Relative profit maximization and Bertrand equilibrium with quadratic cost functions

Relative Profit Maximization and Bertrand Equilibrium with Convex Cost Functions

This study derives pure strategy Bertrand equilibria in a duopoly in which two firms produce a homogeneous good with convex cost functions and seek to maximize the weighted sum of their absolute and relative profits. The study shows that there exists a range of equilibrium prices in duopolistic equilibria. This range of equilibrium prices is narrower and lower than the range of equilibrium pric...

Relativistic Equilibrium Distribution by Relative Entropy Maximization

The equilibrium state of a relativistic gas has been calculated based on the maximum entropy principle. Though the relativistic equilibrium state was long believed to be the Jüttner distribution, a number of papers have been published in recent years proposing alternative equilibrium states. However, some of these papers do not pay enough attention to the covariance of distribution functions, r...

Profit maximization with bankruptcy and variable scale

In a diffusion model of an enterprise with variable scale, conditions are given for the maximization of ‘profit’ (expected total discounted withdrawals) to lead to bankruptcy almost surely. The optimal withdrawal policy is an ‘overflow policy’: the withdrawal rate is zero if the asset level is below a ‘barrier’, and equal to the maximum rate if the asset level is at least equal to the barrier. ...

Customer Selection and Profit Maximization

Profit Maximization and Supermodular Technology

A dataset is a list of observed factor inputs and prices for a technology; profits and production levels are unobserved. We obtain necessary and sufficient conditions for a dataset to be consistent with profit maximization under a monotone and concave revenue based on the notion of cyclic monotonicity. Our result implies that monotonicity and concavity cannot be tested, and that one cannot deci...