I teach undergrad economics at the country’s premier university. This semester, I’m teaching International Trade, Finance and Development Policy.
The semester has just started and based on the course syllabus, part of the requirement is for students to learn (and for me to teach) about international trade models and theories as tools to analyze the causes and effects of trade between and among countries.
In a class I had last week, I got a question from one of my students, J, about the Ricardian One Factor Trade Model (Chapter 3 of International Trade by Krugman, et al) that puzzled me too.
So I answered him the best I can in class but promised I would give a formal reply in our yahoo group and in my blog.
Here’s my reply.
During the lecture I discussed the Ricardian One Factor Model of Labor Productivity and Comparative Advantage, in particular, the part on Trade in the One Factor Model.
In reference to Fig 3-3 (of Krugmans' book and shown below) showing the world relative supply and demand curves for cheese and wine, his question was, why would Home and Foreign not trade at point 2.
Let’s look at or review the assumptions of the Trade in One Factor model again:
- 2 countries: Home and Foreign
- One factor of production in each country: Labor
- Each country can produce 2 goods: wine and cheese
- Notation for Unit labor req for cheese:
o alc* (foreign);
- Notation for Unit labor req for wine:
o alw* (foreign)
- Opportunity cost in cheese production vs wine production for each country is given by:
o Foreign: alc*/alw*
- L = total labor for Home
- L* = total labor for Foreign
- Pc = price of cheese
- Pw = price of wine
- World price or relative price of cheese is given by Pc/Pw (note that relative price of cheese vs wine is not the same in concept as opportunity cost of cheese production vs wine; it is the rate of exchange between Home and Foreign for cheese and wine)
- Qc = quantity of cheese produced in Home; Qc* = quantity of cheese produced in Foreign
- Qw = quantity of wine produced in Home; Qw* = quantity of wine produced in Foreign
- Relative quantity of cheese to wine in world market is given by: (Qc+Qc*)/(Qw+Qw*)
- Profits again are ignored
- Home country is more efficient in wine and cheese production, thus has an absolute advantage in all production: its unit labor requirements for wine and cheese production are lower than those in the foreign country:
o alc /alw < alc* / alw*
In our numerical example, the Unit labor requirements for home and foreign countries are as follows:
TABLE 1. UNIT LABOR REQUIREMENTS FOR CHEESE AND WINE
From the Table 1 above, the opportunity cost of each country in cheese production vs wine production is:
Home: alc/alw = ½, which means it takes 1 hour to produce 1 lb of cheese and it takes 2 hours to produce a gallon of wine, which also means for every hour of unit of labor in Home, a cheese gets produced but only ½ of a gallon of wine gets produced.
Foreign: alc*/alw* = 6/3, or 2/1 in reduced form, which means it takes 2 hours to produce 1 lb of cheese and 1 hour to produce a gallon of wine, which also means, for every hour of unit of labor in Foreign, a gallon of wine can get produced but only ½ a lb of cheese.
Given the unit labor requirements for each good for each country, the opportunity cost also equally implies the internal trade offs being made in their respective domestic economies:
- To produce 1 more unit (lb) of cheese in Home country, it must stop producing or give up ½ gallon of wine (see PPF of Home country in Fig 3-1, p.27 of Krugman book)
- To produce 1 more unit (lb) of cheese in Foreign country, it must stop producing or give up 2 gallons of wine (see PPF of Foreign country in Fig 3-2, p.30 of Krugman book).
Thus, Home country’s opportunity cost in cheese production over wine (alc/alw) < Foreign’s opportunity cost in cheese production (alc*/alw*).
This means Home country has comparative advantage in cheese production.
From Table 1 showing unit labor requirements for each country, it’s clear Foreign is inefficient in the production of both cheese and wine, but has a comparative advantage in wine production:
alw*/alc* < alw/alc
using figures in our numerical example, => 3/6 < 2/1
Now let’s look at Fig 3-3, the subject of J’s question. Let’s break up the graph into bits:
- Horizontal axis: relative quantity of cheese is given by the amount of cheese produced in Home and Foreign combined, Qc+Qc* vs amount of wine produced in Home and Foreign combined, Qw+Qw* yielding the ff equation: (Qc+Qc*)/(Qw+Qw*)
- Vertical Axis: relative price of cheese is given by Pc/Pw. This is the rate of exchange between a pound of cheese and a gallon of wine.
- The RD or relative demand curve is downward sloping because of substitution effects. Recall that the model has 2 goods that could be substituted for each other. As the relative price of cheese rises vs wine, consumers will tend to purchase less cheese and more wine, so the RD for cheese falls vs relative price—hence the downward slope.
- RS or relative supply curve is a stepped curve with 2 horizontal sections and 1 vertical section:
* the vertical section depicts the range of relative prices and quantity of cheese and wine that gets produced AND at which they are traded.
- Fig 3-3 below shows the world market for cheese and wine connecting the 2 markets for both goods produced by both Home and Foreign
Table 2 shows the production decision for each level of relative price of cheese in the world market when evaluated against each country’s opportunity cost in cheese production. For Pc/Pw < ½ and for Pc/Pw> 2, these are extreme cases and shall be ignored for convenience.
TABLE 2. PRODUCTION DECISION VS RELATIVE PRICE OF CHEESE
Going back to Fig 3-3 again, there are 3 possible outcomes for trade: Pt 1, Pt 2, and Pt 3.
- Pt 2 and Pt 3 are pre-trade levels where both Home and Foreign produce both cheese and wine making use of their own internal opportunity costs
- Pt 1 is a convergent, equilibrium and optimal point of production where both countries specialize and trade their output.
Again, my student J’s question was:
Why wouldn’t Home and Foreign trade at Pt 2?
The answer is, Pt 2 is a possible outcome as with Pt 3 but is neither optimal nor an equilibrium/convergent point for the ff reasons:
- At Pt 2, only Q’ relative amount of cheese gets produced, which is less than < (L/alc/L*/alw*) or the relative quantity of cheese produced WITH trade, or less cheese than what could have been produced under trade. Thus, from a world production standpoint, this is an INEFFICIENT POINT.
- At Pt 2, Home produces both wine and cheese and Foreign is specializing in wine (See Table 2 for production decisions vs opp costs). Thus at Pt 2, Home is ‘possibly’ producing only sufficient for its domestic consumption.
- Suppose at Pt 2 both Home and Foreign DO have a chance to trade, the world price of cheese is 1/2 or the relative price of cheese is 1 lb for 2 gallons of wine. At this price level, Foreign will not have an incentive to trade because the world price implies wine is too cheap and cheese too expensive. Stated differently, at this price level, Foreign’s 1 hour of labor used to produce 1 gallon of wine, could be exchanged for ½ lb of cheese only. Thus, Foreign will ‘not likely’ engage in trade at Pt 2 and will seek a level such as Pt 1 where its 1 hour unit of labor producing 1 gallon of wine could be exchanged for a bigger amount: 1 lb of cheese--which makes more economic sense to Foreign.
- Does it make economic sense to Home to produce and trade at Pt 1 too? Yes. By specializing in cheese production, Home can produce for domestic consumption and sell the rest to Foreign at a world price (Pc/Pw) of 1 or 1 lb cheese for 1 gallon of wine. By specializing in cheese and trading at Pt 1, Home is in a way indirectly producing wine at an opportunity cost of 1 is to 1 (or 1 lb of cheese to 1 gallon of wine), which is lesser than its actual, internal opportunity cost of 2/1.
Thus both Home and Foreign will seek and converge at Pt 1, which is not only efficient (more cheese being produced for same level of resources), but also optimal (best for Home and Foreign where they could trade their 1 hour unit of labor producing 1 good for a higher/bigger amount or a better relative or exchange price for their respective products). When economic actors ‘converge’ at a point and persist at this level, then this is the equilibrium point. :)
