Assignment Task:
The following example is used to evaluate your understanding of the term risk averse and the term the certainty equivalent. A utility function is often defined in relation to wealth. Utility is a measure of how satisfied an individual is at various levels of wealth. In economics, a utility function specifies a mathematical function for describing different risk profiles and measures an individual's preference for wealth by assigning a value to a particular level of wealth. The table below indicates the utility value of an individual at different levels of wealth and the numbers reflect how satisfied that individual is if his or her wealth (in thousands) is at £1, £5, £10, £100, and so on.
1. Use the data in the table to draw a graph to show whether the person is risk averse.
2. Discuss the concept of a decreasing marginal utility of wealth for people who are risk averse.
3. Assume that a risk-averse person has a 35% chance of wealth of £5 and a 65% chance of wealth of £100. Calculate the expected value of wealth. Explain how you will estimate the certainty equivalent for the risk-averse person.
4. If there is absolute certainty that £50 can be given without participating in a gambling game, should a risk-averse person take that risk?
Wealth
(£000)
Utility Value
1 0
2 0.6931
5 1.6094
7 1.9459
10 2.3026
20 2.9957
30 3.4012
35 3.5553
40 3.6889
50 3.9120
100 4.6052