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Suggested solutions for the chapter four problems

 1.          Use a general equilibrium depiction of trade equilibrium in the HO model to prove that complete specialization in the production of exports will, in general, lower the standard of living of an economy relative to that found in free trade.

 The country depicted below is in trading equilibrium. Autarky production and consumption occurs at point P0. Once trade begins, equilibrium production occurs at point P1, with increased soybean production and decreased textile production. At the international price ratio PS /PT, consumption occurs at C, which is clearly higher than the country could have attained at P0. Suppose producers were forced to produce at point P2, representing complete specialization in production. The price line (with the same slope*) going through P2 would represent the country's trading opportunities, or its consumption possibilities. Given the country's community indifference curves as drawn, there would be no possible consumption point that would make it as well off as it would be when consuming at point C. Therefore, complete specialization would lead to a lower standard of living relative to free trade.

* A small country could export more without depressing the world price. But a large country would face a flatter TOT (lower Px/Py), placing them on a still lower CIC.



2.          Some have argued that the factor price equalization theorem implies that American wages must fall to the level of those found in the least developed countries of the world. Comment on the validity of this statement.

 The factor price equalization theorem holds in the HO model because of certain assumptions. Specifically, the assumption of identical production techniques leads to the result that workers everywhere will have the exactly the same productivity.  When trade begins, there will be only one price for the good. Hence, these equally productive workers will earn identical wages (because the wage equals the value of the worker's marginal product).

 In reality, workers in different countries have very different productivities and receive different wages according to those productivities. Labor in the United States is more productive than labor in, say, Mexico, and receives a correspondingly higher wage.

3.          Consider the following data on the factor endowments of two countries, A and B:

Factor Endowments A B
Labor force 
(millions of workers)
45 20
Capital stock 
(thousands of machines)
15 10
L/K (workers/machine) 3,000 2,000
K/L (machines/worker) 1/3000 1/2000

Which country is relatively capital abundant? Which country is relatively labor abundant? Suppose that good S is capital intensive relative to good T. Which country will have comparative advantage in the production of S? Explain.

Note that country A has both more labor and more machines than country B. But country A's labor/capital ratio is three thousand-to-one (45,000,000/15,000), while B's is only two thousand-to-one. Thus country A is relatively labor abundant, and country B must be relatively capital abundant. (In other words, country A has three thousand workers for every machine , while country B has two thousand workers per machine.) From the HO theorem, we know the labor-abundant country A will have comparative advantage in the relatively labor-intensive good (T), and the capital-abundant country B will have comparative advantage in the relatively capital-intensive good (S).

 4.          Compare and contrast the classical and HO theories of the commodity composition of trade. Discuss differences in assumptions, post trade production points, and the effects of trade on the distribution of income.

Assumptions: classical theory assumes that labor is the only relevant factor, and that the production of goods in each country requires different amounts of labor input (i.e. technology differs). Thus, labor in the two countries has different productivities -- but these (per unit) input requirements are constant at all levels of output. The HO theory assumes there are two factors, labor and capital, but that technology is exactly the same for each good in both countries. The result is that the classical model reflects constant opportunity costs in production and a straight line PPF, while the HO model reflects increasing opportunity costs and a bowed, or curved PPF.

Production points: From constant opportunity costs and straight line PPF in the classical model, each country will specialize in its comparative advantage good once they begin trading. In the HO model, each country will increase production of its comparative advantage good and export it in exchange for its comparative disadvantage good, but production is not likely to be completely specialized. This is because increasing opportunity costs are incurred as production of either good expands.

Effects of trade on factors: In the HO model, the abundant factor gains from trade since the increased demand (due to trade) for the good that uses its services intensively tends to push up its remuneration (wage or rent) relative to the scarce factor's. On the other hand, the scarce factor loses from trade since consumers are now able import the good that uses the scarce factor intensively. This means that local production of that good will drop and demand for the services of the scarce factor will decline.

Under both models the welfare of the nation rises. With the classical model, everyone gains. Under the assumptions of the HO model, the abundant factor gains more than the scarce factor loses. Thus it would be possible for the winners to compensate the losers, and make everyone better off. Of course, we do not insist that this compensation actually occur. Should we?

 5.          Australia is land abundant; India is labor abundant. Wheat is land intensive relative to textiles. Graphically demonstrate the pre- and post-trade equilibria between these two countries. Find and label the trade triangles for each. Which factors gain and which factors lose when trade arises between these two countries? Explain carefully.

The trade triangles for each are bcd (Australia) and nop (India). Note that bc=op and cd=on for balanced trade. In Australia, landowners (the abundant factor) gain from trade, while labor (the scarce factor) loses from trade. In India, labor (the abundant factor) gains from trade, while landowners (the scarce factor) lose from trade. The argument is the same as in the last part of question 4 (above). Note that the relative price shown in the graph as Pw/Pt is the relative price of wheat.


6.          One of the important changes in the world economy over the past three decades has been the rapid increase in capital investment in the countries of the Pacific Basin (notably Japan and Korea). What are the implications of this investment for the commodity patterns of trade of these two countries say with respect to the US? Explain carefully. (Hint, think about the Rybczynski theorem.)

The Rybczynski theorem tells us that countries that save and invest relatively large amounts in new capital will tend to produce more capital intensive goods over time. Why relatively large amounts? Remember, population grows and other countries can be expected to invest in their own economies as well. As a result of savings and investment rates in these countries that are very high and larger than those in the US, we should expect to import relatively more capital intensive goods (electronics, autos) from these countries as their PPFs change. In return, the goods we export to them will change as well (more technology intensive).

7.          Explain carefully why the assumption of identical technology worldwide eliminates the classical basis for international trade

If technology is the same for all goods in all countries, then the labor required to produce one unit of output in every country is the same and there are no differences in productivity across countries. In terms of our model, this means that the PPFs for both countries will have the same slope, and consequently the same pretrade price ratio. If two countries have the same autarky price ratios, there are no comparative advantage or disadvantage goods, and no reason to trade.

8.        Use the Rybczynski theorem to prove that the more dissimilar countries become in their factor endowments, the more likely is complete specialization to obtain once trade begins.

Suppose the capital abundant country increases its stock of capital and holds labor constant, while the labor abundant country increases its labor force and holds capital constant. The Rybczynski theorem says that the increasingly capital abundant country will produce more and more of the capital intensive good and less of the labor intensive good, thereby expanding its desire to trade. Similarly, the labor abundant country will produce more and more of the labor intensive good and less of the capital intensive good, also expanding trade. Eventually, each country could accumulate enough capital or labor, respectively, so that they are completely specialized in production and are dependent on trade for consumption of their comparative disadvantage goods.

9.          Answer the questions in exercise 3 using the following data on factor endowments of countries C and D:

Factor Endowments C D
Labor force 
(millions of workers)
12 30
Capital stock 
(thousands of machines)
48 60
L/K (workers/machine) 250 500
K/L (machines/worker) 1/250 1/500

Country C has 250 workers per machine (12,000,000/48,000) , while country D has 500 workers per machine. Thus country C is relatively capital abundant and country D is relatively labor abundant. Based on the HO theorem, we know country C will have a comparative advantage in producing S, the capital intensive good.

10.        Based on the information in Item 4.2 and your knowledge of the HO model, what types of goods would you expect Kenya or India to have a comparative advantage in? What about Norway or Japan?

Kenya and India are relatively labor abundant, so they will have a comparative advantage in producing labor intensive goods. Examples could include apparel and leather products (see the table in Item 4.1). Norway and Japan are relatively capital abundant. Their comparative advantage will lie in capital intensive products.

11.        Suppose that country A is labor abundant. It can produce two goods, X and Y. Good X is capital intensive relative to good Y. (a) Derive A's PPF and determine the pretrade relative price of X in terms of Y. (b) Now, suppose that there is technological innovation that makes capital more productive in the X industry, but not in making Y. In a separate diagram, illustrate what would happen to A's PPF and explain your result. Show as well what would happen to the pretrade relative price of X in A. How might this affect A's trade patterns? Explain.

(a) Y is the labor-intensive good. Thus, A's PPF is long along the y-axis. This implies that A has a comparative advantage in Y and a disadvantage in X. A's autarky price of X, Px/Py, is relatively high.

(b) The effect of the innovation is to shift A's PPF to the right along the X axis. Since the innovation has no effect on capital productivity in industry Y, the country's ability to produce Y will not change. The effect of this invention is to lower the pretrade price of X in A. If the price falls enough, that is, if the invention causes a sufficiently high increase in A's ability to produce X, A could become an exporter of X and an importer of Y (provided that the new technology is not available to other countries).

12.        The assumption of identical tastes in the HO model increases the likelihood that comparative advantage will be determined by international differences in factor endowments. True or false? Explain.

True. This point is illustrated in Figure 4.6 of the text, where it is shown how difference in tastes and, hence, demand could reverse the direction of comparative advantage.

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