© 2007 Pearson Addison-Wesley. All rights reserved Chapter 4 Technology and International Income Distribution: The Ricardian Model

© 2007 Pearson Addison-Wesley.All rights reserved

Chapter 4

Technology and International Income

Distribution: The Ricardian Model

Copyright © 2006 Pearson Addison-Wesley. All rights reserved.

A One Factor Ricardian Model (cont.)

1. Labor is the only resource important for production.

2. Labor productivity varies across countries, usually due to differences in technology, but labor productivity in each country is constant across time.

3. The supply of labor in each country is constant.

4. Only two goods are important for production and consumption: food and clothing.

5. Labor Theory of Value: competition allows laborers to be paid a “competitive” wage, a function of their productivity and the price of the good that they can sell, and allows laborers to work in the industry that pays the highest wage.

6. Only two countries are modeled: domestic and foreign.



• Because labor productivity is constant, define a unit labor requirement as the constant number of hours of labor required to produce one unit of output.

aLF is the unit labor requirement for food in the domestic country. For example, if aLF = 2, then it takes 2 hours of labor to produce one liter of food in the domestic country.

aLC is the unit labor requirement for clothing in the domestic country. For example, if aLC = 1, then it takes 1 hour of labor to produce one kg of clothing in the domestic country.

A high unit labor requirement means low labor productivity.



• Because the supply of labor is constant, denote the total number of labor hours worked in the domestic country as a constant number L.


Production Possibilities

• The production possibility frontier (PPF) of an economy shows the maximum amount of a goods that can be produced for a fixed amount of resources.

• If QC represents the quantity of clothing produced and QW represents the quantity of food produced, then the production possibility frontier of the domestic economy has the equation:

aLCQC + aLFQF = L

Total units of food production

Labor required for each unit of clothing production

Total units of clothing production

Labor required for each unit of food production

Total amount of labor resources


Production Possibilities (cont.)


Production Possibilities (cont.)

aLCQC + aLFQF = L

• QC = L/aLC when QF = 0

• QF = L/aLF when QC = 0

• QF = L/aLF – (aLC /aLF )QC: the equation for the PPF, with a slope equal to – (aLC /aLF )

• When the economy uses all of its resources, the opportunity cost of clothing production is the quantity of food that is given up (reduced) as QC increases: (aLC /aLF )

• When the economy uses all of its resources, the opportunity cost is equal to the absolute value of the slope of the PPF, and it is constant when the PPF is a straight line.


The Ricardian Production Possibilities Schedule

• The slope is the ratio of labor coefficient aLC/aLF.

• Before International trade, the country produces and consumes at A, with welfare level shown by the indifference curve y0.


The Ricardian Production Possibilities Schedule


Production, Prices and Wages

• Let PC be the price of clothing and Pf be the price of food.

• Because of competition, hourly wages of clothing makers are equal to the market

value of the clothing produced in an hour: Pc /aLC

Price=Marginal cost=alc*W

hourly wages of food makers are equal to the market value of the food produced in an hour: Pf /aLF

• Because workers like high wages, they will work in the industry that pays a higher hourly wage.


Production, Prices and Wages (cont.)

• If PC /aLC > Pf/aLF workers will make only clothing. If PC /Pf > aLC /aLF workers will only make clothing.

The economy will specialize in clothing production if the price of clothing relative to the price of food exceeds the opportunity cost of producing clothing.

• If PC /aLC < Pf /aLF workers will make only food. If Pf /PC > aLF /aLC workers will only make food.

The economy will specialize in food production if the price of food relative to the price of clothing exceeds the opportunity cost of producing food.


Production, Prices and Wages (cont.)

• If the domestic country wants to consume both food and clothing (in the absence of international trade), relative prices must adjust so that wages are equal in the food and clothing industries. If PC /aLC = Pf /aLF workers will have no incentive to flock to

either the clothing industry or the food industry, thereby maintaining a positive amount of production of both goods.

PC /Pf = aLC /aLF

Production (and consumption) of both goods occurs when relative price of a good equals the opportunity cost of producing that good.


Trade in the Ricardian Model

• Suppose that the domestic country has a comparative advantage in clothing production: its opportunity cost of producing clothing is lower than it is in the foreign country.

aLC /aLF < a*LC /a*

LF

where “*” notates foreign country variables

When the domestic country increases clothing production, it reduces food production less than the foreign country does because the domestic unit labor requirement of clothing production is low compared to that of food production.

4-14Copyright © 2007 Pearson Addison-Wesley. All rights reserved.

Figure 4.2 Free-Trade Equilibrium


Free-Trade Equilibrium

• Autarky equilibrium: point A for home and point A* for foreign.

• Equilibrium terms of trade are the slope of dashed lines.

• Free trade: Home produces at E and consumes at B.

• Free trade: Foreign produces at E* and consumes at B*.

• Each country gains from trade.

• The trade triangles match.


Country Size

• Does the assumption of constant labor costs necessarily require each country to become completely specified with trade?

• No.

• Country size matters.

• Two countries, a large one and a small one, trade.

• The small one cannot provide the good that it has comparative advantage for the entire large (American) market.

• The states has to produce both goods.


Figure 4.2 Free-Trade Equilibrium


Figure 4.3 The World Transformation Schedule


World Production Possibilities

• Home has comparative advantage in clothing. If the world wants to produce clothing, it should be first off the mark.

• Foreign enticed to do so only if the world relative price of clothing reaches the height of its cost ratio, shown by the world PPF.

• Point A adds up the maximum possible food output and point C does the analogous job for clothing production.


Trade in the Ricardian Model (cont.)

• Suppose the domestic country is more efficient in food and clothing production.

• It has an absolute advantage in all production: its unit labor requirements for food and clothing production are lower than those in the foreign country:

aLC < a*LC and aLF < a*

LF

• A country can be more efficient in producing both goods, but it will have a comparative advantage in only one good—the good that uses resources most efficiently compared to alternative production.


Trade in the Ricardian Model (cont.)

• Even if a country is the most (or least) efficient producer of all goods, it still can benefit from trade.

• To see how all countries can benefit from trade, we calculate relative prices when trade exists. Without trade, relative price of a good equals the opportunity

cost of producing that good.

• To calculate relative prices with trade, we first calculate relative quantities of world production:

(QC + Q*C )/(QW + Q*

W)


Relative Supply and Relative Demand

• Next we consider relative supply of clothing: the quantity of clothing supplied by all countries relative to the quantity of food supplied by all countries at each relative price of clothing, Pc /PF.

• It is world relative price.

• Fix unit labor requirement, but allow price to move to see the response of quantity.


Relative Supply

Relative Price of clothing, Pc/Pf

alc/aLF

Rela. Supply yc+yc*/(yf+yf*)


Relative Supply and Relative Demand (cont.)

• There is no supply of clothing if the relative price of clothing falls below aLC /aLF . Why? because the domestic country will specialize in food

production whenever PC /Pf < aLC /aLF

And we assumed that aLC /aLF < a*LC /a*

LF so foreign workers won’t find it desirable to produce clothing either.

• When PC /Pf = aLC /aLF , domestic workers will be indifferent between producing food or clothing, but foreign workers will still produce only food.


Relative Supply


alc/aLF




• When a*LC /a*

LF > Pc / Pf > aLC /aLF , domestic workers specialize in clothing production because they can earn higher wages, but foreign workers will still produce only food.

• When a*LC /a*

LF = PC / Pf, foreign workers will be indifferent between producing food or clothing, but domestic workers will still produce only clothing.

• There is no supply of food if the relative price of clothing rises above a*

LC /a*LF


Relative Supply


alc*/aLF*

alc/aLF

(L/alc)/(L*/aLF*)




aLC/aLF

a*LC/a*

LF RS

Relative priceof clothing, PC/Pf

Relative quantityof clothing, QC + Q*

C

QW + Q*W

L/aLC

L*/a*LF



• Relative demand of clothing is the quantity of clothing demanded in all countries relative to the quantity of food demanded in all countries at each relative price of clothing, PC /Pf.

• As the relative price of clothing rises, consumers in all countries will tend to purchase less clothing and more food so that the relative quantity of clothing demanded falls.

• Key assumption: the two countries shared the same (homothetic) taste pattern.



RD

1

aLC/aLF

a*LC/a*

LF RS

Relative priceof clothing, PC/Pf

Relative quantityof clothing, QC + Q*

C

QW + Q*W

L/aLC

L*/a*LF




Figure 4.4 The World Market for Food


The World Market for Food

• At point A, Foreign specifies to produce L*/alf*, which corresponds to point B in Figure 4.3.

• At point B, both countries produce food only, therefore the total production is fixed here.

• Suppose the equilibrium is point J’, then foreign produces both clothing and food whereas home still produces clothing.

• Therefore, at J’, the production of food reduces. We get the point in J on the world PPF in Figure 4.3.


Figure 4.3 The World Transformation Schedule


Wages and Productivity

• The Perfect Competitive Profit Conditions:

• Unit costs may exceed price, but only if all producers leave the industry.

• Unit costs cannot lower than price due to the free entry.

• If unit costs lower than price, the consequent profits would signal new entrants into the industry.

• 1 /aLC , and 1/ aLF denote both labor’s average product and its marginal product.


Wages and Productivity

• In any industry with positive output, the wage rate must equal the value of labor’s (average or marginal) productivity.

• In any industry forced to shut down because of international competition, it is because the prevailing wage rate would exceed the value of labor’s productivity.


International Wage Comparisons

• Home country exports clothing.

• Suppose the world relative price of clothing is so low and even the home produce food as well (like point B in Figure 4.4).

• No production at clothing.

• What happens for wages at home?

• If foreign worker is twice productive than home workers in producing food, then foreign worker earns twice.



• Suppose the world relative price of clothing lies between the cost ratios in the two countries

• Now the wage ratio reflects (1) the productivity of labor force, and (2) terms of exchange between commodity as well.

• Suppose the world relative price of clothing is so high so that home and foreign produce clothing:


Figure 4.5 Relative Wages and the Terms of Trade


Do Wages Reflect Productivity?

• In the Ricardian model, relative wages reflect relative productivities of the two countries.

• Is this an accurate assumption?

• Some argue that low wage countries pay low wages despite growing productivity, putting high wage countries at a cost disadvantage.

• But evidence shows that low wages are associated with low productivity.


Do Wages Reflect Productivity? (cont.)


Do Wages Reflect Productivity? (cont.)

• Other evidence shows that wages rise as productivity rises. In 2000, South Korea’s labor productivity was 35%

of the US level and its average wages were about 38% of US average wages.

After the Korean War, South Korea was one of the poorest countries in the world, and its labor productivity was very low. In 1975, average wages in South Korea were still only 5% of US average wages.



• If the terms of trade lie strictly between the cost ratios in the two countries, an improvement in the home terms of trade has a proportionally favorable effect on the home relative wage.

• If the terms of trade allow both countries to produce the same commodity, relative wages reflect labor’s productivity in this commodity.


Winners/Losers from Productivity Shocks

• From autarky to trade, each country gains.

• But it is not necessarily true for the increased globalization.

• Unskilled labor problem in advanced countries.

• Environmental problem.

• Ricardian model is not good enough to analyze winners and losers within one country.

• But it is ideal to consider how growth (say, productivity change) affect the international distribution of income.


Winners/Losers from Productivity Shocks

• The productivity improvement for a commodity in a trading country has three possible consequences:– Both countries might gain

– The country that experiences the productivity shock might lose

– The other country might lose.

• Consider case 1 now.

• U.S. produces the first 14 commodities and China produces the rest of the goods from 16.

• Both countries produce 15th good.

• The commodities are ranked by their relative costs.


Both countries might gain

• Suppose China develops a superior technology in good 20th, which does not change the rank of commodities by comparative advantage.

• Normalize the 15th good’s price as a unity to fix the nominal wage in each country.

• The price of commodity must fall due to its productivity improvement (i.e., the supply curve shifts to the right).


Both countries might gain

• In sector 20th, the real wage increases due to a fall of its price.

• But the real wage at Home should equal across sectors to avoid the possible arbitrage.

• Therefore, in sector 15th, the real wage must increase.

• But this implies the real wage must increase in foreign country as well.

• Therefore, both countries gain since wage income is the only source of income.


Some country might lose

• When no commodity produced in common, the nominal wage is different from each other.

• Same story but good 15th now is produced in China.• For the U.S., consider an aggregate price index for those 14

types of goods.• Its supply is vertical since the American labor force is assumed

fixed and fully employed.• After the production shock, if world real incomes increase, this

would ship the aggregate demand curve to the right (income effect).

• But the substitution effect caused by the technological shock of good 20th might shift the aggregated demand curve left.


Figure 4.6 Technological Progress


Some country might lose

• If the substitution effect is dominated by the income effect, then the demand shifts right, ends up with a higher price Pa.

• If Pa increases very much, it leads to a strong deterioration of TOT for China.

• Immiserizing growth happens in China.

• China loses!

• The reverse situation could happen for the U.S.


Figure 3.3 Immiserizing Growth


Comparative Advantage With Many Goods (cont.)

• Goods will be produced wherever it is cheaper to produce them.

• Let w represent the wage rate in the domestic country and w* represent the wage rate in the foreign country. If waL1 < w*a*

L1 then only the domestic country will produce good 1, since total wage payments are less there.

Or equivalently, if a*L1 /aL1 > w/w*

If the relative productivity of a country in producing a good is higher than the relative wage, then the good will be produced in that country.



• Suppose there are 5 goods produced in the world:



• If w/w* = 3, the domestic country will produce apples, bananas, and caviar, while the foreign country will produce dates and enchiladas.

The relative productivities of the domestic country in producing apples, bananas and caviar are higher than the relative wage.



• If each country specializes in goods that use resources productively and trades the products for those that it wants to consume, then each benefits. If a country tries to produce all goods for itself, resources

are “wasted”.

• The domestic country has high productivity in apples, bananas, and caviar that give it a cost advantage, despite its high wage.

• The foreign country has low wages that give it a cost advantage, despite its low productivity in dates.



• How is the relative wage determined?

• By the relative supply and relative (derived) demand for labor services.

• The relative (derived) demand for domestic labor services falls when w/w* rises. As domestic labor becomes more expensive relative to foreign labor, goods produced in the domestic country become more

expensive, and demand for these goods and the labor to produce them falls.

fewer goods will be produced in the domestic country, further reducing the demand for domestic labor.





• Suppose w/w* increases from 3 to 3.99: The domestic country would produce apples, bananas, and

caviar, but the demand for these goods and the labor to produce them falls as the relative wage rises.

• Suppose w/w* increases from 3.99 to 4.01: Caviar is now too expensive to produce in the domestic

country, so the caviar industry moves to the foreign country, causing a discrete (abrupt) drop in the demand for domestic labor.

• Consider similar effects as w/w* rises from 0.75 to 10.





• Finally, suppose that relative supply of labor is independent of w/w* and is fixed at an amount determined by the populations in the domestic and foreign countries.




Transportation Costs and Non-traded Goods

• The Ricardian model predicts that countries should completely specialize in production.

• But this rarely happens for primarily 3 reasons:

1. More than one factor of production reduces the tendency of specialization

2. Protectionism

3. Transportation costs reduce or prevent trade, which may cause each country to produce the same good or service


Transportation Costs and Non-traded Goods (cont.)

• Non-traded goods and services (e.g., haircuts and auto repairs) exist due to high transportation costs.

Countries tend to spend a large fraction of national income on non-traded goods and services.

This fact has implications for the gravity model and for models that consider how income transfers across countries affect trade.


Empirical Evidence

• Do countries export those goods in which their productivity is relatively high?

• The ratio of US to British exports in 1951 compared to the ratio of US to British labor productivity in 26 manufacturing industries suggests yes.

• At this time the US had an absolute advantage in all 26 industries, yet the ratio of exports was low in the least productive sectors of the US.


Empirical Evidence (cont.)


Summary

1. A country has a comparative advantage in producing a good if the opportunity cost of producing that good is lower in the country than it is in other countries.

A country with a comparative advantage in producing a good uses its resources most efficiently when it produces that good compared to producing other goods.

2. The Ricardian model focuses only on differences in the productivity of labor across countries, and it explains gains from trade using the concept of comparative advantage.


Summary (cont.)

3. When countries specialize and trade according to the Ricardian model; the relative price of the produced good rises, income for workers rises and imported goods are less expensive for consumers.

4. Trade is predicted to benefit both high productivity and low productivity countries, although trade may change the distribution of income within countries.

5. High productivity or low wages give countries a cost advantage that allow them to produce efficiently.


Summary (cont.)

7. Although empirical evidence supports trade based on comparative advantage, transportation costs and other factors prevent complete specialization in production.

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© 2007 Pearson Addison-Wesley. All rights reserved Chapter 4 Technology and International Income Distribution: The Ricardian Model