Question

The CEO of a publishing company says she is indifferent between the certainty of receiving $7,500 and a gamble where there is 0.5 chance of receiving $5,000 and a 0.5 chance of reveiving $10,000. Also, she says she is indifferent between the certainty of reveiving $10,000 and a gamble where there is a 0.5 chance of receiving $7,500 and a 0.5 chance of receiving $12,500. a) Draw four points on the utility function of this publishing executive. b) Does she seem to be a risk averter, a risk lover, or risk neutral?

Answer 1

Expected payoff from gamble =  0.5*$5,000 + 0.5*$10,000 = $7500
Certain payoff = 7500

Expected payoff from gamble =  0.5*$7500 + 0.5*$12,500 = $10,000
Certain payoff = 10,000

The four points that can be drawn from the graph are as below:

Since the utility from certainity and gamble is same for both cases, it implies that the lines are plotted on a straight line, else in case of a concave or convex graph, the expected utility from different payoffs will not be proportional. Therefore, cannot yield the same utility. The publisher's utility function is a straight line hence expected utility from each of the combination above is equal. Risk neutral means that each additional unit of money does not increase or decrease the utility from that unit.