The Ricardian ModelTopic 2 (continued)Reference: Krugman, P. and Obsfeld, M. and Melitz, M., International Economics: Theory and Policy, 9th edition, Addison-Wesley (Chapter 3: Page 24-35)

This model of international trade was originally proposed by the British economist David Ricardo, who introduced the concept of comparative advantage in the early 19th century. Here, international trade is solely due to international differences in the productivity of labor.

Assumptions: Two countries: Home and Foreign One-factor economy (Labor is the only factor of production) Two goods can be produced- Wine and Cheese Full Employment of Labor Constant returns to scale Zero profit in production Technology can be summarized by unit labor requirement (the number of hours required to produce a pound of cheese or a gallon of wine). Note that we are defining unit labor requirement as the inverse of productivity.

Production Possibilities at HomeaLW= unit labor requirement in wine at Home (e.g. 2)aLC= unit labor requirement in cheese at Home (e.g. 1)L= total labor supply at home (e.g. 1000)QC= total production of cheeseQw= total production of wineUnder full employment assumption, we must have

Because any economy has limited resources, there are limits on what it can produce and there are always trade-offs. To produce more of one good, the economy must sacrifice some production of another good. These tradeoffs are illustrated graphically by the Production Possibility Frontier (line PF in figure 3-1).

We assume aLW=2, aLC= 1 and L= 1000, then if the economy devoted all its labor to cheese production, it could, as shown in figure 3-1, produce pounds of cheese (1000 pounds). If it devoted all its labor in wine production instead, it cound produce gallons (1000/2=500 gallons) of wine.When the PPF is a straight line, the opportunity cost of a pound of cheese in terms of wine is constant. The absolute value of the slope of the PPF is the opportunity cost. So from equation (2) the opportunity cost of cheese in terms of wine is .

Relative Prices and SupplyThe PPF simply shows the different mixes of goods that an economy can produce. But to determine what the economy will actually produce, we need to look at prices.In our simplified model, with labor as the only factor of production, the supply of cheese and wine will be determined by the movement of labor to whichever sector pays the higher wage.Suppose aLW=2, aLC= 1, PC=$4 and PW=$7. If workers produce cheese, they earn $4 an hour but if they produce wine they earn $3.5 per hour. So workers will be better off producing cheese and the economy as a whole will produce cheese.Alternatively, suppose aLW=2, aLC= 1, but PC=$3 and PW=$7. If workers produce cheese, they earn $3 an hour but if they produce wine they earn $3.5 per hour. So workers will be better off producing wine and the economy as a whole will produce wine.More generally, the economy will produce cheese if the relative price of cheese exceeds its opportunity cost in terms of wine; it will specialize in the production of wine if the relative price of cheese is less than its opportunity cost in terms of wine.Here, = relative price of cheese in terms of wine and = Opportunity cost of cheese in terms of wine.

Mathematically, produce cheese if And produce wine if In absence of trade, Home would have to produce both the goods itself. So we must have . Thus in an autarky economy, the relative prices of goods are equal to their relative unit labor requirement.

Introducing Trade in One-Factor ModelNow we consider another country- Foreign. We assumeaLW*= unit labor requirement in wine at ForeignaLC*= unit labor requirement in cheese at ForeignL*= total labor supply at ForeignAnd Home is less productive than Foreign in wine but more productive in cheese. So we have

The slope of the PPF is the opportunity cost of cheese in terms of wine. As the above equation shows, Foreign's frontier is steeper than Home's.

In absence of trade, Home's relative price of cheese= And Foreign's relative price of cheese= However, with international trade, if the relative price of cheese is higher in Foreign than Home, it will be profitable to ship cheese from Home to Foreign and to ship wine from Foreign to Home. This cannot go on indefinitely. Eventually relative prices will be equalized in both the countries.

Determining the Relative Price after TradeWe need a general equilibrium analysis which takes account of the linkages between two markets.

RS=World relative supply curveRD=World relative demand curveWorld relative price is determined by intersection of RS and RD.The funny 'step' shape (with flat sections linked by vertical sections) of the RS can be explained by the derivation of the RS curve. First, as drawn, the RS shows there is no supply of cheese if world relative price drops below Because here,

So both Home and Foreign will specialize in wine production.

Next when Home will be willing to produce any relative amount of the two goods, producing the flat section of the RS. However, since , Foreign will still specialize in wine production.

With Home will specialize in cheese production and Foreign will continue its wine production. Here since all Home's labor will produce cheese, the production of cheese at Home will be and all Foreign's labor will produce units of wine.So the relative supply of cheese will be

At , we know that Foreign workers are indifferent between producing cheese and wine. Thus we again have another flat section of RS.

Numerically, if we assume: aLW= 2, aLC= 1, aLW*= 3 and aLC*= 6 then and.When the RS intersects RD at point 1, the post-trade price will be in between the pre-trade prices of 1/2 and 2, e.g. 1/2