Asset market equilibrium: A simulation
This paper examines how an asset price is determined in a market, and how it changes as circumstances in the market change, making use of a standard asset price model. The motivation of the paper is to examine if the model can explain a bubble economy in which individuals are risk averse. It is known that if the relative risk aversion of an investor's utility function does not exceed I and is not decreasing, the equilibrium asset price declines when uncertainty increases with respect to the prospect of a dividend receipt. In this paper we examine if there is any utility function which provides the counter example, one in which the asset price rises despite increased uncertainty. Starting from a two period maximization problem with risk aversion, with certain dividends for the two periods, it is shown that if uncertainty is introduced for the second period, the exponential utility function provides this counter example. It is shown that in this particular case that the asset in question has the characteristics of a Giffen good when the asset price is already high. However, when uncertainty is introduced for two periods, the exponential utility function does not provide this counter example. Thus, when uncertainty is not as great, the income effect may raise the asset price despite increased uncertainty. It is also found that a quadratic utility function may explain the collapse of a bubble economy. The standard asset price model is formulated as the pure-exchange economy, without production. Finally, this paper points out that the existence of an asset price may be guaranteed even if production is incorporated into the standard model so long as a certain degree of uniformity is assumed about the distribution of the investors' initial possession of assets. (c) 2008 IMACS. Published by Elsevier B.V. All rights reserved.
simulation asset price bubble relative risk aversion giffen good