Question

4. Suppose Kate has a utility of income function given in the following table Utilit 0 Income 0 100 200 300 400 500 600 700 800 900 1000 12 35 48 58 72 76 78 (a) Kate has a choice between $200 with certainty and receiving $100 with probability 0.5 and receiving $300 with probability 0.5. Which will Kate choose? (b) Kate has a choice between $800 with certainty and receiving $600 with probability 0.5 and receiving $1000 with probability 0.5. Which will Kate choose? (c) Using your answers in (a) and (b), explain whether Kate is risk averse, risk neutral or risk loving

Answer 1

(a)

Expected value with uncertainty = $100 x 0.5 + $300 x 0.5 = $50 + $150 = $200

Since expected value with uncertainty is equal to the value of income with certainty, Kate will choose $200 with certainty.

(b)

Expected value with uncertainty = $600 x 0.5 + $1000 x 0.5 = $300 + $500 = $800

Since expected value with uncertainty is equal to the value of income with certainty, Kate will choose $800 with certainty.

(c)

Since in both cases Kate chooses to receive income with certainty, she is risk averse.