Question

In: Economics

Albert's utility function is U(I) = 100I2 , where Iis income.Stock I generates net-payoffs...

Albert's utility function is U(I) = 100I² , where I is income.

Stock I generates net-payoffs of $80 with probability 0.3, $100 with probability 0.4; and $120 with probability 0.3. Stock II generates net-payoffs of $80 with probability 0.1, $100 with probability 0.8; and $120 with probability 0.1.

(i) Which stock should Albert select, I or II?

(ii) What general point about risk-loving preferences have your illustrated?

Expert Solution

(i)

Albert will choose an option which gives him higher Expected Utiltiy EU

EU from Stock I = 0.3U(80) + 0.4U(100) + 0.3*U(120)

= 0.3(100*80*80) + 0.4*100*100*100 + 0.3*100*120*120

= 192000 + 400000 + 432000

= 1024000

EU from Stock II = 0.1U(80) + 0.8U(100) + 0.1*U(120)

= 0.1(100*80*80) + 0.8*100*100*100 + 0.1*100*120*120

= 64000 + 800000 + 144000

= 1008000

EU from Stock II < EU from Stock If

So, Albert will choose Stock I.

ii)

U = 100I2

dU/dI = 200I

d2U/dI2 = 200 > 0

So, the utility function is convex. So, the risk loving person has the convex preferences. More risk implies more expected utility.

Rahul Sunny answered 2 years ago

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