Exports Xy = NjXy from country i to country j are shown in the lower panel of Figure 1.
Within the interval (La,Lb) both countries are producing the Coumot-Nash good, and they will also both be exporting provided that the F.O.B. price received (which is net of transport costs) exceeds marginal cost. This will be true in Figure 1 provided that P/% > с , as we shall assume.4 When L]=La then exports of the Coumot-Nash are zero because production is also zero, but as country 1 grows then exports also rise, as illustrated by the curve Xn. When Li=Lb, country 2 ceases production of the Coumot-Nash good. Further re-allocations of labor towards country 1 reduce its exports, because demand falls in country 2.5 Thus, the general shape of exports from country 1 are as illustrated by X12, increasing from La and then decreasing after Lb. The corresponding export curve X21 from country 2 is also illustrated.
The conditions in (6) are simply arbitrage conditions, needed to ensure that goods exported from country i to j cannot be profitably re-exported back to i. That is, the price received from re-exporting, pi/Tjj, should not exceed the purchase price in country j, pj. When this condition holds as an equality, the number of firms located in the country with the higher price is zero: import competition eliminates the local firms. To understand this result, note that when pi/T2i=P2> the price in country 1 is sufficiently high to offset fully the barrier created by transporting from country 2. We can think of Р1/Т21 as the F.O.B. (“free on board”) price received for country 2 exports, the price net of transportation charges. When this equals the home price P2, a firm in country 2 will have the same market share in its export and home markets, as can be seen from (3). From (4), the only way for the market shares to add up to unity is for all the firms to be located in country 2; intuitively, the firms in country 1 have been eliminated through import competition.
where a denotes the share of the Coumot-Nash good in the total consumer’s budget (which depends on the relative price of that good).
Our theoretical results indicate that the home market effect should be larger for differentiated goods with free entry than for homogeneous goods with restricted entry. We test this hypothesis in our empirical work. We regress bilateral exports (from one country to each of its trading partners) on domestic- and partner-country GDP (and other controls). We are interested in the elasticity of exports with respect to domestic GDP, since our theory indicates that the size of this elasticity depends on the type of good.
We expect to see higher elasticities for manufacturing goods with few entry barriers, and smaller elasticities for homogeneous goods with more entry barriers (e.g., because they are resource-based). Using Rauch’s (1999) classification, we divide our sample into three; homogeneous goods, differentiated goods, and an in-between category.
It is well-known that international trade flows can be well described by a “gravity equation” in which bilateral trade flows are a log-linear function of the incomes of and distance between trading partners. Indeed, the gravity equation is one of the greater success stories in empirical economics. However, the theoretical foundations for this finding are less clearly understood. The gravity equation is not implied by a plausible many-country Heckscher-Ohlin model (which has nothing to say about bilateral trade flows). An equation of this type does arise, however, from a model in which countries are fully specialized in differentiated goods.
While specialization might characterize manufacturing goods, it is presumably not a feature of homogeneous primary goods. Despite this theoretical presumption, the gravity equation seems to work empirically for both OECD countries and developing countries (Hummels and Levinsohn, 1995). Since developing countries tend to sell more homogeneous goods, it seems puzzling that the gravity equation works well for these countries. Thus, it is hard to reconcile the special nature of the theory behind this equation with its empirical performance.
Our constrained solution enables us to study the welfare effects of bond indexation in a realistic framework. When portfolio constraints are in place, and both nominal and indexed bonds are available to investors, more conservative investors hold in their portfolios relatively more indexed bonds than nominal bonds. These investors benefit substantially from the consumption insurance provided by long-term indexed bonds.
We have also studied the demand for bonds when equities are available as an alternative investment. We find that the ratio of bonds to stocks in the optimal portfolio increases with risk aversion, very much in line with popular investment advice but contrary to the mutual fund theorem of static portfolio analysis. However the demand for long-term bonds is only large when these bonds are indexed, or when inflation uncertainty is low as it has been in the Volcker-Greenspan monetary policy regime since 1983.