3. Consider an economy where all consumers have the following utility as a funct

Question

3.  Consider an economy where all consumers have the following utility as a function of income:

a)  Find the expected income and expected utility of the following situation:  The consumer’s income is $500 with a 65% probability and $2500 with a 35% probability.  Use these numbers, along with the chart, to explain why the consumer is risk averse over these levels of income.  (1 point)

b)  Calculate the MU of income at $1200 and $2500 and explain why these calculations verify your findings in (a).  (1 point)

An insurance company offers consumers with the income stream in (a) $1,150 if the consumer will give the insurance company their income.

c)  Explain why the insurance company makes money off this deal but you cannot tell whether or not the consumer will take the insurance company’s deal.  If the consumer does take the deal, what specifically have you learned about the consumer’s utility that was not in the chart?  (2 points)

Explanation / Answer

a) EV= 65%($500)+35%($2500)=$1200

EU=65%(8)+35%(10)=8.7

since EU<utility at $1200, the consumer is risk averse at $1200

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