A Formal Theory Of Gains From Trade

APPENDIX A: A FORMAL THEORY OF GAINS FROM TRADE Here we explore in more detail the “gains from trade” example given in the text. There, for simplicity, we explored a case in which both countries completely specialize, producing only one good, because their level of desired total consumption just happens to match each country’s total production level with complete specialization. Graphing a joint PPF for the two countries enables us to relax this assumption, while also exploring more fully the concepts of opportunity costs and comparative advantage. Recall that in this example, Portugal can produce a maximum of either 200 cases of wine or 100 bolts of cloth. Portugal’s PPF was shown in Figure 14.1. Realize that the slope of the PPF equals the opportunity of production. So moving left to right starting at the (0, 200) point, a fall (or negative “rise”) of 200 cases of wine is accompanied by a “run” of +100 bolts of cloth. Because the curve is straight, the slope is therefore –2 throughout. Note that this is the value in Table 14.2 for the opportunity cost of Portugal producing one bolt of cloth. At any point, then, reducing wine production by 2 cases (i.e. , a negative “rise” of 2) is needed to increase cloth production by 1 bolt (i.e., to create a “run” of 1 unit to the right). England can produce a maximum of 200 cases of wine or 400 bolts of cloth, as was shown in Figure 14.2. The slope of its production possibilities frontier is –0.5 (= –200/400). For each additional bolt of cloth, England gives up producing half a bottle of wine. Figure 14.7 Joint Production Possibilities Frontier for England and Portugal In Figure 14.7, we create a joint PPF for the two countries. Suppose that they both start out producing only wine. Adding Portugal’s 200 cases to England’s 200 cases, we find that jointly they can produce 400 cases if they produce no cloth, as shown at the point (0, 400). Now suppose that they would like to consume some cloth, and they make a joint decision about where it should be produced. They see that if Portugal produces the first bolt of cloth, it will cost them 2 cases of wine. If England produces the first bolt of cloth, it will cost them only half a case of wine. Clearly, England should produce it. This kind of reasoning will tell England to produce not only the first bolt of cloth but also every succeeding bolt of cloth, as long as possible. Portugal will keep producing only wine, at its maximum level of 200 cases. The possibility of exploiting England’s relatively low-cost cloth production runs out when these two countries reach point A. At point A, England produces the maximum amount of cloth it can— 400 bolts—and Portugal still produces only wine (200 cases). This was the point used as an example in the text, for simplicity. Now if they want to continue to have even more cloth (and less wine), Portugal will have to produce it. Each extra bolt of cloth will now cost 2 cases of wine, up to the point (500, 0), where they both produce only cloth. What if, instead, the countries were to follow their comparative disadvantages, having Portugal change to cloth production first, and England only after Portugal was producing at capacity? Figure 14.8 contrasts the efficient PPF with this case. With inefficient full specialization represented by the point where Portugal produces 100 bolts of cloth and England produces 200 cases of wine, the PPF bends inward. The thick blue line is the efficient production-possibilities frontier, and the thinner gray line reflects the most inefficient production choices. As you can see, following the rule of comparative advantage leads to a much larger PPF than doing the reverse! A similarly inefficient result would follow if you were better at cleaning, and your housemate at shopping, but you tended to shop and your housemate tended to clean. Figure 14.8 Efficient and Inefficient Joint Production Possibilities Frontier As we mentioned in the chapter, along with the concept of comparative advantage economists also discuss absolute advantage. A producer has an absolute advantage when, using the same amount of some resource as another producer, it can produce more. Usually, labor hours are the resource considered. For example, suppose that in a one-hour period you can buy enough groceries for six days or clean three rooms. Your housemate, by contrast, moves more slowly and can buy enough groceries for only three days, or clean only one room, in an hour. You clearly have an absolute advantage in production of both these services. Does this mean you should do all the work?1 (See whether you can figure out the answer before looking at the endnote.) APPENDIX B: AN ALGEBRAIC APPROACH TO THE MULTIPLIER, IN A MODEL WITH TRADE Just as we modified the multiplier in the appendix to Chapter 10 to take account of the impact of taxes, we can now go a step further to consider the effect of trade. Suppose that, in addition to consumption’s depending on income, imports depend on income according to the equation IM = mpim Y, where mpim is the marginal propensity to import (the proportion of additional income spent on imports). The mpim is a fraction. Starting with the equation for aggregate expenditure with a proportional tax that we had derived in the appendix to Chapter10, we can get an equation for aggregate expenditure in an economy including trade, as follows: AE = C + I + G + X – IM = C + mpc(Y - tY + TR) + I +G + X – mpim Y = ( C + mpc T + I – G + X) +[mpc(1 – t) – mpim] Y Solving for Y (using the same method as in the appendix to Chapter 10—but leaving out some of the intermediate steps) yields: 𝑌 − 𝑚𝑝𝑐(1 − 𝑡)𝑌 + 𝑚𝑖𝑝𝑖𝑚 𝑌 = 𝐶̅ + 𝑚𝑝𝑐 𝑇𝑅 + 𝐼 + 𝐺 + 𝑋 1 𝑌= [ ] (𝐶̅ + 𝑚𝑝𝑐 𝑇𝑅 + 𝐼 + 𝐺 + 𝑋) 1 − 𝑚𝑝𝑐(1 − 𝑡)𝑚𝑖𝑝𝑖𝑚 The term in brackets is a new multiplier that includes both proportional taxes and imports that depend on domestic income. This multiplier here is even smaller than the previous two. For example, if mpc = .8, t = .2, and mpim = .1, the new multiplier is 1/(1 – .64 + .1) or 1/(0.46) or approximately 2.2. This is because any increase in Y now “leaks” not only into saving and taxes but also into increases in imports (which takes away from demand for domestic products). 1 No. Comparative, not absolute, advantage should guide the assignment of tasks. Although you have an absolute advantage over your housemate in both activities, your housemate has a comparative advantage in shopping. That is, to get enough groceries for six days would “cost” only two rooms’ worth of cleaning if your housemate does it (taking two hours). But if you shop for six days’ worth of food, the opportunity cost is more—the three rooms you could have cleaned. Therefore, on efficiency grounds at least, your housemate should shop and you should clean. (You can also come to the same result by examining your own comparative advantage—in cleaning.)