Pricing under Spatial Competition and Spatial Monopoly: Reply
回应Capozza和Van Order关于空间竞争下企业定价高于垄断者的结论，指出其模型存在方程根选择错误，并通过引入动态调整和消费者剩余分析，证明较大根才是稳定均衡。
IN A RECENT PAPER D. R. Capozza and R. Van Order (C.V.) [1] claim to show that there exist conditions under which a competitive firm in industry equilibrium in a spatial environment will charge a higher mill price than a spatial monopolist. This conclusion seems contrary to our intuition and consequently the conditions under which it arises should be made very clear. This paper argues that the C.V. result is not necessarily correct. In particular, there is an apparent error in the three sentences following equation (27). The positive roots of equation (27) are both possible candidates for equilibrium price.2 The difficulty is that there are no grounds for choosing between the two roots within the structure of the model. Capozza has argued, in correspondence, that the smaller root is inappropriate because demand is negative. However, demand is only negative at the border of the market area and one could equally well argue that this is a case of natural monopoly, induced by the cost structure. These remarks are made within the assumptions that C.V. makq in their paper. We can, however, shed further light on the matter by introducing some new elements. In particular, (i) we explicitly impose some simple dynamics on the system, and (ii) we use consumer surplus as a measure cf welfare. (i) Let us suppose that firms are price setters and assume a zero conjectural variation. Under these conditions it is not difficult to show that the larger positive root is stable and the smaller is unstable. (ii) The total of consumer surplus at price m and market radius Do is given by