1.考虑一个拥有SH熟练工人和UH非熟练工人的国家。有两种最终产品，分别用0和1索引，并且各自的生产函数为

F0（S; U）= minfS; Ug，F1（S; U）= S + U。

b。在a的上下文中，确定0 <SH <UH时的产出和要素价格。对于SH> UH> 0，请执行相同的操作。

C。假设p0 = p1 <2。为该经济体建立带有单位收益曲线的图表，并显示在任何因子>赋SH> 0和UH> 0的情况下会发生什么。在这种情况下，您对因子价格了解多少？

d。显示为该经济体设定的生产可能性，并确认关于您在a，b和c中获得的产出的结论。

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2.考虑一个LH> 0劳动单位和KH> 0资本单位的母国。有两种消费商品，以索引！ 2 f0; 1g。好的 ！可以使用生产功能定义的技术生产

F！ （K; L）= x！ K + z！ L，

b。在这两种情况中的每种情况下，可能的均衡相对价格p0 = p1是多少？解释。

C。显示这种经济的勒纳图。形容多元化。在给定价格p0和p1的情况下，KH或LH对商品0和1的产出增加的影响是什么？

d。在一张图中显示两国的生产可能性边界。

e。选取一些p0 = p1 2（x1 = x0; z1 = z0）并使用a中开发的图表来显示如果p0 = p1是均衡价格比率，均衡看起来是什么样的。谁出口什么？您对两国的要素价格了解多少？当贸易中断时，两国中的p0 = p1会发生什么？提示：Örst绘制预算约束，而不是约束曲线；然后逆向工程必须定义什么曲线。

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1. Consider a country with SH skilled workers and UH unskilled workers. There are two Önal goods, indexed by 0 and 1, and the respective production functions are

F0(S;U)=minfS;Ug, F1(S;U)=S+U.

Essentially, workers must work in a team of one skilled worker and one unskilled worker to produce good 0, and they can produce good 1 by themselves. Write p! for the price of good ! 2 f0; 1g and write wS and wU for skilled and unskilled wages.

a. Suppose p0=p1 > 2. Set up a diagram with the unit-revenue curves for this economy and show the possible factor prices (wS;wU) implied by this diagram, assuming that both goods are produced.

b. In the context of a, determine output and factor prices when 0 < SH < UH. Do the sameforthecaseSH >UH >0.

c. Suppose p0=p1 < 2. Set up a diagram with the unit-revenue curves for this economy and show what will happen given any factor endowments SH > 0 and UH > 0. What do you know about factor prices in this case?

d. Show the production possibility set for this economy and conÖrm the conclusions about output you reached in a, b and c.

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2. Consider a home country with LH > 0 units of labor and KH > 0 units of capital. There are two consumption goods, indexed by ! 2 f0;1g. Good ! can be produced using a technology deÖned by the production function

F! (K; L) = x! K + z! L,

whereK0iscapitalandL0islabor. Writep0 andp1 forthepricesofgood0and good 1, respectively, and v and w for the factor prices of capital and labor. Everyone has the same homothetic preferences with indi§erence curves that never hit the axes.

a. In a diagram with output of good 0 on the horizontal axis and output of good 1 on the vertical axis, describe the production possibility frontier of this economy. Carefully label everything and show how the diagram changes as parameters change from z1=z0 > x1=x0 to z1=z0 < x1=x0 (show both diagrams.)

b. What are the possible equilibrium relative prices p0=p1 in each of these two cases? Explain.

c. Show the Lerner diagram for this economy. Describe the cone of diversiÖcation. What is the e§ect of increases in KH or LH on the output of goods 0 and 1, taking the prices p0 and p1 as given?

Now suppose there is also a foreign country with consumers who have the same prefer- ences as consumers in the home country. The endowments of capital and labor in the foreign country are KF 2 (0;KH) and LF = LH, and the technology is the same as in the home country. For the remainder, consider only the case z1=z0 > x1=x0.

d. Show the production possibility frontiers of the two countries in one diagram.

e. Pick some p0=p1 2 (x1=x0; z1=z0) and use the diagram developed in a to show what the equilibrium looks like if this p0=p1 is the equilibrium price ratio. Who exports what? What do you know about factor prices in the two countries? What happens to p0=p1 in each of the two countries when trade is shut down? Hint: Örst draw budget constraints, not indi§erence curves; then reverse engineer what indi§erence curves must be like.

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