Effect of price elasticity of demand in monopolies with gradient adjustment

• A monopoly with isoelastic demand function is studied.
• Reduced rationality monopolist uses gradient adjustment.
• If marginal cost is small, increasing elasticity leads to stable dynamics.
• For large marginal cost, dynamic can be unstable for both small and large elasticity.

We study a monopolistic market characterized by a constant elasticity demand function, in which the firm technology is described by a linear total cost function. The firm is assumed to be boundedly rational and to follow a gradient rule to adjust the production level in order to optimize its profit. We focus on what happens on varying the price elasticity of demand, studying the effect on the equilibrium stability. We prove that, depending on the relation between the market size and the marginal cost, two different scenarios are possible, in which elasticity has either a stabilizing or a mixed stabilizing/destabilizing effect.