Revisiting Pareto Inferior Trade with a Stochastic Ricardian Model and Transaction Cost : A Preliminary Investigation under Symmetry

We consider a 2×2 Ricardian model under uncertainty to see if there is Pareto inferior trade, as Newbery and Stiglitz (RES, 1984). Their model is a partial equilibrium model while ours is a general equilibrium with transaction cost. We claim that expected welfare unambiguously improves as trade begins and transaction cost declines. This result is consistent with Newbery and Stiglitz: consumers are unambiguously better o . In addition, we find that the income of workers in a risky sector declines when transaction cost is high and that does not exceed the autarky level, which is analogous to Pareto inferior trade. * Visiting Assistant Professor, Department of Economics, Kumamoto Gakuen University, Japan † Visiting Researcher, RIEB, Kobe University, Japan (after April 1, 2013: Associate Professor, College of Economics, Nihon University, Japan) conditions in the respective regions. The weather is either good or bad. For further symmetry, weather conditions of the two regions are perfectly negatively correlated at 50% probability. Turnovsky (1974) provides various versions of Ricardian model under uncertainty. Our model is another version of his model: uncertainty only in one production sector. The discussions are developed as follows. We set up the basic framework and derive the equilibrium conditions both for autarky and interregional trade in Section II (technical proofs for remarks provided in this section are provided in the appendix). The model is then numerically examined in Section III. For the simulation, parameters are determined to be symmetric. Further inferences and concluding comments are given in Section IV. II The Model We consider a model of two regions on an island, the East (E) and theWest (W). E and W are divided by high mountains, which make trade between E and W costly. Both regions are capable of two products, agricultural (A) and manufacturing (M) goods. E and W are assumed to produce identical agricultural and manufacturing goods using identical technologies. Goods can be traded, but trading between the regions is costly. The di erence between the regions is weather. If E has a wet year, W has a dry year (drought). Conversely, if W has a wet year, E has a dry year. The harvest of the agricultural good is conditional on the weather: wet is good while dry is bad for A. The production of M is not a ected by the weather. The timeline of this model is as shown in Figure 1. In the beginning (t = 0), producers and consumers make predictions about the future weather to generate expected prices as a basis for allocating their resources. After the allocations, producers start production. Before production is completed, weather occurs in each region (t = 1). After that, actual income is generated and actual consumption takes place (t = 2). We call the phase before completion of production ex ante and after completion of production ex post. M is produced by labor and A is produced by labor and weather conditions. The production functions of A and M are represented by classical technologies A = Ω × αAL and M =αML, where L and Ω are labor input and weather conditions, respectively, and αA and αM are the marginal products of labor for the respective goods ( input coe cients are thus βA αA and βM αM). 1 Let pij be the price of i {A,M}in region j {E,W}. Similarly, let wij be the corresponding wage rate. The profit maximization and utility maximization problems of each region are 1 Turnovsky (1974) assumes technologies of both sectors include stochastic factors while ours incudes them only in one sector. Tomoru HIRAMATSU and Tetsuya SAITO 30