Multiple-Quality Cournot Oligopoly and the Role of Market Size

We model an oligopoly where firms can choose the quality level of their products by incurring set-up costs that generally depend on quality level. If the set-up cost is independent of product quality, firms may choose to supply both types of quality.We focus on the long run equilibrium where free entry and exit ensure that the profit for each type of firm is zero. Using this framework, we study the implications of an increase in the market size. We show that for the existence of an equilibrium where some firms specialize in the low quality product it is necessary that the set-up cost for the lower quality product, adjusted for quality level, is lower than that for the higher quality product. In the case where the unit variable costs are zero, or they are proportional to quality level (so that unit variable costs, adjusted for quality, are the same), we show that an increase in the market size leads to (i) an increase in the fraction of firms that specialize in the high quality products, (ii) the market shares (both in value terms and in terms of volume of output) of high quality producers increases, and (iii) the prices of both types of product decrease. In the case where higher quality requires higher set-up cost (per unit of quality) but lower unit variable cost (per unit of quality), subject to certain bounds on the difference in unit variable costs, we obtain the result that an increase in the market size decreases the number of low quality firms, increases the number of high quality firms, and decreases the prices of both products. In the special case where the set up cost is independent of quality level, we find that all firms will produce both type of quality levels. In this case, an increase in the market size will reduce the value shares of low quality products, but will leave their volume share unchanged; and the market expansion induces a fall in the relative price of the low quality product, and in the prices of both products in terms of the numeraire good. We carry out an empirical test of a version of the model, where set-up costs now refer to set-up costs to establish an export market, and they vary according to the quality of product that the firm exports to that market. We show that the data supported the hypothesis that the average qualities of the product are higher for bigger export markets.