Heckscher-Ohlin and Two-Cone ModelThe full employment conditions are, .Econ 441 Alan DeardorffProblem Set 3 - Answers Heckscher-Ohlin and 2-Cone ModelPage 1 of 14Problem Set 3 - AnswersHeckscher-Ohlin and Two-Cone Model1. Which of the following characterize the Heckscher-Ohlin Model?a. Perfect mobility of factors across industries Yesb. Perfect mobility of factors across countries Noc. Constant returns to scale Yes d. The law of diminishing returns Yese. Identical technologies across industries Nof. Identical technologies across countries Yesg. Monopolistic competition Noh. Perfect competition Yesi. Full employment Yesj. Balanced trade Yesk. Factor intensity reversals No (These are assumed not to occur.)l. Identical homothetic preferences Yes (This is not a necessary assumption for all results of the model, but it is an assumption that we will routinely use.)2. Suppose that the price of a good, X, is 0Xp and that potential producers of that good in acountry face factor prices w0 and r0. The three figures below show three ways that these prices might appear in an isoquant-isocost diagram. What can you say, in each case, about what will happen in the X industry in this country? That is, will the good be produced, can these prices constitute an equilibrium, and if so, what technique of production will be used to produce X?This says that a dollar’s worth of X requires more factors than can be bought with one dollar. Therefore good X will not be produced at these prices.Econ 441 Alan DeardorffProblem Set 3 - Answers Heckscher-Ohlin and 2-Cone ModelPage 2 of 14Here producers of X exactly break even, spending one dollar on factors that will produce one dollar’s worth of X, if they use the least-cost technique of producing it. That least-cost technique is the tangency between the unit isocost line and the unit-value isoquant, and it therefore uses 0XL and 0XK to produce one dollar’s worth of X. (Unless 10Xp, this is not one unit of X itself, so these are not the unit factor requirements aLX and aKX. We cannot determine these from the information given.)Here, all of the points on the isoquant inside the isocost line are ways to produce a dollar’s worth of X at a cost of less than one dollar, thus making a profit. This situation will attract entry into the industry, seeking this profit, and will continue to do so until either the factor prices change (at least one of them rising due to the increased demand for factors) or the price of X falls (due to the increased supply of X). This cannot be an equilibrium situation.3. The Edgeworth Box below shows the contract curve of a country as well as a particular allocation, A0, along that contract curve at which the country would produce, given certain prices, 0Cp and 0Fp. Its outputs at A0 are C0 and F0.Econ 441 Alan DeardorffProblem Set 3 - Answers Heckscher-Ohlin and 2-Cone ModelPage 3 of 14a. What is the wage-rental ratio, w0/r0, in this initial equilibrium? Are you able to determine the factor prices, w0 and r0, individually? The ratio is shown by the slope of the straight line tangent to both isoquants at A0. We cannot determine w0 and r0, individually.b. Identify in the figure the allocations of labor and capital to each of the industries,0CK, 0CL 0FK, and 0FL, as well as their ratios, 000/CCCLKk  and 000/FFFLKk . See figure above.c. Now consider the different allocation, also along the contract curve, shown as A1. Inorder for the country to produce there, how would prices have to differ from 0Cp and 0Fp? The relative price of cloth must rise in order for the economy to move from A0 to A1. That is, 0011//FCFCpppp .d. How do the factor allocations you looked at in part (b), and their ratios, differ at A1 from what they were at A0? These are shown by the arrows in the figure above, fromwhich we see that 01CCKK , 01CCLL , 01FFKK , 01FFLL , 01CCkk , 01FFkk .e. Using the full employment conditions for the two factors, show that the capital-labor ratio of the country as a whole, k=K/L, is a weighted average of the ratios in the twosectors, kC and kF. The full employment conditions areLLLFC, KKKFC.From the first, CFLLL . ThereforeLLkLLkLLLKLLLKLKLKLKKLKkCFCCFFFCCCFCFC1which is a weighted average.f. In part (d), you should have found that both ratios, kC and kF, fell in going from A0 to A1. Does this mean, in view of the result in part (e), that k has fallen also? Why or why not? The ratio k has not fallen, since it is just the ratio of the factor endowments, which are given. The reason that kC and kF were both able to fall without lowering k is that the weights, in the weighted average of part (e), have changed. By reallocating resources into the cloth sector, LC/L rises, putting more weight on the larger of the two capital-labor ratios. This makes up for the fall in both of them.g. Draw isoquants for both industries through point A1. Now identify the wage-rental ratio, w1/r1, as you did in part (a). How does it compare to w0/r0? The wage-rental ratio must be smaller at A1 than at A0: w1/r1<w0/r0. That is, the isoquants are flatter there than at A0. The reason is that the capital-labor ratios have both fallen, so that the industries move along their isoquants toward less capital and more labor, and when that happens they get flatter, due to their curvature. I’d be willing to bet that most of you, at least when you first drew the new isoquants, drew them steeper.Econ 441 Alan DeardorffProblem Set 3 - Answers Heckscher-Ohlin and 2-Cone ModelPage 4 of 144. Starting from the unit-value isoquants shown below and using the factor endowments at point E, carefully construct the rest of the pieces of the Lerner diagram for this economy. Suppose that this country spends half of its income on Cloth, C, and half on Food, F. What does it export and what does it import?The construction of the Lerner Diagram determines the factor prices, w0 and r0, that are consistent with producing both goods, and it also determines the ratios of factors employed at those factor prices in both sectors and thus the diversification cone. Since E is in that cone, the country will in fact diversify. The parallelogram construction determines the two factor allocations and thus the isoquants representing the country’s output, C0 and F0. The value of these outputs equals the value of their inputs (since profits are zero), and the two additional isocost lines