HW3 Solution Key



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HW3 Solution Key

UCDavis, 160a, Winter 2008 Prof. Farshid Mojaver


The Specific Factors

1. Suppose that there are three factors: Capital, Labor, and Land. Bread requires inputs of land and labor, while steel requires capital and labor.

a. Which factors are mobile and which are specific?

b. Assume that Canada’s endowments of land and capital are 10 units of capital and

100 land, while the U.S.’s are 50 units of capital and 100 land. Which good does each country export? Why?



c. How does trade affect the returns to land, labor, and capital in the U.S. and in

Canada? (Be sure to provide the details on whose real incomes go up or down,

which prices go up or down in which countries, and, if the effects are

indeterminate, then explain why.)


a. Labor is the “mobile” factor because it is used in both sectors. Therefore, it is assumed to be perfectly mobile within the country. Capital is a specific factor for the steel-producing sector because it can only be used to produce steel. Land is a specific factor in the bread-producing sector because it can only be used to produce bread.
b. Canada is relatively land abundant because its ratio of the two specific factors, land to capital, is T/KCAN = 100/10 = 10 > 2 = 100/5 = U.S.’s ratio of land to capital. The

U.S. is relatively capital abundant because its ratio of capital to land is K/TU.S. =

50/100 = ½ > 1/10 = 10/100 = Canada’s ratio of capital to land.

Therefore, Canada’s comparative advantage is in exporting of bread because it is the good that requires the specific factor, land, in production and Canada has land in relative abundance to capital, as compared to the U.S above. Likewise, the U.S. will export steel because its production requires the specific factor, capital, which the U.S. has in relative abundance, compared to Canada.



c. In the U.S. trade implies the export of steel, raising the relative price of steel [(PS/PB)US increases]. In the specific factors model, this implies that the mobile factor, labor, will move from bread production and into steel production because it is more lucrative. This labor movement eventually equalizes wages at a higher equilibrium wage rate (w* increases). However, the price of steel increases more than wages because the labor demand schedules are downward sloping. Thus, capital owners increase the production of steel and increase the productivity of these machines because they now have more laborers to work the night shift. Therefore, the rate of return to owning a machine (MPK = rK) increases for these capitalists. Additionally, the price of bread decreases (relatively) so capitalists enjoy both higher rental rates of capital ownership and higher purchasing power (with respect to both goods but it is a bit more complicated with respect to steel). Thus, U.S. capitalists are definitively better off.
Unfortunately, labor leaves the U.S. bread sector, making the land less productive with fewer itinerant farmers to tend it. Therefore, the rate of return to owning land, or “land rents” (MPT = rT) decreases in the U.S. Additionally, relative prices of steel have gone up so landowners’ real incomes fall. U.S. landowners are definitively worse off.

In Canada, bread prices increase, relative to steel prices. [(PS /PB)CAN decreases.]

This draws Canadian labor out of the steel factories and into the fields to tend the

wheat crops. (Canadian workers cannot move to U.S.) This makes Canadian land more productive and land rents (MPT = rT) go up in Canada. This, combined with a relative decrease in the Canadian price of steel, due to competition with U.S. imports, and an increase in the price of bread that is not as great as the increase in land rents, makes Canadian landowners definitively better off in terms of real income. Unfortunately, Canadian capitalists are definitively worse off. The relative price of steel decreases and labor leaves, leaving machines standing idle during the night shift. This decreases the productivity of those machines and therefore decreases the rental rate of capital ownership (MPK = rK decreases). At the same time the price of bread increases and the price of steel does not decreases as much as the rental rate of capital. Therefore, Canadian capitalists have less purchasing power and lower real incomes with respect to both goods.



The effect of trade on laborers in both countries is indeterminate. For all workers, in both countries, nominal wages have gone up (w* increases). However, for U.S. workers real incomes with respect to bread have gone up [(w/PB)US increases], while real wages with respect to steel products have gone down [(w/PS)US decreases]. For Canadian workers, real wages with respect to bread have gone down [(w/PB)CAN increases], while real wages with respect to steel products have gone up [(w/PS)CAN increases]. So, the real effects on their standard of living depend on the mix of these products that each group of workers consumes (depends on their tastes or preferences). If Canadians consume very little bread, relative to steel, they can still be better off. If Americans consume very little steel, relative to bread, they can be better off. Unfortunately, if such is not the case then workers of either nationality may be worse off. (Note: Graphs, like Figure 3-7 for each country, might be helpful in answering this question but they were not required.)
2. In the specific factors model, again suppose that the relative price of manufactured goods decreases. That is, assume that the price of agricultural goods increases while the price of manufactured goods is unchanged (i.e. ΔPA/PA > 0 and ΔPM/PM = 0). Arrange the following terms in ascending order:
ΔRT/RT > ΔPA/PA > ΔW/W > 0 = ΔPM/PM > ΔRK/RK


  1. In the (standard) Specific Factors Model, analyze the effects on factor prices of an increase in the relative price of good X. That is,

    1. Show how a rise in the price of good X, holding the nominal price of good Y constant, would change the market equilibrium values of the

      1. nominal wage

      2. nominal rental on capital employed in X

      3. nominal rental on capital employed in Y

      4. real wage

      5. real rental on capital employed in X

      6. real rental on capital employed in Y

Use the usual Specific Factors diagram to help you get your results, together with other relationships that you know must hold, but also be sure to say explicitly what you have found and why.
Holding the price of good Y constant, the rise in price of good X shifts the W = PXMPLX curve (labor demand curve for the X sector) upward, as shown below:



Thus, the rise in PX causes more labor to be employed in the X sector (LX rises) and less in the Y sector (LY falls). These changes in turn, since capital stocks in the sectors are fixed in the specific factors model, mean that the ratios of capital to labor, on which marginal products depend, change as follows:

KX/LX falls

KY/LY rises.

It follows, since in each sector MPL rises with K/L and MPK falls with K/L, that

MPLX falls MPLY rises

MPKX rises MPKY falls

From the figure we see immediately that the nominal wage rises, from W1 to W2, as does the nominal rental price of capital in the X sector (since the triangle above W2 and below PX'MPLX is larger, meaning that payments to X-sector capital increase, while the quantity of capital there has not changed), while the nominal rental price of capital in the Y sector falls (the triangle for it gets smaller).


As for real factor prices, these can be inferred from the ratios of their nominal prices to goods prices, which are equal to marginal products, as shown in the list below.
W = PXMPLX = PYMPLY rises, from figure

RX = PXMPKX rises, from figure, or because PX and MPKX both rise

RY = PYMPKY falls, from figure, or because MPKY falls
W/PX = MPLX falls

W/PY = MPLY rises

hence effect on real wage is ambiguous
RX/PX = MPKX rises

RX/PY = (RX/PX)(PX/PY) rises, since both terms rise

hence real rental on X-sector capital rises
RY/PY = MPKY falls

RY/PX = (RY/PY)/(PX/PY) falls, since numerator falls and denominator rises



hence real rental on Y-sector capital falls


    1. We still assume that the relative price of good X increases due to trade. Which of your answers would be changed if it was the nominal wage that was fixed, instead of the nominal price of Y? (Hint: in this case, since W = PXMPLX = PYMPLY, and since the shift of labor into the X sector has caused MPLX to fall and MPLY to rise, the constant wage requires that PX rises while PY falls.

Now the figure is a little bit more complicated. In addition to what is shown above, we would need to lower the price of good Y to get W back where it started. Just note that real variables are unaffected by nominal ones, so the answers for real factor prices must be the same as above. (Each ratio of a factor price to a goods price depends just on a real marginal product and, in some cases, the relative prices of the goods, but never on any nominal prices alone.)

W = PXMPLX = PYMPLY, and since the shift of labor has caused MPLX to fall and MPLY to rise, the constant wage requires that PX rise while PY falls. Thus RX = PXMPKX rises, since both PX and MPKX rise, and RY = PYMPKY falls, since both PY and MPKY fall.

Hecksher_Ohlin Model

Jeopardy Answers

  1. term used to describe Argentina if Argentina has more land per unit of capital than Brazil.

Land abundant country

  1. term used to describe aluminum production when aluminum production requires more energy per unit of capital than steel production.

Aluminum is an energy intensive industry

  1. general term used to describe the amount of a factor needed to produce one unit of a good.

Unit Factor Requirement

  1. the two key terms used in the Heckscher-Ohlin model; one to compare industries, the other to compare countries.

Labor (capital) intensive industry; labor (capital) abundant country

  1. term used to describe when the capital-labor ratio in an industry varies with changes in market wages and rents

Variable factor proportions

  1. term describing the ratio of the unit-capital requirement and the unit-labor requirement in production of a good.

Capital intensity

  1. the assumption in the Heckscher-Ohlin model about unemployment of capital and labor. Zero

  2. interpretation given for the slope of the production possibility frontier.

Opportunity cost of production (Y in terms of X)

  1. the H-O model theorem that would be applied to identify the effects of a tariff on the prices of goods and factors. Stolper-Samuelson Theorem


I. MC Question: 1.D, 2.B, 3.D, 4.C, 5.C, 6.B, 7.B

True False questions

Question1

“Opening up free trade does hurt people in import-competing industries in the short run. But in the long run, when people and resources can move between industries, everybody ends up gaining from free trade.”



False – Opening up free trade is likely to hurt some people. Owner of specialized factors in import-competing industries and owners of factors used intensively in import-competing industries will lose from free trade both in the short and in the long run.
Question2

“American workers gain from free trade with China because free trade lowers prices of clothing in the United States and American workers spent very large portion of their income on clothing”



False – Free trade lowers clothing prices in the United States but it lowers real wage of American worker too. Since wage income is the main source of American workers we may conclude that their income goes down with opening up trade with China.


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