Increasing returns, the choice of technology, and the gains from trade.

1. Introduction

Models of international trade based on increasing returns have been studied intensively in the past three decades. In the literature, the source of increasing returns may be external or internal. For models based on external returns to scale, a firm's cost decreases with total industry level of output. A firm is assumed to be too small to affect the industrial level of output significantly. An example of a model based on external increasing returns is Ethier (1982). Internal returns to scale come from spreading fixed costs of production. With a constant marginal cost, a firm's average cost decreases with its output, as the fixed cost can be distributed over a larger level of output. An example of a model based on internal increasing returns is Horstmann and Markusen (1986). In both papers, labor is the only factor of production. The manufacturing sector exhibits increasing returns to scale, while the agricultural sector has constant returns to scale.

However, the two models differ in their conclusions on whether the opening of international trade is always beneficial. Under internal increasing returns, Horstmann and Markusen (1986) show that trade always increases a country's welfare, and Venables (1985) shows that this result is robust to the alternative assumption that domestic and foreign markets are segmented rather than integrated. Under external increasing returns, Ethier (1982) shows that if trade leads the smaller country to specialize completely in the production of agricultural goods and the larger country to specialize completely in the production of manufactures, the smaller country benefits from trade only when certain conditions are satisfied. These conditions require either that the percentage of income spent on manufactured goods be relatively low or the degree of returns to scale be large or that countries differ significantly in terms of their sizes. If none of these conditions are satisfied, then the smaller country loses from the opening of international trade. Thus, the opening of trade is more likely to be beneficial to the smaller country under internal increasing returns than under external increasing returns. What is the reason behind this difference of results?

We may not expect models based on different specifications of increasing returns to lead to similar results: Under internal increasing returns, with a fixed cost and a constant marginal cost, average cost is bounded asymptotically by the constant marginal cost; with external increasing returns, average cost may decrease without being bounded asymptotically by a given level of marginal cost. However, if internal increasing returns also lead to average cost unbounded asymptotically, will the implications of trade be similar under different specifications of the source of increasing returns?

In this paper, the impact of international trade is studied in a two-sector general equilibrium model in which the returns to scale are internal. The innovation of this paper is that it incorporates the choice of technology into a firm's profit maximization. One contribution of this paper is that it shows that the production function generated from internal increasing returns and the choice of technology leads to a degree of the returns to scale similar to that based on external increasing returns. This allows us to analyze the case that average cost is not bounded asymptotically by a given level of marginal cost and makes the comparison of results based on different specifications of the returns to scale feasible. The incorporation of the choice of technology into our study is also justified by the observation that firms do choose their technologies optimally in reality. We show that the main result in Horstmann and Markusen's (1986) partial equilibrium model that trade always increases a country's welfare generalizes to this general equilibrium model. Trade always increases a country's welfare in a two-sector model in which the agricultural sector has constant returns to scale and average cost in the manufacturing sector may decrease without being bounded asymptotically by a given level of marginal cost. Thus, the difference of results between internal and external increasing returns does not arise from whether average cost is bounded asymptotically by a given level of marginal cost.

One natural question is why trade is always beneficial for the smaller country under internal increasing returns while it may get harmed under external returns to scale. To answer this question, we need to understand why the opening of international trade may decrease the smaller country's welfare when the returns to scale are external. This is achieved through three steps. First, I show that the specification of external increasing returns leads to the result that only the larger country produces manufactured goods. One assumption in the literature on external increasing returns is that a firm's cost is affected by domestic aggregate output, not by world aggregate output. Average cost pricing is usually assumed in models of external increasing returns. Since average cost decreases with the level of domestic aggregate output, the country with a higher labor endowment has a lower price of manufactures. With the opening of trade, if the smaller country produces any manufactures, then average cost and thus the price of manufactures in the smaller country will be higher than those in the larger country. However, without transportation costs, prices of manufactures should be the same all over the world since otherwise international arbitrage will happen. Thus, with the opening of trade, the production of manufactures will be concentrated in the country with a higher labor endowment.

Second, I establish the negative relationship between the price of manufactures and the welfare of a representative consumer living in the smaller country. The representative consumer's utility is determined by her wage income, the price of manufactures, and the price of agricultural goods. The price of agricultural goods is always normalized to one. As the agricultural sector is assumed to have constant returns to scale, without loss of generality, the wage rate can be normalized to one if the smaller country produces some agricultural goods. With the opening of trade, the price of agricultural goods and the wage rate do not change since the smaller country still produces agricultural goods. Thus, a necessary and sufficient condition for trade to lead to a decrease of the utility for the representative consumer in the smaller country is that trade leads to an increase of the price of manufactures. (1)

Third and finally, I illustrate why the price of manufactures with trade may be higher than in the smaller country before trade. (2) The price of manufactures with trade may increase if trade leads to a decrease in the supply of manufactures, which is caused by a decrease of the world level of workers employed in the manufacturing sector. Before trade, both countries have some workers employed in the manufacturing sector, and the world level of workers employed in the manufacturing sector is the sum of workers in the two countries. With the opening of trade, only workers in the larger country may work in the manufacturing sector. Even if all workers in the larger country work in the manufacturing sector, the world output of manufactures may be lower than that before trade. If this leads to an increase of the price of manufactures, then the smaller country loses from trade. For the smaller country, though the price of manufactures is higher after trade and it imports manufactures, it could not revert to its production pattern before trade, as the production of manufactures has to be concentrated in the larger country after trade.

More specifically, before trade, the number of workers in each country employed in the manufacturing sector increases with the percentage of income spent on manufactures. If the percentage of income spent on manufactures is high, the percentage of workers in each country employed in the manufacturing sector before trade is high. After the opening of trade, if labor endowments in the two countries do not differ significantly, the total number of workers in the world working in the manufacturing sector after trade (which is the labor endowment of the larger country) will be smaller than that before trade (which is the sum of manufacturing workers in both countries). If the degree of increasing returns is not high enough, with the opening of trade, the price of manufactures increases. As the price of manufactures increases (Ethier 1982, p. 1261), a typical worker in the smaller country loses from the opening of trade.

With external increasing returns, the larger country always benefits from trade. With the opening of trade, there are two cases for the pattern of production for the larger country. In the first case, the larger country produces both types of goods. (3) The larger country benefits from trade as the wage rate and the price of agricultural goods do not change and the price of manufactures decreases. In the second case, the larger country produces only manufactures. There are two possibilities: First, if the price of manufactures decreases, the larger country benefits from trade for the same reason as in the first case; second, if the price of manufactures increases, the larger country still gains from trade because the wage income for a worker in the larger country increases directly with the price of manufactures while only part of the wage income is spent on manufactures.