Question

Suppose U(X)=15+X.

a. Graph this utility function

b. Suppose you have a binary lottery with a 40% chance of $0 and a
60% chance of $100. Draw

the probability tree of this lottery.

c. Show the lottery in Part B on your graph from Part A. You need
to show: U(0), U(100), EV,

U(EV), EU, U(CE) and the CE. Be sure to label everything
clearly.

d. What can you say about the CE and EV for this lottery? Why?

Answer #1

a.

X | U(X) |

0 | 15 |

25 | 40 |

50 | 65 |

75 | 90 |

100 | 115 |

125 | 140 |

d.

As CE and EV are equal then the individual is risk neutral and there is no risk premium.

Suppose U(x)=x0.5
a. Graph this utility function.
b. Suppose you have a binary lottery with a 40% chance of $25 and a
60% chance of $100. Draw
the probability tree of this lottery.
c. Show the lottery in Part B on your graph from Part A. You need
to show: U(25), U(100), EV,
U(EV), EU, U(CE) and the CE. Be sure to label everything
clearly.
d. What can you say about the CE and EV for this lottery? Why?

3. Suppose U(X)=15+X.
Hint: See the Risk Graph notes posted in Moodle
a. Graph this utility function
b. Suppose you have a binary lottery with a 40% chance of $0 and
a 60% chance of $100. Draw the probability tree of this
lottery.
c. Show the lottery in Part B on your graph from Part A. You
need to show: U(0), U(100), EV, U(EV), EU, U(CE) and the CE. Be
sure to label everything clearly. **If the TA cannot read...

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7.
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u(x1, x2) = x
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1 x
2/3
2
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UA(X,Y) = X^1/2*Y^1/2
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