Global dynamics in a commodity market model

We study the global behavior of the price dynamics in a commodity market governed by a balance between demand and supply. While the dependence of demand on price is considered instantaneous, the supply term contains a delay, leading to a delay–differential equation. A discrete model is naturally defined as a limit case of this equation. We provide a thorough study of the discrete case, and use these results to get new sufficient conditions for the global convergence of the solutions to the positive equilibrium in the continuous case. For when the equilibrium is unstable, we provide some bounds for the amplitude of the oscillations that are quite sharp when the delay is large.