Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
1 Unilateral Trade Liberalization in Canonical CES/Monopolistic Competition Case with Homogenous Firms To analyze unilateral trade liberalization, in both the canonical CES/monopolistic competition case with homogenous …rms and the case with heterogeneous …rms considered in our paper, one needs to use the trade balance condition to solve for real wages. However, unlike the case with heterogenous …rms, the trade balance condition in the canonical CES/monopolistic case is not that hard to analyze. The reason is that all …rms are homogenous and choose the same option. As a result, with homogeneous …rms, there is just one equilibrium (trade balance) condition with one unknown variable, wage at Home (Country 1), that can be used directly to show that Proposition 1 In the canonical CES/monopolistic competition case with homogenous …rms unilateral trade liberalization by one of the countries bene…ts each trading partner. Proof. Part 1 (Derivation of the equilibrium condition). Consider the canonical CES/monopolistic competition case of 2 countries that can potentially di¤er in their sizes and all production parameters. There are Li consumers, who supply 1 unit of labor each, and Ni identical …rms in country i, i = 1; 2. To sell qij units of output in market j; each …rm in country i faces marginal labor costs M Cij = iceberg transportation cost, ii = 1 and ij ij i; where ij is the > 1. In addition, each …rm faces a …xed cost of production i so that its total pro…t is i = (pii wi M Cii ) qii + (pij wi M Cij ) qij Given the CES preferences, in market j this …rm sets a price pij = wi ij wi i= ( of substitution between any 2 varieties. Due to free entry in each country as ij = 1 (rii + rij ) wi i, i i: 1) ; where is the elasticity = 0: Since we can re-write the zero pro…t condition becomes rii + rij = wi ij i: Next, consider the labor market clearing condition in country i: Ni (M Cii qii + M Cij qij + Since M Cii qii + M Cij qij = (rii + rij ) ( w i 1) i) = Li : ; from the zero pro…t condition, we get Ni = Li = i: This means that a number of …rms in each country does not depend on trade costs, which signi…cantly simpli…es the analysis. After normalizing wage in country 2 to 1, w2 1; the only variable that remains unknown is w1 ; which can be found from the trade balance condition, N1 r12 = N2 r21 : Note that Ni = Li = and i 1 rij = Rj (Pj ) 1 1 (pij ) 1 wi ij = wj Lj i 1 Nj 1 wj 1 j 1 + Ni 1 wi ij i : Hence, the trade balance condition can be re-written as (w1 ) 1 (T B) : 1 N2 ( 2) 1 12 1 ) ( 1 + N1 (w1 12 1 ) 1 1 21 2 ) ( 1 = N1 (w1 2 1) 1 + N2 ( Part 2 (Unilateral trade liberalization by Country 1). Consider a fall in be re-written as h 1 N1 (w1 1 ) + N2 ( 2) 21 i (w ) 1 1 or N1 ( = N2 ( 2 1 " 1 12 1 ) " 1 21 2 ) or (w1 ) ( 1 1 1) 1 2) ( (w1 ) ( where the RHS > 0 does not change with 1 h = N2 ( 1 12 1 ) ( 1 2 (w1 ) ( 1) 1 1 2) ( + N1 (w1 21 2 ) 1 1 ( 2) 1 2 1 (w1 ) ( 2 # 1 12 1 ) 1 1 21 ) (w1 ) 12 1 ( 2) 1 21 : 1) ; Condition (TB) can i( 1 21 2 ) 1 ; 2 # ; 1 2) N2 ( ; (1) 1 (w1 ) ( 12 1 ) N1 ( 12 1 ) 21 . Moreover, both the numerator and denominator in the LHS 1 = 1 21 2 ) 1 2 are positive. (This follows from (TB), 2 where since ij means (w1 ) ( ( 12 1 ) 1 1 1 12 1 ) 21 2 < 1 ( = ( 2) 1 1 1 1 1 1; N2 ( 2 ) + N1 (w1 12 1 ) N2 ( 2 ) + N1 (w1 1 ) ( 21 ) > 1; the denominator in the LHS is smaller than the denominator in the RHS, which denominator.) As 21 . (w1 ) 1 2) ; i.e., the numerator in (1) has to be positive, and so does the falls, the LHS of (1) has to remain the same since the RHS of (1) does not depend on This means that w1 falls (the numerator of the LHS in (1) is decreasing with w1 ; while the denominator increases with w1 ; so that the whole LHS increases with w1 for given 21 ). Welfare in Country 2, W2 , can be found from 1 (W2 ) = which means that it rises with lower (W1 ) w1 What can we say about 21 1 = 1 1 P2 21 . 1 2) = N2 ( + N1 (w1 1 12 1 ) ; Welfare in Country 1, W1 , is w1 P1 1 = N1 ( 1 1) 1 w1 + N2 : 21 2 ? Multiplying both the numerator and denominator of the LHS of (1) by w1 yields 2 ( 1 1 1) (w1 ) ( 1 21 1 w1 1 2) 2 ( ( 2) 1 w1 1 12 1 ) = N2 ( N1 ( 2) 1 1 12 1 ) : Since the denominator falls with a lower w1 , then the numerator has to fall as well, implying that 1 21 w1 has to decrease with a decline in W1 increases as 21 21 . Going back to the expression for (W1 ) falls. Thus, we proved that with lower 21 both countries gain. 2 1 , this proves that