Chapter 3
1.
In 1986, the price of oil on world markets dropped sharply. Since the United States is an oil-importing country, this was widely regarded as good for the U.S. economy. Yet in Texas and Louisiana 1986 was a year of economic decline. Why?
It can deduce that Texas and Louisiana are oil-producing states of United States. So when the price of oil on world markets declined, the real wage of this industry
fell in terms of other
goods. This might be the reason of economic decline in these two states in 1986. 2。An economy can produce good 1 using labor and capital and good 2 using labor and land. The total supply of labor is 100 units. Given the supply of capital, the outputs of the two goods depends on labor input as follows:
To analyze the economy ’s production possibility frontier, consider how the output mix changes as labor is shifted between the two sectors. a. Graph the production functions for good 1 and good 2.
Q1 Q (K1 ,L1 )
1
Q2 Q2 (K2 ,L2
)
Production Function for Good 1
100 100
87.4 90
80.7 93.9 80
73.6 70 66
60 57.5 50 48.6 40 38.1 30 20 25.1 10 0 0
Output
0 10 20 30 40 50 60 70 80 90 100
Function for Good 2
Output
Labor Input for Good 1 Production
100 90 80 70 60 50 40 30 20 10 0
0
0
10
52.5
39.8
61.8
69.3
75.8
81.5 86.7
91.4 95.5
100
1
20
30
40
50
60
70
80
90
100
Labor Input for Good 2
b. Graph the production possibility frontier. Why is it curved?
Q2 Q (K ,L )
2
2
2
Q
2
100
L 2
PPF Q
1
100
L
Q1 Q (K1,L1
1
)
1
The PPF is curved due to declining marginal product of labor in each good. The total labor supply is fixed. So as L 2.
1 rises, MPL 1 falls; correspondingly, as L 2 falls, MPL 2 rises. So PP
gets steeper as we move down it to the right.
The marginal product of labor curves corresponding to the production functions in problem2 are as follows:
a. Suppose that the price of good 2 relative to that of good 1 is 2. Determine
graphically the wage rate and the allocation of labor between the two sectors. With the assumption that labor is freely mobile between sectors, it will move from the low-wage sector to the high-wage sector until wages are equalized. So in equilibrium, the wage rate is equal to the value of labor ’s marginal product.
MPL1 P
1
MPL P
2 2
P / P1
2
2
2
The abscissa of point of intersection illustrated above should be between (20, 30). Since we only have to find out the approximate answer, linear function could be employed. The labor allocation between the sectors is approximately L rate is approximately 0.98.
b. Using the graph drawn for problem 2, determine the output of each sector. Then
confirm graphically that the slop of the production possibility frontier at that point equals the relative price.
1=27 and L 2=73. The wage
Q2 Q (K2 , L2
2
)
Q
2
slope
1 2
100
PPF
L 2
Q
1
100
L 1
Q1 Q (K1 , L1
1
)
The relative price is P 2/P1=2 and we have got the approximate labor allocation, so we can employ the linear function again to calculate the approximate output of each sector: Q1=44 and Q2=90.
c. Suppose that the relative price of good 2 falls to 1. Repeat (a) and (b).
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The relative decline in the price of good 2 caused labor to be reallocated: labor is drawn out of production of good 2 and enters production of good 1 (
Ｌ1=62, L 2=38). This also
leads to an output adjustment, that is, production of good 2 falls to 68 units and production of good 1 rises to 76 units. And the wage rate is approximately equal to 0.74.
Q2 Q (K2 ,L2
2
)
Q
2
slope
1 2 1
slope
100
PPF
L
2
Q
1
100
L
1
Q1 Q (K1 ,L1
1
)
d. Calculate the effects of the price change on the income of the specific factors in
sectors 1 and 2.
With the relative price change from P 2/P1=2 to P2/P1=1, the price of good 2 has fallen by 50 percent, while the price of good 1 has stayed the same. Wages have fallen too, but by less than the fall in P 2 (wages fell approximately 25 percent). Thus, the real wage relative to P2 actually rises while real wage relative to P good 2 is needed.
3.
In the text we examined the impacts of increases in the supply of capital and land. But what if the mobile factor, labor, increases in supply?
1 falls. Hence, to determine the welfare
consequence for workers, the information about their consumption shares of good 1 and
4
a． Analyze the qualitative effects of an increase in the supply of labor in the specific
factors model, holding the price of both goods constant.
For an economy producing two goods, X an Y, with labor demands reflected by their marginal revenue product curves, there is an initial wage of w1 and an initial labor allocation of L x=OxA and Ly=OyA. When the supply of labor increases, the right boundary of the diagram illustrated below pushed out to Oy’. The demand for labor in sector Y is pulled rightward with the boundary. The new intersection of the labor demand curves shows that labor expands in both sectors, and therefore output of both X and Y also expand. The relative expansion of output is ambiguous. Wages paid to workers fall.
W
MPLx P
MPL y P
x
y
w
w
1
2
A B
O
y
O
y
b． Graph the effect on the equilibrium for the numerical example in problems 2 and 3,
given a relative price of 1, when the labor force expands from 100 to 140.
With the law of diminishing returns, the new production possibility frontier is more concave and steeper (flatter) at the ends when total labor supply increases. L1 increase to 90 from 62 and L Q2=77.
2 increases to 50 from 38. Wages decline from 0.74 to
1=85 and
0.60. This new allocation of labor leads to a new output mix of approximately Q
5
Q2 Q (K2 , L2
2
)
Q 2
140 100
PPF
L
2
Q
1
140
100
L 1
Q1 Q (K1 ,L1)
1
Chapter 4
1． In the United States where land is cheap, the ratio of land to labor used in cattle rising is
higher than that of land used in wheat growing. But in more crowded countries, where land is expensive and labor is cheap, it is common to raise cows by using less land and more labor than Americans use to grow wheat. Can we still say that raising cattle is land intensive compared with farming wheat? Why or why not?
The definition of cattle growing as land intensive depends on the ratio of land to labor used in production, not on the ratio of land or labor to output. The ratio of land to labor in cattle exceeds the ratio in wheat in the United States, implying cattle is land intensive in the United States. Cattle is land intensive in other countries too if the ratio of land to labor in cattle production exceeds the ratio in wheat production in that country. The comparison between another country and the United States is less relevant for answering the question. 2． Suppose that at current factor prices cloth is produced using 20 hours of labor for each
acre of land, and food is produced using only 5 hours of labor per acre of land. a. Suppose that the economy’s total resources are 600 hours of labor and 60 acres of
land. Using a diagram determine the allocation of resources.
aLC / aT C (LC /QC) / (T C/QC) aLF / aT F (LF /QF) / (T F/QF)
LC /T C LF /T F
LC 20T C
LF 5 T F
We can solve this algebraically since L=LC+LF=600 and T=TC+TF=60. The solution is LC=400, TC=20, LF=200 and TF=40.
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LF
Food
Land
TC
TF
LC
Cloth
Labor
b. Now suppose that the labor supply increase first to 800, then 1000, then 1200 hours.
Using a diagram like Figure4-6, trace out the changing allocation of resources.
L 800: T C 33.33, LC 666.67, T F 26.67, LF 133.33 L 1000 : T C 46.67, LC 933.33,T F 13.33,LF 66.67
L 1200 : T C 60, LC 1200, T F 0, LF 0.( c o m p lsept eec i atl i o zan )
Food
Land
Cloth
0l
1200
0l
1000
0l
800
Labor
c. What would happen if the labor supply were to increase even further?
At constant factor prices, some labor would be unused, so factor prices would have to change, or there would be unemployment.
3.
The world ’s poorest countries cannot find anything to export. There is no resource that “
is abundant — certainly not capital or land, and in small poor nations not even labor is
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abundant.”Discuss.
The gains from trade depend on comparative rather than absolute advantage. As to poor countries, what matters is not the absolute abundance of factors, but their relative abundance. Poor countries have an abundance of labor relative to capital when compared to more developed countries. 4.
The U.S. labor movement — which mostly represents blue-collar workers rather than professionals and highly educated workers — has traditionally favored limits on imports form less-affluent countries. Is this a shortsighted policy of a rational one in view of the interests of union members? How does the answer depend on the model of trade?
In the Ricardo ’s model, labor gains from trade through an increase in its purchasing power. This result does not support labor union demands for limits on imports from less affluent countries.
In the Immobile Factors model labor may gain or lose from trade. Purchasing power in terms of one good will rise, but in terms of the other good it will decline.
The Heckscher-Ohlin model directly discusses distribution by considering the effects of trade on the owners of factors of production. In the context of this model, unskilled U.S. labor loses from trade since this group represents the relatively scarce factors in this country. The results from the Heckscher-Ohlin model support labor union demands for import limits. 5.
There is substantial inequality of wage levels between regions within the United States. For example, wages of manufacturing workers in equivalent jobs are about 20 percent lower in the Southeast than they are in the Far West. Which of the explanations of failure of factor price equalization might account for this? How is this case different from the divergence of wages between the United States and Mexico (which is geographically closer to both the U.S. Southeast and the Far West than the Southeast and Far West are to each other)?
When we employ factor price equalization, we should pay attention to its conditions: both countries/regions produce both goods; both countries have the same technology of production, and the absence of barriers to trade. Inequality of wage levels between regions within the United States may caused by some or all of these reasons.
Actually, the barriers to trade always exist in the real world due to transportation costs. And the trade between U.S. and Mexico, by contrast, is subject to legal limits; together with cultural differences that inhibit the flow of technology, this may explain why the difference in wage rates is so much larger. 6.
Explain why the Leontief paradox and the more recent Bowen, Leamer, and Sveikauskas results reported in the text contradict the factor-proportions theory. The factor proportions theory states that countries export those goods whose production is intensive in factors with which they are abundantly endowed. One would expect the United States, which has a high capital/labor ratio relative to the rest of the world, to export capital-intensive goods if the Heckscher-Ohlin theory holds. Leontief found that the United States exported labor-intensive goods. Bowen, Leamer and Sveikauskas found that the correlation between factor endowment and trade patterns is weak for the world as a whole. The data do not support the predictions of the theory that countries' exports and imports reflect the relative endowments of factors.
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In the discussion of empirical results on the Heckscher-Ohlin model, we noted that recent work suggests that the efficiency of factors of production seems to differ internationally. Explain how this would affect the concept of factor price equalization. If the efficiency of the factors of production differs internationally, the lessons of the Heckscher-Ohlin theory would be applied to “effective factors ”which adjust for the differences in technology or worker skills or land quality (for example). The adjusted model has been found to be more successful than the unadjusted model at explaining the pattern of trade between countries. Factor-price equalization concepts would apply to the effective factors. A worker with more skills or in a country with better technology could be considered to be equal to two workers in another country. Thus, the single person would be two effective units of labor. Thus, the one high-skilled worker could earn twice what lower skilled workers do and the price of one effective unit of labor would still be equalized.
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7.
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