### Highlights

- There are three important tools that we make use of:
- Price line (representing relative prices)
- Production possibility frontier (representing the production side of the economy)
- Indifference curves (representing the consumption side of the economy)

- Given the above tools, we identify the equilibrium outcome.

- To do so, we impose seven assumptions:
- Agents are rational; i.e., producers maximize profit, and consumers maximize their satisfaction as reflected in their utility functions.
- There are only two countries (A and B) and two goods (S and T)
- There is no money illusion; i.e., only relative prices matter.
- The relative price turns out to be the slope of price line in absolute value.
- Changes in income shifts the price line, and changes in relative prices rotate the price line.

- Resources and technologies are fixed; i.e., production possibility frontier is given and remains the same
- The slope of production possibility frontier determines the opportunity cost of producing one extra unit of one good (say, S) in terms of the other good (say, T).
- Depending on the shape of the frontier, the above opportunity cost may be constant (linear case) or increasing (concave case).

- Both industries in both countries are perfectly competitive; i.e., marginal cost of production (slope of production possibility frontier) is equal to marginal revenue (measured by relative prices).
- The optimal allocation of resources, therefore, is at the point of tangency between production possibility frontier and price line.

- Within a given country (say, A), labor can move freely between the two sectors: S and T.
- Factor earnings in the two sectors are, therefore, equal.

- There exists a community indifference curve, representing the consumption preference of the community

- How do we use the above tools and assumptions?
- First, we assume that both countries are closed economies (a.k.a., aurtaky)
- We model the optimal amount of production (the point of tangency between production possibility frontier and price line)
- We model the optimal amount of consumption (the point of tangency between community indifference curve and price line)

- We will, then, open up these two economies to see what happens to the optimal allocations under autarky.

- First, we assume that both countries are closed economies (a.k.a., aurtaky)

- Using the above tools, one can derive national supply and demand curves for each country.
- National Supply Curve: Begin with an initial point of tangency between production possibility frontier and price line. Then change the relative price, and see what happens to the initial optimal allocation. Repeat this over and over again, and capture the changes in relative prices and quantity produced. This exercise yields the national supply of, say, S.
- National Demand Curve: Begin with an initial point of tangency between community indifference curve and price line. Then change the relative price, and see what happens to the initial optimal allocation. Repeat this over and over again, and capture the changes in relative prices and quantity demanded. This exercise yields the national demand for, say, S.

Click here to see the graphs in details.

- The intersection of national supply and demand curves for a given country (say, A) determines the equilibrium relative price in that country. This is known as autarky relative price at equilibrium.

If at autarky country A has a lower relative price of S, then country A has

in S andcomparative advantagein T.comparative disadvantage

- The source of comparative advantage, therefore, could be modeled by differences in national supply and demand in different countries. This is the base for classical models of international trade.