The price of the final product after vertical integration
研究上游垄断企业向前整合导致下游市场垄断时，最终产品价格如何变化。作者提出新标准，通过比较边际收益与边际成本来判断价格升降，并推广到上游边际成本可变的情形。
One of the main strands in the studies of vertical integration investigates the behavior of final product price when the forward integration by the upstream monopolist leads to a monopoly in the market for downstream product. So far the price of final product is known to remain the same as before if the production technology of downstream industry is using inputs only in fixed proportions. As in the case of variable proportions technology, the most up-to-date results had been reported by Parthasaradhi Mallela and Babu Nahata (1980), and Fred Westfield (1980). Mallela and Nahata studied the case when the downstream technology is representable by a constant elasticity of substitution (CES) production function and the demand for final product exhibits a constant price elasticity. They found that the price of the final product must rise after integration when the substitution elasticity has a value not less than unity. On the other hand, Westfield presented an alternative analytic framework by introducing the concept of benchmark price of the intermediate good, which will sustain the (integrated merger's) monopoly equilibrium configuration of final product market as a competitive configuration before integration as well. But there is an inherent problem in Westfield's approach: All of his criteria utilize the values of parameters evaluated at the configuration of not current but benchmark price, and therefore those values are not to be observed directly or computed easily from the observation of the real world. In the benchmark configuration, the downstream market exhibits the same equilibrium price and quantity as those in monopoly which would be induced by the vertical merger. If one knows precisely what the benchmark configuration, especially the price of final product, will be, then no further analysis will be necessary! There is another aspect of this problem that has never been addressed to so far. All the pre-existing results assume a constant upstream marginal cost, excluding many standard cases where the upstream monopoly is a natural one. Thus it will be worth investigating what happens when the upstream marginal cost is variable. In this note, I propose an alternative set of criteria which will generalize and improve the pre-existing ones by comparing the marginal revenue of downstream industry directly with the marginal cost of vertical merger at the current level of production before integration. Although this marginal cost might not be observable, this comparison yields the conditions consisting of parameters whose values are observable from the current configuration. Assume that the demand for final product exhibits a nonincreasing marginal revenue schedule. Then whenever the vertical integration yields a marginal cost for producing the final product which is higher (lower) than the marginal revenue at the current level of production, the integration with monopolization will surely lead to a decrease (an increase) of quantities produced and the corresponding increase (decrease) in the price of final product. All the analyses below will be carried out according to this criterion. I will investigate the conventional case where the final product is produced from one primary factor and one intermediate factor. The primary factor is sold at a constant competitive price that is set at unity and the intermediate factor is sold by the upstream monopolist at the price s. Assume that the technology of downstream industry is representable by a linearly homogeneous neoclassical production function. Then the down*Associate Professor of Economics, Department of Economics, Seoul National University, Seoul 151, Korea. I appreciate the comments of A. Mas-Collel, D. Abreu, W. Thomson, and an anonymous referee. I also gratefully acknowledge the fellowship support from the Harvard-Yenching Institute.