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Microeconomic principles : Uncertainty - Essay Example

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1. An individual is said to be risk averse if he prefers a certain income over a fair gamble that is associated with an expected income that is equal to the certain income. The degree of risk aversion is then the extent to which the individual prefers the certain income over the uncertain income…
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Microeconomic principles : Uncertainty
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"Microeconomic principles : Uncertainty"

Download file to see previous pages Figure 1: Risk Aversion and the concavity of the utility function Consider a rational individual with a typical upward rising concave (implying diminishing Marginal Utility) utility function U(.) defined over money incomes X. Suppose the individual can either play a lottery where two possible outcomes are possible: X1 a low income and X2 a high income. Further assume that both are equally likely. That is, both occur with probability = ?. Thus if X1 is realized the individual gets U(X1) and if X2 realizes, the individual derives U(X2). Then, the expected income from the lottery is ?[X1+X2] and the expected utility is ? [U(X1) +U(X2)]. The scenario is depicted in the diagram above. Now, observe that the utility derived by the individual from a certain income of ?[X1+X2] which is equal to U?[X1+X2] lies above ? [U(X1) +U(X2)], the expected utility from the lottery with an expected earning of ?[X1+X2]. This shows that the individual prefers a certain income over an above a lottery with an expected income that is equal to certain income. Thus, the individual is risk averse. Further, note that the further U?[X1+X2] lies above ? [U(X1) +U(X2)], the more risk averse is the individual, since the preference for the certain income is even greater in that case. This implies that the more concave the utility function the greater will be the risk aversion of the individual. Now, consider Mr. D’s utility function. ...
A risk neutral agent in contrast to a risk-averse agent is indifferent between picking a certain income and playing a lottery which has the equal expected income. Therefore, Mr. D is not influenced by the fact that the income from the lottery is attached to some risk bearing which is not true in case of the certain income. The indifference implies that in making decisions, Mr. D would compare expected incomes between choices and pick the option associated with the highest expected income. 2. We shall assume =2 and =3. The resulting utility functions are shown in the diagram below (figure 3). We are concerned with the rational decision in Mr. D’s case. Now, Mr. D is rational if he picks the option that generates the greatest utility for him. In the present context, when =2, if Mr. D tries to earn $60000 the expected income is. The resulting expected utility therefore is $70000. This is point A on the diagram below (figure 3). Alternatively, if Mr. D decides to stay within speed limits, the certain income=expected income=$30000. Therefore, the utility obtained in this case=expected utility obtained = $60000.This is point C in figure 3. Therefore, if =2, pursuing the income of $60000 generates a higher utility. Thus, taking the risk of breaking the speed limit to earn $60000 is the rational choice. Again if =3, and Mr. D tries to earn $60000 the expected income remains equal to. However, the resulting expected utility now is 3(35000) = $105000. This is shown as point C in the diagram below (figure 3). The utility derived from the certain income now is = $90000. This is point D in figure 3. Therefore, the expected utility of pursuing the yearly income of $60000 yields is higher compared to that of pursuing the income of $30000. Thus, when =3, the ...Download file to see next pagesRead More
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