Question

5. Understanding risk aversion 

Suppose your friend Eleanor offers you the following bet: She will flip a coin and pay you $1,000 if it lands heads up and collect $1,000 from you if it lands tails up. Currently, your level of wealth is $3,000. The graph shows your utility function from wealth. Use the graph to answer the following questions. 

The shape of your utility function implies that you are a _______ individual, and, therefore, you _______ accept the wager because

the difference in utility between A and C is _______ the difference between C and B.

Which of the following best explain why the pain of losing $1,000 exceeds the pleasure of winning $1,000 for risk-averse people? Check all that apply. 

• Risk-averse people are relatively wealthy and simply do not need the additional money, 

• Risk-averse people overestimate the probability of losing money. 

• The more wealth that risk-averse people have, the less satisfaction they receive from an additional dollar. 

• The more wealth that risk-averse people have, the more satisfaction they receive from an additional dollar.

Answer 1

I have wealth level of $3000. If coin lands up on heads, I end up earning a total wealth of $3000 + $1000 = $4000, and if coin lands up on tails, I'll end up with wealth level of $3000 - $1000 = $2000.

The utility function as shown plotted on the graph is concave shaped, implying that I am a risk-averse individual.

Difference in utility between A and C = |65 - 55| = 10 in absolute terms

Difference in utility between C and B = |70 - 65| = 5 in absolute terms

Given this, I will not accept the wager because the difference in utility between A and C is greater than the difference between C and B (10 > 5).

In other words, this non-acceptance occurs because on losing the wager, that is paying away $1000, with end wealth of $2000, I lose more utility (10) than what I gain on winning the wager and ending up with wealth of $4000 (5) (thus, explaining risk averse shape).

As already seen above, the pain of losing $1000 exceeds pleasure of gaining $1000 (that is utility lost on losing is more than utility gained on winning) for a risk-averse individual because at high levels of wealth, an additional dollar generates a lower satisfaction addition (so, diminishing marginal returns).

Thus, correct option is (c) only.