On average, only 12 of the quantity produced in country 2 is sold, so the average capacity utilization in country 2 is 12. The price in country 2 is higher and the quantity produced is lower because the average capacity utilization in country 2 is lower. If country 1 exports, marginal cost in country 2 must be higher than in country 1 and total supply to country 2 (domestic production plus imports) must be higher in country 2.
This causes the price in country 1 to fall and the price to rise in country 2. The total quantity consumed by buyers in country 1 is the sum of domestic production and exports. We then have the expected profits of the seller in country 1 and the seller in country 2.
The intuition is clear: capacity utilization (fraction of output sold) is higher in country 1 and therefore the price is lower in country 1. In the low demand condition, a high price is quoted in country 2, but there are no transactions at this price . In the Appendix, I work out an example in which there are two strictly positive realizations of demand in country 2.
In this example, there are always transactions in country 2, but in the period of low demand the export price is the same (after taking into account transport costs) as the domestic price.
DELIVERY TO ORDER (FULL INTEGRATION)
It makes a big difference to the welfare analysis because buyers from country 1 have lost their priority of buying at the low price and may now be forced to buy at the high price (in the high demand state). Exotic trade patterns may also exist where country 2 exports and imports the same good at the same time. In state 2, when everyone wants to consume, only half of the buyers in country 1 can buy at the low price and the other half are forced to buy at the high price.
Since sellers in country 1 offer relatively more at the low price, and since the number of buyers buying at the low price (in country 2) is the same in both countries, country 2 imports at the low price. Since only sellers in country 2 supply at the high price and since some buyers from country 1 buy at the high price, country 2 exports at the high price. To obtain cross-shipping, we need an equilibrium in which the supplies of the two sellers are asymmetric: Seller 1 supplies only the low price while Seller 2 supplies both prices.
After the line is formed, buyers arrive at the market (come online) one at a time in a process that does not require real time (this happens in meta time). They choose to shop with the cheapest available offer after factoring in shipping costs. Sellers are price takers and expect to be able to sell to the first group at price p1 and to the second group at price p2 if it arrives.
The first market opens with certainty at price p1 and the second market opens with. Therefore, country 1 in the high demand state exports ε units at the low price and imports ε units at the high price. To see this point, note that the first market price clears the market in the low demand state.
It is also assumed that the buyer sees the location of the seller at the time he places his order online. Seller m assumes that he can sell to the first group at price (net of shipping cost) p1 m and to the second group (if . arrives) at price p2 m. In the high demand state there are exactly half of the buyers from each country who cannot buy at the first market price and want to buy in the second market.
So, in state 2, country 2 exports at the high price and imports at the low price. The exports in state 1 at the low price, the imports in state 2 at the low price and the exports in state 2 at the high price.
CONCLUSIONS
In the presence of transport costs, the full distribution of order-by-order integration gives interesting trading models. In the high-demand state there is cross-shipping: Country 2 imports at a low price and exports at a high price. Note that cross-shipping occurs on two different "conditional goods": Country 2 imports a good that will be delivered regardless of country and exports a good that will be delivered only to the high-demand country.
In the fully integrated case, a symmetric equilibrium in which each seller supplies an equal quantity to each of the two hypothetical markets requires free transportation. When transportation is expensive, the first market price received by seller 1 is higher than the first market price received by seller 2 because all buyers from country 1 are in a low demand state. I now modify the example in Section 2.1 and assume that in state 2 it can have two strictly positive realizations.
But the number of buyers who want to spend in country 2 is 12 or 1 with the same. Since the minimum number of buyers who will arrive in country 2 is 12, we say that the first 12 buyers to arrive buy in the first market. I use the following notation: xj i m = supply to market i in country j by seller m; pj i = price in country j market i.
To write the first order conditions for (A1), I use the indicator function: I(j≠m) = 1 if j≠m and zero otherwise and qj i for the. When τ = 0, the price in the first market of country 2 is the same as the price in country 1 and production is the same in both countries. But country 2 exports the good because the average price in country 2 is higher and a smaller quantity is needed to meet demand at the higher average price.
