 β ( β = L + L ) β (β 2 ) β 2 β α + β 2 ( α) (β ) β ( β 2 ) β 2. Alexander Tarasov (University of Munich) Topics in Trade Summer / 2

21 An Example (continue): The trade equilibrium Since we assume that L = L and K > K (the foreign country is capital abundant), then K L > K + K L + L > K L. This immediately implies that (as we derived before) p a > p w > p a. Moreover, compare to the autarky equilibrium, r w goes down. This means that w p i goes up (workers gain), while r p goes down (capital holders lose). Inequality i increases. Alexander Tarasov (University of Munich) Topics in Trade Summer 20 2 / 2