A Simultaneous Moves Approach to the Complicated Simple Economics of Vertical Mergers

We use a simultaneous move approach to modeling a vertical merger between a monopolist over an input with one of two competing downstream duopolists for general demand curves. As with a successive stages model, one can decompose the changes in the merged firm’s two prices (the price of its final good and the price that it charges its competitor for the input) into a change in the stand-alone profit-maximizing price and a cross-product effect that is a form of vertical pricing pressure. The model provides support for predicting downstream pricing effects with the difference between the elimination of double marginalization and downstream vertical pricing pressure (which we refer to as “Net Downstream Pricing Pressure” or “NDPP”). It also reveals why standard measures of upstream vertical pricing pressure overstate the incentive to raise rivals’ costs. We simulate the model for a wide set of parameters for four different functional forms of demand. Compared with the successive stages model, the fraction of cases that give rise to an increase in the Fisher Index is much smaller. In the simulations, the “NDPP” statistic is a strong predictor of the change in the Fisher Index.