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国际经济学(第九版)特定要素模型CH4 Specific Factors

国际经济学(第九版)特定要素模型CH4 Specific Factors

9979997藏宝阁香港马会 www.shixinhuamu.com
The Specific Factors model

Maarten Bosker

Outline
? Introduction

? The Specific Factors Model
? International Trade in the Specific Factors Model ? Income Distribution and the Gains from Trade ? Political Economy of Trade: a first view - Extension: International Labor Mobility

Introduction
? If trade is so good for the economy (see Ricardian model), why is there sometimes such opposition? ? Two main reasons why international trade has strong effects on the distribution of income within a country:
? Resources cannot move immediately or costlessly from one industry to another ? Industries differ in the factors of production they demand

? The Ricardo model assumes these two away:
? Labor only factor of production in all industries ? Labor can costlessly move between industries

Introduction
? The Specific Factors model relaxes these two assumptions of the Ricardian model ? As we will see, this has important consequences: Countries as a whole still benefit from trade, but it may hurt significant groups within the country (particularly in the short run)
? e.g. workers with specific skills may lose their job and have a difficult time finding a new job in a different industry

The Specific Factors model
The Specific Factors Model

The Specific Factors model
Assumptions of the model: ? ? ? ? ? Two goods (say cloth and food) Three factors of production: labor (L), capital (K) and land (T) Cloth produced using labor and capital Food produced using labor and land Perfect competition in both markets

? Labor is a mobile factor: it can move between sectors ? Land and capital are specific factors: they can only be used in the production of food and cloth resp.

Specific Factors model
? As in Ricardian model, we first focus on what each economy can produce ? Subsequently we can ask what will happen if the country opens up to trade ? We start by asking: how much of the two goods can a country produce?

? This depends on their production technologies ? They can be summarized by a production function

Specific Factors model
? The production function for cloth gives the quantity of cloth that can be produced given any input of capital and labor:

QC = QC (K, LC)
? Similarly, the production function for food gives the quantity of food that can be produced given any input of land and labor: QF = QF (T, LF) ? Where:
? QC and QF are the output of cloth and food resp. ? K is the capital stock ? T is the amount of land available ? LC and LF is the amount of labor employed in cloth and food resp.

Production possibilities
? For example, the production function for cloth (similar for food):

e.g. a Cobb Douglas production function: QC = KαL1-α

Production possibilities
? Why does it look like this? ? The shape of the production function reflects diminishing marginal returns
? Adding one worker to the production process (without increasing the amount of capital) means that each worker has less capital to work with ? Therefore, each additional unit of labor adds less output than the last

? In other words: the marginal product of labor, which is the increase in output that corresponds to an extra unit of labor, decreases with the number of people already employed

Production possibilities
? The marginal product of labor in cloth production (again similar in food production)

Note: this is the derivative of the production function w.r.t. labor (L) !

Production possibilities
? Note, that also: ? Output (QC ) = the area under the marginal product curve

dQc = MPLc dLc

Production possibilities
? For the economy as a whole, the total labor employed in cloth and food must equal the total labor supply (people can only work in one of the two sectors at the same time): LC + LF = L ? How does the economy’s mix of output change as labor is shifted from one sector to the other? ? When labor moves from food to cloth, food production falls while output of cloth rises … but by how much? ? Using the production functions in cloth and food, plus the labor market equilibrium, we can derive the production possibilities frontier of the economy

The production possibilities frontier
QF (increasing ?) Food production function Production possibility frontier(PP) Q2 1'
F

QF =QF(T, LF)

2' 3'

LF (increasing?)

L2F
1

Q2 C

PP

QC (increasing ?)

L2C 2
3 AA Cloth production function QC =QC(K, LC)

Labor allocation(AA)

LC (increasing ?)

Opportunity costs in the Specific Factors Model
? The slope of the PPF measures the opportunity costs of cloth in terms of food: how much food could be produced using the resources now used to produce one unit of cloth ? To produce one extra unit of cloth, we need 1/MPLC units of labor (remember: dQC = MPLC dLC) ? These units of labor could have instead been employed in food production, producing MPLF / MPLC units of food (remember: dQF = MPLF dLF) ? Opportunity cost of producing one extra unit of cloth is -(MPLF / MPLC) units of food

Opportunity costs in the Specific Factors Model
? This is not constant! (as in the Ricardian model, where unit labor requirements
did not depend on the amount already produced)

? It depends on how much food and cloth are already produced ? The opportunity costs of producing a good rises with the amount of the good already produced ? Why? Because of diminishing returns to labor in each sector: ? We need more and more labor to produce one additional unit of a good. Instead we can use this labor also to produce the other good. Since, producing one less good frees up more and more labor, we could have produced more and more of the other good

Opportunity costs in the Specific Factors model

Q3F Q2 F

Q3 C Q2 C

Prices, wages and labor allocation
? How much will each sector produce? ? It is always optimal to use all available land for food production, and all available capital for cloth production. But… how much labor will each sector employ? ? This depends on labor demand and labor supply ? Labor supply is easy: L ? Labor demand: ? In each sector, employers will demand the number of workers that maximizes their profits:

Prices, wages and labor allocation
m ax ? PC Q C ( K , L C ) ? w C L C
LC

?

=> d ? PC Q C ( K , L C ) ? w C L C ? / d L C ? 0
? From this it easily follows that: wC = MPLC PC ? Similarly, for the food sector: wF = MPLF PF

In both sectors: Wages equal the value of the marginal product of labor = an additional worker earns exactly the value of what he/she adds to total production

Prices, wages and labor allocation
We can plot both sectors’ labor demand curves in one Figure
Note: we obtain cloth’s curve by multiplying earlier figure for MPLc by Pc

Prices, wages and labor allocation
? Where the labor demand curves intersect gives us the equilibrium wage and allocation of labor between the two sectors Why?

? The two sectors must pay the same wage because labor can move between sectors
? If the wage were higher in the cloth sector, workers would move from making food to making cloth until the wages become equal ? Or, if the wage were higher in the food sector, workers would move in the other direction

Prices, wages and labor allocation
? This wage equality between sectors also gives us a relationship between relative prices and opportunity costs: ? wF = wC <=> MPLF PF = MPLC PC <=>

-(MPLF/MPLC) = -(PC/PF) ? At the production point the PPF is tangent to a line with slope given by the relative price of cloth in terms of food (with a minus sign) ? This pinpoints the amount produced of both goods =>

Production in the Specific Factors model

What happens when prices change?
? How do the allocation of labor and the distribution of income (among workers, capital owners and land owners) change when the prices of food and cloth change? ? Two cases: 1. A proportional change in prices (prices of both goods increase with the same %) 2. A change in relative prices (prices of both goods change, but each with a different %)

A proportional increased in prices
W PC 1 X MPLC P C
increases by 10%

PC 2 X MPLC

PF 2 X MPLF W
PF increases by 10%

2

W2
Increase by 10% in the salary

PF 1 X MPLF

W1

1

Labor in the cloth sector LC

Labor in the food sector, LF

A proportional change in prices
? Relative prices unchanged: output remains the same

? Wages rise in the same proportion: no reallocation of workers
? Real wages (the ratio of wages to the prices of goods) do not change: ? Workers earn 10% more, but each extra also buys them 10% less of each good (both prices have increase by 10%) ? Also, owners of land and capital can ask 10% more for their output, but also have to pay 10% more to their workers ? No real changes!

A change in relative prices
? Things do change when relative prices change!

?

Suppose that the price of cloth rises, whereas the price of food remains the same
Relative price of cloth goes up Now what happens? 1. Allocation of labor between sectors changes 2. Welfare of workers, land owners and capital owners changes

? ?

=>

A change in relative prices

A change in relative price
? Increase in price of cloth, will result in an increase in wages paid in the cloth sector ? This attracts people from the food sector who start working in the cloth sector ? In the end… wages will not rise as much as prices. Why not?
? MPLc drops because more people now work in the cloth sector; and remember that wc = MPLc Pc ! ? Intuition: higher wages attract more workers, but because more people want to work in cloth now, employers can reduce wages a bit and still get enough people to do the job

A change in relative prices
? Also, cloth output will rise

A change in relative prices
Summing up: If relative price of cloth goes up, ? ? ? ? Wages go up, but less than prices Some people move from food to cloth sector Cloth output rises Does everybody gain from this, or not?

Income distribution and a change in relative prices
? What does this mean for the welfare of workers, land owners and capital owners? ? Capital owners are better off
1. They earn more: output goes up, and the price of cloth rises by 10% whereas wages only rise by 7% 2. Also: they can buy more food for a given amount of cloth they produce (relative price of cloth has risen)

? Land owners are worse off
1. They earn less: output goes down, and wages rise by 7% whereas the price of food unchanged 2. Also: they can buy less cloth for a given amount of food they produce (relative price of cloth has risen)

Income distribution and a change in relative prices
? Finally, workers 1. Wages go up, but 2. Price of cloth has gone up even more so that they can buy less cloth: relative wage in terms of cloth falls 3. But, since price of food remains unchanged, they can buy more food: relative wage in terms of food rises Ambiguous whether they are better off or not, it depends on their preferences for food and cloth
?
?

?

If they really like food, so that food is a very large part of their consumption, they will be better off If they really like cloth, they will be worse off

Income distribution and a change in relative prices
? More general:

In the Specific Factors model, a change in relative price will
? Benefit the owners of the factor specific to the sector whose relative price increases ? Hurt the owners of the factor specific to the sector whose relative price decreases

? And, the effect on the mobile factor is ambiguous

The Specific Factors model
Trade in the Specific Factors Model

Trade in the Specific Factors model
? Suppose a country opens up to trade, when will it actually start trading? When world relative prices are different from the prevailing prices without trade

? Why?
If they are the same, the country is equally well off producing all its goods itself
? No good from other countries is cheaper to import ? And, no other country will find one of the country’s goods particularly attractive (no exports)

Trade in the Specific Factors model
? To see if relative prices change due to trade, we first need to know the prevailing relative prices when a country does not trade (relative prices in autarky) ? (as always) these prices are determined by relative demand (RD) and relative supply (RS) ? Relative demand (RD): if relative price of a good goes up, relative demand of that good goes down ? Relative supply (RS): if relative price of a good goes up, relative supply goes up => together RS and RD determine prices =>

Relative prices in autarky

Relative prices with Trade
? When a country opens up to trade, prices change because

1. Relative demand changes: people in other countries have different preferences than those in your own country (e.g. at the same relative prices they are willing to buy more cloth and less food)
2. Relative supply changes: firms in other countries can produce goods at higher or lower cost than firms in your own country ? different technologies (Ricardian model) ? different resources (amount of land, labor or capital)

How does trade change relative prices?
? For simplicity: assume preferences are the same all over the world, so that relative demand does not change ? Suppose that for a given relative price of cloth in terms of food, the foreign country is willing to produce relatively less cloth, because it is for example ? less productive in cloth production (less skills / technology) ? more productive in food production (more skills / technology) ? less capital per worker (more workers/machine = less efficient) ? more land per worker (fewer workers/acre = more efficient) ? In this case the world’s RS curve lies to the left of the country’s own RS curve, and opening up to trade changes relative prices =>

How does trade affect relative prices?
? The relative price of cloth in the country goes up!

How does trade affect relative prices?
? Why?

? The country can produce cloth relatively cheaply, because it for example:
? is more productive in cloth production than the rest of the world ? has more capital / worker available to produce cloth

? As a result, prices for cloth in the country are relatively low compared to the rest of the world ? When it opens to trade: other countries start to buy cloth in the country, this increased demand raises the price of cloth

Gains from Trade The SpecificFactors Model ?!? Factors model in the Specific
Home Foreign Free Trade

+

? =

Gains from trade?
? Without trade the country’s production of cloth and food (QC and QF) necessarily equals its consumption (say DC and DF): ? QF = QF and DF = DF ? With trade it becomes possible to produce more/less than consumed and export/import the rest ? In particular, in our example, the country starts to produce more cloth and less food (relative price of cloth goes up) ? It can consume all this, but it can also start to export cloth (selling it at P2C) and import food (buying it at P2F) ? Is it better of when doing this?

Gains from trade?
? Well, first of all it cannot spend more than it earns: PC x DC + PF x DF = PC x QC +PF x QF ? Rewriting this budget constraint gives a relationship between a country’s imports and exports:

(DF - QF) = (PC / PF) x (QC – DC )
? This tells us how much a country needs to export in order to finance its imports
? if it sells one more unit of cloth on world markets it gets PC for it, with this money it can buy (PC / PF) units of food in return

Gains from trade!
? Without trade it produces and consumes Q2F and Q2C

?

With trade it produces Q1F and Q1C

Q2 F
It can always trade these goods and consume any bundle of goods along the budget constraint ? So also those in the blue area, where both the amount of cloth and food consumed are larger than in autarky !
slope = -P2c/P2F

Q2 C

Country as a whole always gains from trade!

Gains from trade!... but not for all?
? Trade always benefits a country as a whole (i.e. it expands consumption possibilities). Unfortunately, this does not mean that everybody gains from trade ? Trade has strong effects on the income distribution within a country ? Why? Remember that trade changes relative prices!
? Benefit the owners of the factor specific to the sector whose relative price increases: the exporting sector ? Hurt the owners of the factor specific to the sector whose relative price decreases: the sector that faces toughest competition from imports ? Effect on mobile factors is ambiguous

Income (re)distribution and the Gains from Trade
? However, trade benefits a country as a whole by expanding choices ? Possible to redistribute income so that everyone gains from trade! ? Those who gain from trade could compensate those who lose and still be better off themselves.

? That everyone could gain from trade does not mean that they actually do – redistribution usually hard to implement

Trade and Income redistribution
? Trade creates winners and losers in the Specific Factors model ? In the real world this effect of trade may actually be smaller or larger

? Why smaller? ? The specific factors cannot move to the other sector (completely immobile) ? In the real world this is usually not the case: people can acquire new skills, machines can be changed, land can be replanted or used to build a factory on => Heckscher-Ohlin model

Trade and unemployment
? Why larger?

? Opening to trade shifts jobs from import-competing to exporting sectors
? In the Specific Factors model, workers move costlessly between sectors ? However, in the real world this may not happen instantaneously
? Finding new jobs in the exporting sector may not be easy

? Opening to trade may lead to an increase in (short-run) unemployment

Trade and unemployment – some evidence
In the US at least, this effect appears to be relatively small: ? From 1996 to 2008, only about 2.5% of involuntary displacements stemmed from import competition or plants moved overseas ? Also there is little correlation between import penetration and unemployment:

The Political Economy of Trade (see Ch.9-12)
? We just saw that trade creates winners and losers, but that it increases welfare in a country as a whole ? Role for the government to provide a safety net for groups losing a lot from trade (e.g. low-skilled workers in the EU) ? This is not easy: ? Identifying losers and winners is not easy ? Optimal trade policy must weigh one group’s gain against another’s loss ? Actual trade policy often dominated by small interest groups (farmers in the EU), whereas those that gain from trade (typically all consumers!) are much less informed and organized to counterlobby
(see the striking example on p.98 of the book, or…)

Summary: Trade & the Specific Factors model
1 International trade often has strong effects on the distribution of income within countries -- produces losers as well as winners

2 Income distribution effects arise for two reasons: ? Factors of production cannot move costlessly and quickly from one industry to another ? Changes in an economy’s output mix have differential effects on the demand for different factors of production
3 International trade affects the distribution of income in the specific factors model ? Factors specific to export sectors in each country gain from trade, while factors specific to import-competing sectors lose. ? Mobile factors that can work in either sector may either gain or lose

Summary: Trade & the Specific Factors model
4 Trade nonetheless produces overall gains in the sense that those who gain could in principle compensate those who lose while still remaining better off than before 5 Most economists would prefer to address the problem of income distribution directly, rather than by restricting trade 6 Those hurt by trade are often better organized than those who gain, causing trade restrictions to be adopted that are far from “optimal”

The Specific Factors model
Adapting the Specific Factors model:

International Labor Mobility

International Labor Mobility
? So far, labor can move freely between sectors within a country, but not between countries ? Not such a bad assumption, as in the real world restrictions on international labor mobility are very severe
(it is much easier to move goods, capital or money across borders)

? However, if workers were allowed to migrate, what would happen to income in the two countries. Who benefits, and who loses? ? The Specific Factors model can be adapted to analyze these questions:

International Labor Mobility
? Suppose two countries each produce the same good (food) using land and labor (with diminishing returns to labor) ? NOTE: no trade because both countries produce the same good ? But, workers may want to move to the other country (trade in factors of production instead of in goods)

? Why? They might be able to earn higher real wages in one country compared to the other
? Technology differences ? Different land to labor ratios

International labor mobility
? People move across border until real wages are equal in the two countries: you can buy the same things for your wages in both countries (equal purchasing power of wages) ? Suppose initially more people live and work in Home than in Foreign: OL1 in Home > L1O* in Foreign
? In each country real wages are determined by the MPLF (remember that wF = PF MPLF <=> (wF / PF) = MPLF) ? The MPL depends on the technology of each of the two countries, and, because of diminishing returns, it falls the more people are already working in the food sector

International labor mobility – real wages
? Without labor mobility: real wage in Home lower than in Foreign (C < B) If people can migrate, what happens? They move from Home to Foreign! When does this stop? When real wages in the two countries are equal (A) What happens? Who gains and who loses?

? ? ? ?

?

International labor mobility – winners and losers
? Workers initially in Home gain (also those who moved to Foreign): their real wage rises Workers initially in Foreign lose: their real wage falls Output in Foreign rises (+dQF) Output in Home falls (-dQH) But, overall world output rises (red triangle): labor moves to places where it is more productive! Landowners in Foreign gain, their output rises + they pay lower wages Landowners in Home lose, their output falls + they pay higher wages

?

? ? ?

+dQF

-dQH

? ?

International labor mobility – some evidence
? Does migration lead to the wage changes predicted? ? Over the 1870 – 1913 period, migration did move the world toward more equalized real wages

International labor mobility – some evidence
? Immigration in the US has come and gone and come again

? Immigrants as % of total US population in the 20th century:

Immigration in the US economy
? Recent migration, mostly concerns workers with the lowest skill levels: increase in the supply of low-skilled workers ? If anything, what did this do? ? reduced real wages for low-skilled US workers (increased competition with immigrants), while raising real wages for the more educated (goods/services produced by lowskilled workers become cheaper) ? widening income gap between high and low skilled workers



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