A Partial Walk Through Lectures on Chapter 2

Professor Panagariya

Tydings Hall

A Partial Walk through Lectures on Chapter 2

1. The Setting: Imagine a simple world: two countries, two commodities and one factor of production. Table 1 summarizes the data on technology and factor endowments.

Table 1: Technology and Factor Endowments

2. Absolute and Comparative Advantage: Absolute labor costs per unit are lower in HC for both goods (2 < 12 and 4 < 6), giving it absoluteadvantage in both goods. Per-unit cost of C relative to W is lower in HC than FC (2/12 < 4/6), giving HC comparative advantage in C. Per-unit cost of W relative to C is lower in FC than HC (6/4 < 12/2), giving FC comparative advantage in W.

3. Specialization According to Comparative Advantage Improves World Efficiency: Suppose initially both countries produce what they consume. Now let each country produce more of the good of its comparative advantage and less of the other good. This means letting HC produce more of C and FC produce more of W. In particular, suppose we let HC produce 1 extra unit of C, moving 2 units of labor from W to C. This entails reducing the production of W by ½ unit (see Table 2).

To ensure we continue to have the original amount of W, let FC produce an extra ½ unit of this good. This requires moving 3 workers from C to W, reducing the output of C by ¼ unit. The net effect on the world output is ¾ extra unit of C with no less of W. We have increased the world output using the same technology and resources as before. By dividing the extra output of C between HC and FC, we can make them both better off relative to autarky.

Table 2: Specialization Leading to Increased World Output

4. Production Possibilities Frontiers: We can represent the two economies’ total productive capacities using the production possibilities frontier (PPF). Given only one factor of production, we have constant opportunity costs of production as reflected in the constant slope of the PPF everywhere. As usual, the slope of the PPF gives the opportunity cost of production of the good on the horizontal axis in terms of the good on the vertical axis. In HC, you have to give up ½ unit of W to produce one extra unit of C. In FC, this cost is 2 units of W.

5. Autarky Equilibriums: Consider the autarky equilibrium under perfect competition in each country. Letting wage in HC be w, the average and marginal cost of production of C is 2w and that of W, 4w. Perfect competition leads to price being equated to the marginal cost. Therefore, we have

(1)PC = 2w,PW = 4w, and PC/PW = ½

Thus, the relative price of C equals the opportunity cost of production of C. Analogously, for FC, we have

(2) PC* = 12w*,PW* = 6w*, and PC*/PW* = 2

We use an asterisk (*) to denote the variables associated with FC.

6. Free Trade Equilibrium: Allow the two countries to trade freely. Assume zero transport costs. Consumers in both countries want to buy C in HC and producers in both countries want to sell C in FC. This raises the price of C in HC and lowers it in FC. The international prices settles somewhere between the two autarky prices: ½ < PCI/PWI < 2.

For now suppose the international price ratio, PCI/PWI, settles at 1. (At this point, we do not explain how we determined this to be the precise equilibrium international price ratio. We take up this task a little later below.)

In HC, the opportunity cost of producing C is ½ bushel of wheat while the international price of the good is 1 bushel of wheat. Given this difference, all resources in HC move into producing C. HC produces 50 units of C and, given PCI/PWI = 1, consumes along the dotted “consumption possibilities curve” in the left-hand panel of Figure 2.

In FC, the opportunity cost of C is 2 bushels of wheat. With the international price of C being 1 bushel of wheat, no producer finds it profitable to produce C there. FC specializes completely in W. Its consumption possibilities curve is given by the dotted line in the right-hand side panel in Figure 2.

7. Wages: Compare the real wages under autarky and free trade. Since the prices are different before and after trade, we compare wages denominated in terms of each good. Note that labor being the only factor of production, all income is wage income.

In HC the total wage income under both autarky and free trade is 50 units in terms of C. Since these are spread over 100 workers, the wage per worker is 50/100 = ½ unit of C. Thus, measured in terms of C, the wage under free trade is no less than under autarky. In terms of W, the import good, the total wage income is 25 and 50 bushels under autarky and free trade, respectively. These translate into wage rates of 25/100 = ¼ and 50/100 = ½ under autarky and free trade, respectively.

We conclude that wages under free trade when measured in terms of the export good, C, are the same as under autarky and when measured in terms of the import good, W, they are higher. Since the worker consumes both goods, he/she is able to afford a higher living standard under free trade. For example, under free trade, he/she can buy as much C as under autarky and twice as much W.

In FC also, the wage rate under free trade is the same as under autarky when measured in terms of its export good, W, and higher when measured in terms of its import good, C. With 300 workers, the wage in terms of W is 50/300 = 1/6 bushel under both free trade and autarky. But in terms of C, it is 25/300 = 1/12 unit under autarky and 50/300 = 1/6 unit under free trade. Under free trade, the worker in FC can buy as much wheat as under autarky and twice as much C.

Comparing the wages between HC and FC under free trade, we see that their ratio is (½)/(1/6) = 3. That is to say, the wage in HC is three times that in FC.

Three conclusions follow from the above observations on wages. First, low absolute productivity is not a barrier to reaping benefits from trade. The lower wage in FC (which is nevertheless higher than its autarky wage) allows it to compete HC in C even though its productivity in that good is absolutely lower than that of the latter. Second, low wages abroad are not a barrier to HC reaping the benefits of free trade. The higher productivity of HC in W allows it to compete with HC in that good despite the latter’s lower wage. Finally, the higher wage in HC relative to FC under free trade does not represent exploitation of the workers in FC: the higher wage in HC is not at the expense of FC since the real wage in FC has also gone up as a result of trade.

8. Determination of the International Price Ratio: In Figure 2, we assumed the international price ratio to be 1. Let us now derive this price endogenously. For this, we need to know the demand conditions. Suppose all consumers spend half of their incomes on C and half on W. Using D to denote demand, this means

(3)PCI (DC + DC*) = PWI (DW + DW*) or

PCI/ PWI = (DW + DW*)/(DC + DC*)

Assuming HC specializes completely in C and FC in W, the total world supply of W relative to C is (0 + 50)/(50 + 0) = 1. In equilibrium, the relative demand and relative supply are equal, yielding PCI/ PWI = 1. Since 1 is higher than the opportunity cost of C in HC and lower than that in FC, at his price, HC will indeed specialize completely in C and FC in W. Thus, our assumption regarding the specialization is correct.

Alternatively, suppose the demands were such that the expenditure on C was three times that on W. Then, assuming complete specialization by HC in C and by FC in W, we obtain PCI/ PWI = 3. But at this price ratio, both HC and FC will specialize in C. Our assumption that FC specializes completely in W and the conclusion PCI/ PWI = 3 are incorrect. The highest PCI/ PWI that can be sustained is 2. At this price, HC will still specialize completely in C and FC will produce both C and W.