# HW3 Solution Key

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## HW3 Solution Key

UCDavis, 160a, Winter 2008 Prof. Farshid Mojaver

The Specific Factors Model and Factor Movement

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 ΔRK/RK ΔPA/PA ΔPM/PM ΔW/W
3.Make an argument that

1. there is tendency for labor to migrate from the rest of the world to US

2. migration improves US GDP but lowers the GDP of the ROW

3. migration is beneficial for the migrants but huts workers in the host country

4. owners of land/capital in the host country are better of as a result of labor migration

5. the world as a whole is better as a result of migration

Answer Key to Q3: Look at Lecture notes
4. In the specific factors model for manufacturing goods and agriculture, consider a decrease in the stock of land. For example, suppose natural disaster decreases the quantity of arable land for planting crops.

1. Redraw Figure 5.12 starting from the initial equilibrium point B.

2. What is the effect of this change on the quantity of labor in each industry and on the equilibrium wage?

3. Now suppose that international community wants to help the country struck by the natural disaster and decides to do so by increasing its level of FDI. That is, the rest of the world increases its investment in physical capital in the stricken country. What is the effect of this policy on the equilibrium wage? What is the total effect on the equilibrium wage of the disaster and subsequent FDI investment (Increase, decrease or ambiguous)? Does the agriculture industry benefit or lose from the FDI?

a).

b). As we could see from the figure, labor hired in Manufacturing industry increases, while labor in agriculture industry decreases. The equilibrium wage also decreases.

c).

Increasing the country’s FDI level would lead to an increase in wage level. While the total effect on the equilibrium wage of the disaster and the subsequent FDI investment is ambiguous and depends on the magnitude of the FDI. For example, when the new VMPL line for Manufacturing industry is the red dash line, the new equilibrium wage W'' is lower than the original equilibrium wage W; when the new VMPL line for Manufacturing industry is the purple dash line, the new equilibrium wage W'' is higher than the original equilibrium wage W; finally when the new VMPL line is the blue solid one, the FDI exactly cancels the negative impact of the disaster on wage, that is, the equilibrium wage keeps the same level as before the disaster. In each case, it is clearly that the agriculture industry is further damaged by the inflow of FDI: its production scale is further decreased because of loss of labor to manufacturing industry.

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