Hyperbolic Discounting and Secondary Markets

We study the effect of hyperbolic discounting on competitive equilibria in secondary markets for a durable good. Under exponential discounting, secondary markets are irrelevant in our model. They do not affect the price in the initial period and are neutral to the allocation. Under hyperbolic discounting, secondary markets are not neutral: they do affect price and allocation. The price in the unique competitive Markov equilibrium is lower than the price in the absence of secondary markets. This affects the equilibrium supply of the durable good in the initial period. We characterise all stationary competitive equilibria in terms of prices. In particular, we obtain that there are stationary competitive equilibria in which trade occurs in each period and the allocation of the durable good is inefficient. Furthermore, we show that there exist competitive equilibria with increasing, decreasing, and cycling price paths, despite the stationarity of the market environment.