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Chapter 3 Specific Factors and Income Distribution. In chapter 2 we know that international trade make everyone better off. In fact, some people get gains from trade and the other one can be hurt by trade.
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Chapter 3 Specific Factors and Income Distribution
In chapter 2 we know that international trade make everyone better off. In fact, some people get gains from trade and the other one can be hurt by trade. • Recardian Model neglects effects of trade on the distribution of income. The specific factors model allows trade to affect income distribution.
For example: • To understand why governments have protected sectors of the economy from import competition, it is necessary to look at the effects of trade.
商务部部长薄熙来 2005妙语连珠 ·“你给我们的企业加上半斤的压力,我就要给它撤掉八两的负担。” ·“中国出口8亿件衬衫才能买一架空客A380飞机。” ·“老想爬到岸上去寻求保护的人,是很容易感冒的。” ·“欧美对我纺品设限, 马可·波罗都会遗憾……”
There are two main reasons why international trade has strong effects on the distribution of income: • Industries differ in the factors of production they demand. • Resources cannot move immediately or costlessly from one industry to another. • An example: the rice production of Japan.
The specific factors model was • developed by Paul Samuelson • and Ronald Jones in 1971.
-----Paul Samuelson 1970 Nobel Laureate in Economics for the scientific work through which he has developed static and dynamic economic theory and actively contributed to raising the level of analysis in economic science
I am the Professor of Economics at the University of Rochester. My field is international economics and most of my research has been on the pure theory of international trade. -------Ronald Jones
Chapter Organization • The Specific Factors Model • International Trade in the Specific Factors Model • Income Distribution and the Gains from Trade • The Political Economy of Trade: A Preliminary View
The Specific Factors Model (特定要素模型) • 一、The definition of specific and mobile factors • The specific factor (特定要素) is the factor of production that can not move between sectors. • The mobile factor (流动要素) is the factor of production that can move between sectors.
二、Assumptions of the specific factor Model • The economy can produce two goods, manufactures and food. • There are three factors of production; labor (L), capital (K) and land (T ). • Manufactures are produced using capital and labor (but not land).
Food is produced using land and labor (but not capital). • Labor is therefore a mobile factor that can be used in either sector. Land and capital are both specific factors that can be used only in the production of one good. • Perfect Competition prevails in all markets.
三、The production function(生产函数) • How much of each good does the economy produce? We should see the production function. • What is the production of function • The production function for manufactures (food) tells us the quantity of manufactures (food) that can be produced given any input of labor and capital (land).
The production function for manufactures is given by • QM = QM (K, LM) (3-1) • The production function for food is given by • QF = QF (T, LF) (3-2)
The full employment of labor condition • LM + LF = L(3-3) • The economy-wide supply of labor must equal the labor employed in food plus the labor employed in manufactures. • We can use these equations and derive the production possibilities frontier of the economy.
四、Production Possibilities(生产可能性) • To analyze the economy’s production possibilities, we need only to ask how the economy’s mix of output changes as labor is shifted from one sector to the other. • Capital and land are specific factors, do not shift.
Figure 3-1 below illustrates the relationship between labor input and output of manufactures(It is similar for food).
Output, QM QM = QM (K, LM) Labor input, LM Figure 3-1: The Production Function for Manufactures
The shape of the production function reflects the Law of Diminishing Marginal Returns(边际收益递减规律). • Adding one worker to the production process means that each worker has less capital to work with. Therefore, each additional unit of labor will add less to the production of output than the last. That is the marginal product of labor, or diminishing returns.
Marginal product of labor, MPLM MPLM Labor input, LM Figure 3-2: The Marginal Product of Labor (劳动边际产品) • The marginal product of labor, which is the increase in output that corresponds to an extra unit of labor.
The production possibility frontier can be derived by The combination of diagrams of production function for manufactures and for food . • The production possibility frontier shows how much food it can produce for any given output of manufactures and vice versa.
Output of food, QF (increasing ) 1' 2' QF =QF(K, LF) Q2F 3' L2F PP Output of manufactures, QM (increasing ) Labor input in food, LF(increasing ) L Q2M L2M 1 2 3 L AA Labor input in manufactures, LM (increasing ) QM =QM(K, LM) Figure 3-3: The Production Possibility Frontier in the Specific Factors Model Economy’s production possibility frontier (PP) Production function for food Production function for manufactures Economy’s allocation of labor (AA)(劳动分配)
The line AA indicates the allocation of labor between manufactures sector and food sector. • The curve PP shows how the output of the two good varies as the allocation of labor is shifted from food to manufactures.
To increase output of manufactures by one unit, the economy must reduce output of food by MPLF / MPLM (1 / MPL M -----单位工业品所需劳动投入). • The slope of PP(-MPLF / MPLM the opportunity cost of manufactures in terms of food) is the number of units of food output that must be sacrificed to increase manufactures output by one unit.
We can now see why PP has the bowed shape it does, because the slop of PP is different at different position of line.
We have now shown how output is determined, given the allocation of labor. • The next step is to ask how a market economy determines the allocation of labor.
五、Prices, Wages, and Labor Allocation • How much labor will be employed in each sector? we need to look at supply and demand in the labor market. • Demand for labor: • The profit-maximizing employers will demand labor up to the point where the value produced by an additional person-hour equals the cost of employing that hour(wage).
The demand curve for labor in the manufacturing sector can be written: • MPLM× PM = w (3-4) • (The wage equals the value of the marginal product of labor in manufacturing.) • The demand curve for labor in the food sector can be written: • MPLF × PF = w (3-5)
The wage rate must be the same in both sectors, because of the assumption that labor is freely mobile between sectors. • The wage rate is determined by the requirement that total labor demand equal total labor supply: • LM + LF = L (3-6)
Figure 3-4: The Allocation of Labor Wage rate, W Wage rate, W PFX MPLF (Demand curve for labor in food) 1 W1 PMX MPLM (Demand curve for labor in manufacturing) Labor used in manufactures, LM Labor used in food, LF L1M L1F Total labor supply, L
We can see how the wage rate and employment in each sector are determined given the prices of food and manufacture in Figure 3-4.
Relationship between relative prices and output. • At the production point the curve PP must be tangent to a line whose slope is minus the price of manufactures divided by that of food. • -MPLF/MPLM = -PM/PF (3-7) • It derived from equations (3-4) and (3-5) • MPLM× PM = MPLF × PF = w
Output of food, QF 1 Q1F PP Output of manufactures, QM Q1M Figure 3-5: Production in the Specific Factors Model Slope = - (PM /PF)1
Conclusion: • The output of manufactures and foods • are determined by relative prices.
What happens to the allocation of labor and the distribution of income when the prices of food and manufactures change? • There are two cases: • an equal proportional change in prices. • a change in relative prices.
An equal proportional change in prices. • When both prices change in the same proportion, no real changes occur. • The wage rate (w) rises in the same proportion as the prices, so real wages are unaffected. • The real incomes of capital owners and landowners also remain the same.
PF2 X MPLF Wage rate, W PM2 X MPLM Wage rate, W PM1 X MPLM 2 W2 PF1 X MPLF 1 W1 Labor used in manufactures, LM Labor used in food, LF Figure 3-6: An Equal Proportional Increase in the Prices of Manufactures and Food PM increases 10% PF increases 10% 10% wage increase
How about the changes of prices which is not the same in both sectors? Does it effects the welfare or the allocation of resources?
5、A change in relative prices. • When only PM rises, labor shifts from the food sector to the manufacturing sector and the output of manufactures rises while that of food falls. • The wage rate (w) does not rise as much as PM since manufacturing employment increases and thus the marginal product of labor in that sector falls.
Wage rate, W Wage rate, W PF1 X MPLF 2 Wage rate rises by less than 7% W 2 1 PM2X MPLM W1 PM1X MPLM Labor used in manufactures, LM Labor used in food, LF Amount of labor shifted from food to manufactures Figure 3-7: A Rise in the Price of Manufactures 7% upward shift in labor demand
The effect of a rise in the relative price of manufactures can also be seen directly by looking at the curve PP in Figure 3-8. • A rise in the relative price of manufactures shifts the production point from 1 to 2 (higher output of manufactures and lower output of food).
Output of food, QF Q1F 1 Q2F 2 PP Output of manufactures, QM Q2M Q1M Figure 3-8: The Response of Output to a Change in the Relative Price of Manufactures Slope = - (PM/PF)1 Slope = - (PM /PF) 2
How to determine relative prices • of manufactures ?
Equilibrium relative quantities and prices • (均衡的相对产出和相对价格) • Equilibrium relative quantities and prices are determined by the intersection of the relative supply curve RS with the relative demand curve RD in Figure 3-9.
RS: • Since higher relative prices of manufactures lead to higher output of manufactures relative to that of food, we can draw a relative supply curve QM/QF as a function of PM/PF • RD: • Relative demand curve by downward-sloping as mentioned in chapter 2.
Figure 3-9: Determination of Relative Prices Relative price of manufactures, PM/PF RS 1 (PM /PF )1 RD Relative quantity of manufactures, QM/QF (QM /QF )1
六、Relative Prices and the Distribution of Income • Suppose that PM , not Pf ,increases by 10%. Then, we would expect the wage to rise by less than 10%, say by 5% (Figure 3-7). • What is the economic effect of this price increase on the incomes of the following three groups?
Workers • We cannot say whether workers are better or worse off; this depends on the relative importance of manufactures and food in workers’ consumption. • Because workers find that their real wage in term of manufactures, W/PM ,falls; while their real wage in term of food, W/Pf , rises.
Owners of capital They are definitely better off. Because the real wage rate in terms of manufactures has fallen, so that the profits of capital owners in terms of what they produce rises; In the other hand, PM in turn has risen relative to Pf .