# ROLE OF DIFFERENTIATING GOODS: Modeling Bilateral Trade 2

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).

The first-order conditions (2) are four equations that determine the market shares, given prices; the zero-profit conditions (7) are two equations that determine the price in each country, given the market shares. Solving these simultaneously, the number of firms in each country is then determined by (5). In Appendix 1, we discuss some properties of this model under the assumption of Cobb-Douglas preferences, so that a is constant and ту = 1, j=l,2. We also assume that transportation costs between the two countries are identical, denoted by Ti2=,t2i=T.
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In the remainder of this section we summarize the properties of the model using Figure 1. This graph shows allocations of labor between the two countries on the horizontal axis, keeping the world labor supply (L1+L2) fixed.

In general, there is an inverse relationship between country size and the price of the Coumot-Nash good. Larger countries have more firms, and greater competition leads to lower prices. This inverse relation between country size and prices is illustrated by the lines Pi and P2 in the top panel of Figure 1. For allocations of labor between the countries in the interval (La,Lb), both countries will be producing the Cournot-Nash good. This does not guarantee that they will both be exporting the good, since transportation costs might make exports unprofitable for one or both countries. Nevertheless, we will illustrate the case where exports occur whenever production does, while noting below the conditions to ensure this.

As country 1 grows within the interval (LA,LB), its price falls while the price in country 2 rises, until point В is reached. At this point the F.O.B. price received from exporting to country 2, net of transportation charges, is just equal to the home price in country 1 (р2/т = Pi), and no firms in country 2 produces the Coumot-Nash good. Firms in country 1 are indifferent between selling at home or abroad, earning the same profits per unit in each location. For this reason, further growth of country 1 has no impact on the equilibrium prices, which are fixed at P in country 2 and Р/ x in country 1. Conversely, when country 1 is small (Li

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