Relation between Utility Theory of Money and Risk Aversion

 Utility Theory and Risk aversion

There is an important relationship between utility theory of money and risk aversion. The person may have three kind of attitudes towards the risk. They are: aversion to risk which means they do not prefer risk and wants to avoid it, indifference to risk which means they ignore about risk factor and treat all the projects equally, and preference for risk which means they want to take risk with the aim of getting higher return.

Before explaining this concept we have to understand about risk aversion. So, what is risk aversion ? The behaviour of not taking risk by the person is called risk averison. Risk averser person always wants safe side. If there are two choice for him or her i.e. 100% guarantee of  getting 20,000 and 50% chance of getting 40,000 or getting nothing. The risk averse person chooses the first option because they don't want to take risk. Okay, let's dive into the concept now.

Concept:

Most of the managers prefer less risky projects. However, some managers may choose risky project and some managers are indifferent to risk. The reason for this is to be found in the principle of diminishing marginal utility of money. The utility theory of money and risk aversion explain the relationship between money income and its utility. On the basis of this relationship we can easily find the preference of the managers.

Risk Aversion concept is mainly concerned with the idea of diminishing marginal utility of money. The diminishing marginal utility of money says that the satisfaction of the persons will be decreasing as increase in additional income they received. Let us suppose, if someone with no money receives $ 2000, it can satisfy his or her most immediate needs. If such person receives again $ 2000, it will be useful for him or her but the utility derived from the second amount will be less than the first amount received. This implies that marginal utility of money Diminishes with the increase in additional amount of money.

Figure:

The concept of diminishing, constant and increasing marginal utility of money can be explained with the help of following figure.

In the above figure, x-axis represents money income or wealth and y-axis represents the total utility of money. The figure shows three curves OM, ON, and OP. OM represents diminishing marginal utility of money curve, ON represents constant marginal utility of money curve and OP represents increasing marginal utility of money curve.

When money income is OY1, the total utility derived is OU1 at point A. When money income increases to OY2, the total utility received are OU2, OU3, and OU4 depending upon the total utility curve. When total utility curve is OM, the total utility derived from the income OY2 is OU2, when total utility curve is ON, the total utility derived from OY2 income is OU3 and when total utility curve is OP, the total utility derived from income OY2, is OU4.

When the person is at the curve OM, such person is risk averter, when the person is at the curve ON, such person is risk neutral and when the person is at curve OP, such person is risk seeker. In other words, if marginal utility of money diminishes, the person is risk averter, if marginal utility remains constant, the person is risk neutral and if marginal utility of money increases, the person is risk seeker.