The Amazing Geometry of Price Competition with Quality Dependent Production Costs

Endogenous Market Coverage with Quality Dependent Production Costs

“…1.25d 0.545d 0.545d 0.625d 0.625d the fact that the maximum surplus that a firm can offer is nonlinear with the quality level. 11 As expected, the consumer surplus has a discontinuity at  =0 545,b u tt h ed e c r e a s ei ss o slight that it can hardly be seen in the graph. In all the other points, the consumer surplus is increasing with .…”

“…Considering these, we then solve the first stage of the game and determine the equilibrium vector of qualities. The second stage of the game has been solved by Pires et al (2022) considering all possible market configurations and determining the set of quality vectors where each market region holds. Consequently, the main emphasis in this paper is in solving the first stage game.…”

“…The partial coverage and the interior full coverage solutions are mutually exclusive, but for certain quality vectors none of them holds. Instead, in the second stage game, the equilibrium involves a corner solution where the low-quality firm full coverage constraint is binding (Pires et al, 2022). The interior SPNE candidate under corner full coverage is given by: Proposition 4 If firms are restricted to choose qualities such that a corner full coverage duopoly equilibrium occurs in the second stage of the game, the SPNE candidate qualities, ( * * 1  * * 2 ) are a solution of the following system:…”

“…W ed e r i v et h es u b g a m ep e r f e c tN a s hequilibria exploring the equilibrium quality choices and identifying when each possible market coverage configuration holds, considering also monopoly scenarios, which are not explored in Wauthy (1996) and Liao (2008). Our analysis builds on the results of Pires et al (2022) regarding the price-competition game, using them as the starting point of our analysis and concentrating on the first stage of the game, where firms decide their quality levels. We show that as long as quality investment costs are infinitesimal a monopoly will never be a subgame perfect equilibrium.…”

“…The figure is adapted from Pires et al (2022) as we do not distinguish the various types of low quality monopolies. It is obtained by representing the limits of each market region presented inPires et al (2022)…”