Learning and Price Volatility in Duopoly Models of Resource Depletion

Abstract

We introduce learning into a Hotelling model of a non-renewable resource market. By combining learning and scarcity we add significantly to the dynamics implied by learning and substantially enhance the volatility of commodity prices. In our learning model we show how a self confirming equilibrium exists but is not constant over time. As scarcity increases the SCE shifts from a non-cooperative rational expectations equilibrium to a cooperative rational expectations outcome. As a result prices trend at a rate faster than the rate of time preference. We show the existence of escape dynamics which generate substantial volatility in commodity prices despite the fact the model is subject only to i.i.d shocks. The shifting SCE significantly alters escape dynamics with the time to escape shortening and the magnitude of dynamics reducing as scarcity rises. In terms of the Hotelling model, a shifting SCE and variable escape dynamics introduces greater volatility at low frequencies and substantially larger cyclical volatility. These price fluctuations show sharp upward breaks in price and non-linear, non-stationary and asymmetric price fluctuations. We show these results are robust to a range of extensions, including extractions costs, stochastic shifts in demand and learning assumptions closer to rational expectations.

Keywords: Commodity Prices, Escape Dynamics, Hotelling, Learning, Scarcity, Self Confirming Equilibria

JEL Classification: D43, D83, Q31