On input market surplus and its relation to the downstream market game
研究投入市场价格变化（如价格合谋）的福利效应，通过将投入市场剩余问题与寡头厂商集体最大化函数联系起来，放松了以往简化假设，证明投入需求曲线下方面积等于下游博弈均衡对应的函数变化。
Abstract In order to analyze the welfare effects of price changes in input markets – following for example a price‐fixing conspiracy – economists have studied the relationship between the surplus measured in the input markets and the surplus in the output markets. The latest results hinge on simplifying assumptions, which are relaxed here by linking the input markets surplus question to another stream of literature, which characterizes functions that oligopolists collectively, yet unintentionally, maximize. It is shown that the area under the input demands is equal to the change in a function for which critical points coincide with the equilibria of the downstream game. A particular case of these functions is the exact potential function.