Homework 5 Solution (pdf)

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factor endowments of the home country in the world (home + foreign) endowment, andsome endogenous variables that do not vary with the distribution of factor endowmentsacross countries (the world endowment of each factor is fixed) as long as FPE obtains,and the home country remains labor-abundant. Discuss the determinants of trade in thiscase. Compare this with the gravity equation derived in question 3c.<strong>Solution</strong>:**VT = 2 p1(y1− d1)= 2 p1(y1− s1(y1+ y1)) = 2 p1(y1(1− s1)+ s1y1) ,wL + rKwhere s1 =is the share of the home country in the world income,w wwL + rK*L w *= L + L , and K w = L + K . To determine output of good use the full employment ofresources in the home country in HO model:y1a1L( w,r)+ y2a2L( w,r)= Ly1a1K ( w,r)+ y2a2K( w,r)= KInverting yields:⎛ y1 ⎞ 1 ⎛a2KL − a2LK⎞⎜ ⎟ =⎜⎟ .⎝ y2⎠ a1La2K− a2La1K⎝ a1LK − a1KL ⎠To determine the demand for good 1 in the home country, use the homotheticity of thepreferences:www wL + rK* wL + rK a2KL − a2LKd1 = s1y = ( y1+ y1) = .w ww wwL + rKwL + rK a a − a aVT = 2 p1(y1− d1)2( waL+ ra1K)=( a2a1La2K− a2La1K2( waL+ ra1K)=w( a a − a a )( wL + rK=( a=( a1L1L1Laa2K2K2K2( wa− aL − a1LwL + rKK −wL + rK2K( a2L1K− a1 wwK 2Lw w 2K2L(( a)L − aK)(wL+ rK1 w ww 2K2L2L1Kww− ( wL + rK)(a2KL − a2LK))+ ra)1 L 1Kwww( aw w 2KLwL + a2KLrK − a2LKwL2La1K)( wL + rK )www− wLa2KL + wLa2LK− rKa2KL +2( wa− a+ ra)( a)r[LK− KL ] − aL)w[KLK− a))2LrKa− LK1L1Kw ww ww w 2K2L2La1K)( wL + rKww1K)( a2Kr + a2Lw)K L LK[− ]w ww2La1K)( wL + rK ) K K2( wa1L+ ra= .( a a − a1L2KAnd so, given that the FPE holds and the world endowments do not change, thevolume of trade is greater for “more” dissimilar countries. It depends on the product ofthe home capital endowment and the difference between the home country and the worldwL Llabor/capital ratios, K( − ) . In contrast, with the gravity equation in the case ofwK K2LKrK])Kww)
intra-industry trade and increasing returns to scale (see Problem 3c), the country size doesw wnot matter as long the relative endowments do not change: LK − KL = z , orw wwL = K( L / K ) + z / K . Then the amount of trade does not depend on the size of thehome country, as measured by K given that( L,K ) ∈ FPE .w wL = K( L / K ) + z /Kw, and
Page 5 and 6: * −σyy(p / p)τAnd so, c h = and
Page 7: The welfare of the foreign country

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