Lecture 2 (Chapter 2)
Labor Productivity and Comparative Advantage:
The Ricardian Model
The Concept of Comparative Advantage using a modern example
On Valentine’s Day the U.S. demand for roses is about 10 million.
Growing roses in the U.S. in the winter is difficult.
§ Heated greenhouses should be used.
§ The costs for energy, capital, and labor are substantial.
Resources for the production of roses could be used to produce other goods, say computers.
Suppose that in U.S. 10 million roses can be produced with the same resources as 100 thousand computers. In Mexico 10 million roses can be produced with the same resources as 30 thousand computers.
Production possibilities for a given amount of resources in each country
Roses (in millions) Computers (in thousands)
U.S. 10 100
Mexico 10 30
§ Note that resources used in making 10 million roses in U.S are not necessarily equal to the resources employed to make that many roses in Mexico. In this example Mexico is relatively less productive in computer production compared to U.S.
Opportunity cost
§ Note that the opportunity costs (the value of the next best option foregone) of production in the two countries are different.
§ The opportunity cost of rose production is defined as the number of computers that must be given up to produce more roses.
US Mexico
Opportunity cost of producing 10 million roses 100 30
(in terms of thousands of computers not produced)
§ Here the opportunity cost of rose production is lower in Mexico and for that we say Mexico has comparative advantage in rose production. U.S. has comparative advantage in computer production because the opportunity cost of computer production is lower in U.S.
US Mexico
Opportunity cost of 100 thousand computer 10 10*3.33
(in terms of millions of roses not produced)
Benefits from Trade
§ If each country specializes in the production of the good with lower opportunity costs, trade can be beneficial for both countries.
Hypothetical Changes in Production
Roses (in millions) Computers (in thousands)
U.S. -10 +100
Mexico +10 - 10
Total 0 + 70
The example in shows:
§ If each country exports the goods in which it has comparative advantage (lower opportunity costs), then all countries can in principle gain from trade.
§ Once every country specializes in production of goods that has a comparative advantage in, and then trades its excess supply, world production increases.
§ The extra production is the result of better allocation of resources.
§ This extra production can be divided between the trading countries allowing them to achieve higher consumption levels.
Absolute Advantage versus Comparative Advantage
§ If it takes the same amount of resources to produce 10 million roses in both countries then we say US has absolute advantage in computer production because it can produce more computers with the same resources or it takes less resources to produce computers in US than in Mexico.
§ If it takes fewer resources to produce 10 million roses or 30 thousand computers in US then we say US has absolute advantage in both goods.
§ However comparative advantage does not depend on absolute advantage. In the example above US has comparative advantage in computer production regardless of the amount of resources it uses for computer production (regardless of whether the resources used to produce 10 million roses in US is larger the same or less than that in Mexico).
What determines comparative advantage?
§ Why relative productivities are different in the two countries? This could be because of technological differences in the two countries or the quality of the resources (or factors of production available) in the two countries (i.e., fertile land and suitable weather in Agriculture, capital and skilled labor).
A Ricarian like Example
Consider two goods (say wine and cheese) produced using labor only and two countries (Home, Foreign *)
· Define unit labor required a. This is hours of labor required to produce one unit of output. This is represented with a for home and a* for the foreign country.
· Note that a=L/Q (hours per unit of Q) thus 1/a=Q/L or simply labor productivity
Unit Labor Requirement
(Hours of work required to produce)
Cheese (1 lb) Wine (1 gal)______
In Home aLC = 1 aLW = 2
In Foreign a*LC = 6 a*LW = 3
In Home, in the 1 hr that it takes to produce 1 lb cheese how many gal of wine could have been produced. The answer is .5 because it takes two hrs to produce 1 gal of wine. This is the opportunity cost of cheese production (in terms of wine). For opportunity cost of wine we ask how much cheese could have been produced in the 2 hrs that it takes to produce 1 gal of wine. The answer is 2.
Opportunity Cost (before trade)
Cheese (1 lb) Wine (1 gal)
in terms of gal of Wine forgone in terms of lb of Cheese forgone
In Home aLC /aLW = 0.5 aLW /aLC = 2
In Foreign a*LC/a*LW = 2 a*LW /a*LC = 0.5
In Home one must give up .5 gal of wine to obtain 1 lb of cheese
Thus the OC of cheese is .5 gal of wine.
One must give up 2 lb of C to obtain 1 gal of W thus OC of W is 2 lb of C
In Foreign must give up 2gal of wine to obtain 1lb of C, thus OC of C is 2gal of wine
The OC of wine is 0.5 lb of cheese
· Here Home has absolute advantage in both goods because it takes fewer resources to produce wine and cheese in Home country (MPL is higher in Home). That is:
aLC < aLC* and aLW < aLW* or MPLC > MPL*C and MPLW > MPL*W
But absolute advantage is irrelevant to trade. In the example Home has comparative advantage in Cheese because its opportunity cost of Cheese production is lower (0.5< 2) that is:
OC of Cheese in Labor Productivity in Wine Relative to Cheese
Home Foreign Home Foreign
aLC /aLW < aLC* /aLW* => MPLw/MPLc < MPLw*/MPLc*
or MPLc/MPLw > MPLc*/MPLw*
– Opportunity cost of cheese is lower in home country because Home is relatively more productive in cheese production (less productive in wine production)
– Home has a comparative advantage in cheese.
· With two goods there is only one price ratio in each country
o Note that opportunity cost of wine and cheese are just reciprocal of each other
§ Wine is relatively cheap in Home and wine is expensive.
§ In Foreign cheese is relatively expensive and wine is cheap
· Now trade and make money
Start with 1 gal of foreign wine, sell it in US mkt in exchange for 2 pounds of US cheese and then sell each pound of US cheese for 2 gallons of foreign wine in foreign mkt and make 3 gallons of wine profit!
All in all, this condition is rather confusing. Suffice it to say, that it is quite possible, indeed likely, that although Foreign may be less productive in producing both goods relative to Home, it will nonetheless have a comparative advantage in the production of one of the two goods.
If Home is twice as productive in wine production relative to Foreign but three times as productive in Cheese, then Home's comparative advantage is in Cheese, the good in which its productivity advantage is greatest. Similarly, Foreign's comparative advantage good is wine, the good in which its productivity disadvantage is least. This implies that to benefit from specialization and free trade, Home should specialize and trade the good in which it is "most best" at producing, while Foreign should specialize and trade the good in which it is "least worse" at producing.
The Ricardian Model
Assumptions
This is a model of two goods (say wine and cheese), two countries (Home and Foreign *), and one factor of production labor. Wine and cheese are produced with labor only.
· Labor is homogeneous within every country
• mobile domestically and immobile internationally.
• supply of labor is fixed in each country (say at L and L*).
· Technology is represented by ULR or constant marginal productivity of labor in both countries.
· Perfect competition prevails in all market
• There are no other costs involved (transportation costs, etc.)
This is a General Equilibrium Analysis: Now let us looking at the whole economy
· General Equilibrium v.s Partial Analysis
o PE is a study of a mkt for a commodity in isolation
§ Increase in Supply of C leads to a decrease in Price of C
o GE incorporates impact on other goods (Wine) and “factors”, like L.
· Production Possibilities
• The production possibility frontier (PPF) of an economy shows the maximum amount of a good (say wine) that can be produced for any given amount of another (say cheese), and vice versa.
• The PPF of our economy is given by the following equation:
aLCQC + aLWQW = L (1)
Note that opportunity cost, reflected by the slope of PPF, is constant in each country and given by the ratio of ULR in the two sectors, that is aLC / aLW
Relative prices before trade:
· Denote with PC the dollar price of cheese and with PW the dollar price of wine. Denote with WW the dollar wage in the wine industry and with WC the dollar wage in the cheese industry.
– Under perfect competition price of each good is equal to its marginal cost: i.e. PC = MCC
– MCC = WC aLC ,wage rate in Cheese industry x labor required to produce a unit of wine that is aLC
– So PC= WC aLC
– Thus WC =PC / aLC or (WC = PC . MPLC)
§ That is the hourly wage in Cheese (Wine) industry is equal to the value of what a worker can produce in an hour.
– If WW = WC that is if PW /aW = PC /aC or PW /PC = aW /aC
then both QC and QW will be produced
– In the absence of trade, both goods are produced, and therefore
PC / PW = aLC/aLW.
Or PC / PW = MPLw/MPLc
(optional)
– If WC > WW that is if PC /aC >PW /aW or PC /PW > aC /aW then no Wine will be produced QW =0 and QC = L/aLC
§ i.e, when the relative price of cheese (PC/PW) exceeds its opportunity cost (aLC / aLW), then the economy will specialize in the production of cheese.
– If WC < WW that is if PC /aC <PW /aW or PC /PW < aC /aW
then no Cheese will be produced QC =0 and QW = L/aLW
Home Equilibrium with No Trade
From our previous example, we have aLC = 1, aLW = 2 and L=120 in Home country.
Home: QC + 2QW = 120
In absence of trade consumption in every country is constrained to its production. Before trade Home country produces and consumes at point A where its production possibility frontier is tangent the highest social indifference curve in autarky U1.
We will refer to point A as the “no-trade” or the “pre-trade” equilibrium for Home.
We are assuming that there are many firms in each of the wine and cheese industries, so the firms act under perfect competition, i.e. taking the market prices for wine and cheese as given. The idea that perfectly competitive markets lead to the highest level of well-being for consumers – as illustrated by the highest level of utility at point A – is an example of the “invisible hand” that Adam Smith (1723-1790) wrote about in his famous book The Wealth of Nations. Like an “invisible hand,” competitive markets lead firms to produce the amount of goods that results in the highest level of well-being for consumers.
Foreign Equilibrium with No Trade
· In Foreign country we have: a*LC = 6 , a*LW = 3 and L* = 300 so the production possibility frontier for foreign country is given by:
Foreign : 6Q*C + 3Q*W = 300
2Q*C + Q*W = 100
· Similarly the Foreign country produces and consumes at point a.
· Before trade prevailing prices in every country is equal its opportunity cost.
Case Study: Us Comparative Advantage in Wheat Production
The U.S. textile and apparel industry faces intense import competition, especially from
Asia and Latin America. Employment in this industry in the United States fell from about 1.5 million people in 1990 to less than 1 million in 1999. One example of this import competition is the response of a U.S. fabric manufacturer, Burlington Industries, which announced in January 1999 that it would reduce its production capacity by 25% due to increased imports from Asia. Burlington closed seven plants and laid off 2,900 people, about 17% of its domestic force. After the layoffs, Burlington Industries employed 17,400 persons in the United States. With 1999 sales of $1.6 billion, this means that its sales per employee were $1.6 billion/17,400 = $92,000 per worker. This is exactly at the average for all U.S. apparel producers, as shown in Table 2.2.
The textile industry is even more productive, with annual sales per employee of $140,000. In comparison, the average worker in China produces $13,500 of sales per year in the apparel industry, and $9,000 in the textile industry. Thus, a worker in the United States produces 7 times more apparel sales than a worker in China and 16 times more textile sales.