1. Consider the Grossman and Rossi-Hansberg model of small open economy. There are two sectors x and y, both of which are competitive. There are two factors: unskilled labor, skilled labor. A production of good j requires a continuum of tasks by unskilled labor, by skilled labor. Each task is done by a single factor. In industry j, a firm needs at, units of factor f to perform a typical f task once. Since there is a continuum of tasks, one can consider off as (constant) rate of f requirement as tasks are performed. The total measure of f task to produce one unit of good j is normalized to be 1. Thus, an is the factor requirement of f in the production of one unit of j when there is no offshoring. You may assume {oh} are fixed: tut = am, = 1 and tixs, = 411 2. Only unskilled labor tasks are offshored. Task i, if offshored, will require azofit,(i) units of foreign labor. Here ,t3 is a shift parameter. Let w and te are the domestic and foreign wage rates of unskilled good. Thus, different tasks require possibly different offshoring costs. Assume that t(i) G(i) = tv(i) for i in [0,1] and 9(1) > 0 and weakiftt1(0) < azajw. Let d E [0,1] be defined by to' flt.,(d) = tu. Choosing good x as numeraire, the international price of good y is 1 and wage rate for skilled labor is a. (a) Suppose t(i) = 1 + What values of c e w' f3 are consistent with the condition that both goods are produced as well as with other economic conditions such as non-negativity and d < 1? (b) Suppose c = h. What are the values of to and a? (c) Suppose c decreases a little bit from it's. How does to and a respond? (d) The above functional form and parameterization can be improved upon. Come up with some other functional form for t(i) and parameterization that are economically meaningful and analyze the model. 2. Consider a differentiated goods model of international trade with 'border effects.' There are two countries. Labor is the only factor of production and labor is used as numeraire. Country i, i = 1,2 produce Ni (unique) varieties of differentiated goods. Representative consumer of country j has utility function: Ur = (4.1 +Ehri, (414)2, where clit is the consumption in country j of a variety k produced in country i. The domestic prices of varieties produced in country i are all equal to p'. However, their prices in country j are all equal to p'i = Ti.or where > 1 for i # j and = 1 if i = j. The total export of from country i to country j is Niel if i # j. (a) Note that W is linearly homogeneous. Thus, the minimum expenditure function e(qi,u) facing country j satisfies e(ctu) = e(ttl)u. Here, ie = (pi?, - - -,p14,pr --,p24) is the consumer price vector facing country j. (The maximum u obtained under budget Yi and prices qJ satisfies e(qi,u) = e(qj, 1)u = Yi. Thus, u ter and 6(0,1) can be interpreted as an index for prices qr.) Obtain e(qi , 1) (under the simplifying assumptions on prices) and the corresponding consumption bundle that reaches the utility level of 1 at the minimum cost. Using these results, obtain the consumption demand ell when income of country j is Y'. (b) Compute the elasticity of substitution, say, between cid and 4'. Compute the price elasticity of demand el assuming that the number of varieties is very large. Suppose that the production of a unit of differentiated good requires a fixed input of 1 units of labor and a variable input of 1 unit of labor per unit of output. From the profit maximization condition and the zero profit condition, obtain output yl of each variety in country j. (c) The GDP of country i is given by = APpiyi. Derive a gravity equation relating the bilateral trade volume to {Ye} , i 1,2 and {V} , i,j 1, 2. 3. Now, suppose instead that there is a homogeneous good z in addition to the differentiated goods in the economy. There are no border effects so prices of a variety are the same in both countries. The endowments of skilled labor and unskilled labor in country 1 is (2,1) and those in country 2 is (1,2). The utility functions of both skilled and unskilled labor in both countries are given by: Uj = z4u4, where z is a homogeneous good supplied competitively and td (NI (eke). +N2 (c2.01) . The production of a differentiated good requires the fixed input of one unit of skilled labor for its headquarter services and one unit of unskilled labor for each unit of its production. Thus, the cost of a differentiated good is cd(y) = s+ toy, where y is the volume of output of a particular variety, s is skilled labor wage and to is unskilled labor wage. The production function of the homogeneous good in each country is z = hit+, where 4,1 are amounts of skilled labor and unskilled labor employed in the production of z. (a) Using z as numeraire, obtain the demand for z and es as a function of prices and aggregate income V. (b) Compute the Integrated World Equilibrium production of homogeneous good z and a differen-tiated good y, the number of varieties of differentiated goods N and the price of differentiated goods p, skilled labor wage a and unskilled labor wage to and aggregate income Y. Explain each equation you use to solve for the equilibrium. (c) Suppose the headquarter and assembly in the differentiated goods can be fragmented across countries. Given the endowment allocation of (2,1) and (1,2) of country 1 and country 2, can the integrated World Equilibrium be replicated in a free trade equilibrium? Justify your answer.
Attachment:- sinternationalf11.pdf