1. 1. Consider a Ricardian model with a continuum of goods, indexed by z [0, +), and two countries, indexed by i = N, S, each endowed with Lc units of labor. wi denotes the wage in each country. Constant unit labor requirements in country c and industry z are given by: ai (z) = ieiz , where S > N > 0 and S > N > 0. Hence North ( N) has an absolute advantage in all goods and a comparative advantage in high-z goods. Households have identical Cobb-Douglas preferences in both countries: + Ui = ln ci (z) dz. 0 (a) Solve implicitly for the relative wage, wN /wS , and the cut-o good, z. Solution: Note that this problem is inspired by Krugman (1986) A Tech aS (z) nology GapModel of International Trade. We denote A (z) aN (z) , which is a increasing and continuous function of z. From the production side of the economy, we know that p (z) = min {aN (z) wN , aS (z) wS} Furthermore, given the functional form, there exists a marginal good z R+ , the switching point in the chain of comparative advantage, such that North will produce only the goods z z and South will produce only the goods z zz. must satisfy in equilibrium: S e(S N )z = wN /wS N Our online Tutors are available 24*7 to provide Help with International Economics Homework/Assignment or a long term Graduate/Undergraduate International Economics Project. Our Tutors being experienced and proficient in International Economics sensure to provide high quality International Economics Homework Help. Upload your International Economics Assignment at Submit Your Assignment button or email it to info@assignmentpedia.com. You can use our Live Chat option to schedule an Online Tutoring session with our International Economics Tutors. http://www.assignmentpedia.com/economics-homework-assignment-help.html For further details, visit http://www.assignmentpedia.com/ or email us at info@assignmentpedia.com or call us on +1-520-8371215

2. Conditional on wages, goods should be produced in the country where it is cheaper to do so. In equilibrium, we also know that the value of imports must be equal to the value of exports, which implies: (1 z) LS = wN /wS zLN Equations (3) and (4) implicitly dene and z. (b) Study the welfare implications in both countries of a decrease in S. Solution: A decrease in S corresponds to uniform technological catch-up in the South. Let z and wN /wS denote the cut-o good and the relative wage in the new equilibrium. In this case, we have z z and wN /wS wN /wS . At a given relative wage, the technological advance generates z to increase and South has a trade surplus which will pressure the wN /wS down. North and South both gain from trade. Consider the South rst. The change in the indirect utility function is given by z 1 1 US = 0 ln a S (z) ln aS (z) dz z 1 1 + z ln a S (z) ln aN (z) (wN /wS) dz 1 + ln wS ln wS dz z NaN (z) w aN (z) wN There are three regions: (i) z [0, z] , i.e. goods produced by South before and after, (ii) z [z, z ] , i.e. goods produced by South after but by North before and (iii) z [z , 1] , i.e. goods produced by North before and after. The rst term is positive because S < S. The second term is positive because international specialization requires aN (z) wN a (z) w z [z, z ], S S, z and hence 1/a S (z) 1/ wN /wS aN (z) if wN /wS wN /wS . The third terms is positive because wN /wS wN /wS . So the South gains from trade. Now consider the North. The change in the indirect utility function is given by z wN /wS wN /wS UN = ln ln dz 0 a S aS z wN /wS 1 + ln a (z) ln aN (z) dz z S 1 1 1 + ln ln dz z aN (z) aN (z) http://www.assignmentpedia.com/economics-homework-assignment-help.html For further details, visit http://www.assignmentpedia.com/ or email us at info@assignmentpedia.com or call us on +1-520-8371215 3. Let = wN /wS , the rst term is positive because / = A (z) /A (z ) = Se(N S )(z z)/ S. Hence N < S and z > z implies a S/ < aS/. The second term is positive for the same reason as in the South. The third term is trivially equal to zero. So the North gains from trade as well. (c) Study the welfare implications in both countries of an decrease in S. [Maintain the assumption that TN > TS.] Explain the dierence between the setting here and that in 1(b). Solution: First notice that an increase in S to is such that aS (z) S a S (z) for all z, i.e. the South experiences a technological advance. It requires less labor units to produce one unit of the good z. This results in z z and . At given relative wages, the technological loss causes z to decrease and the South has a trade decit which will pressure the down. Consider the South rst. The change in the indirect utility function is given by z 1 1 US = 0 ln a S (z) ln aS (z) dz z 1 1 + z ln a S (z) ln aN (z) wN /wS dz 1 + ln wS ln wS dz z NaN (z) w aN (z) wN There are again three regions: (i) z [0, z] , i.e. goods produced by South before and after, (ii) z [z, z ] , i.e. goods produced by South after but by North before and (iii) z [z , 1] , i.e. goods produced by North before and after. The rst S S ) term is positive because a S (z) < aS (z) , i.e. e( z < 1. The second term is positive because international specialization requires a S (z) /aN (z) (wN /wS) wN /wS , z z [z, z ], and hence 1/a S (z) 1/ wN /wS aN (z). The third terms is positive because wN /wS wN /wS . So the South gains from trade. Now consider the North. The change in the indirect utility function is given by z wN /wS wN /wS UN = ln ln dz 0 a S aS z wN /wS 1 + ln (z) ln aN (z) dz z aS 1 1 1 + ln ln dz z aN (z) aN (z) Let = wN /wS . The third term is trivially equal to zero. z z [z, z ] , international specialization requires wN aN (z) > wS aS (z). The rst term http://www.assignmentpedia.com/economics-homework-assignment-help.html For further details, visit http://www.assignmentpedia.com/ or email us at info@assignmentpedia.com or call us on +1-520-8371215 4. wN /wS aS (z ) aS (z) is positive i = , z [0, z], i.e. eS z S (wN /wS z ) aS (z) aS (z) ( S S )z e . 2. Continue with the environment in Question 1 but now assume that z [0, +) and that households have non-homothetic preferences in both countries: + Ui = ci (z) dz, 0 with ci (z) = 0 or 1 for all z. In addition, we assume that all households are endowed with one unit of labor in both countries. (a) Compute ci (z) as a function of wi in both countries. Solution: Note that this entire exercise is inspired by Matsuyama (JPE, 2000). First, notice that an increase in utility is created by an increase in diversity, not an increase in the consumption of the same good. Furthermore, given the functional form we are considering, we know that the order in which the consumers purchase goods is such that they consume rst the lower index goods and then the higher index good as long as it can aord it. This is because p (z) = min {wN aN (z) , wSaS (z)} is increasing in z given a (.) are increasing and continuous in z. Since the household purchases all the lower-indexed goods and expands its range of consumption upward as far as it can aord, 1 if z [0, z(wi)] ci (z) = 0 if z (z(wi) , ) for i = N, S, where z(wi) is implicitly dened as z(wi) min (aN (z) wN , aS (z) wS) dz = wi 0 Notice that the highest good the consumer consumes, z(wi), can also be viewed as the utility level of the consumer with income wi as z(wi)U (z(wi)) = 1 dz = z(wi)0 (b) Solve implicitly for the relative wage, wN /wS , and the cut-ogood, z. Solution: wN /wS Like in Question 1, e cient international specialization requires S e(S wNN )z = N wS The dierence between Questions 1 and 2 comes from the trade balance condi- tion. Given that South will produce all the goods z such that z z, p (z) = http://www.assignmentpedia.com/economics-homework-assignment-help.html For further details, visit http://www.assignmentpedia.com/ or email us at info@assignmentpedia.com or call us on +1-520-8371215 5. z wSaS (z) , the value of South imports is max wS wSaS (z) dz, 0 , i.e. ei0 ther the South will export the remainder of its income after consuming all the lower goods produced in the South or it wont have any income left and wont export. South will spend the remainder of its income on exports if z something remains. The value of their exports is min wN , 0 wSaS (z) dz , i.e. the North will either spend all of its income on the lower range of goods produced by South by importing or purchasing all the South produced goods. z z Hence, if wN wSaS (z) dz, the trade balance condition is 1 aS (z) dz =0 0 z wN /wS and if wN > wSaS (z) dz, the trade balance condition becomes 0 z z 1 0 aS (z) dz = 0 aS (z) dz. It can be rearranged and summarized as z 1 aS (z) dz = if wN /wS 1/2 20 z aS (z) dz = wN if wN /wS < 1/21 wS0 Given the North has an absolute advantage in all goods, i.e. aN (z) < aS (z) z, we know that wN /wS = aS (z) /aN (z) > 1. Hence, there exists an z 1 equilibrium where z solves 0 aS (z) dz = from the trade balance condition. 2 wN /wS solves the A (z) schedule given the solution to z. However, notice that z 1 given aN (z) < aS (z) z, < 1 and B (z) = aN (z) dz = which denes the0 2 z. There are several dierences from the previous case which all come directly from the non-homotheticity of preferences. The unit labor requirements do not appear in the trade balance condition because of the Cobb-Douglas preferences. In this case, a change in a (.) aects the labor market equilibrium through the prices as it will shift the demand towards the North goods when aS (z) decreases. To restore the balance of trade, the North will expand the range of good it produces. Furthermore, there is an asymmetry between aS (.) and aN (.). A decrease in aN (.) will only aect the price of North goods and the consumer will increase the range of North goods keeping uncha