Ch-Uncertainty

[Nikkita]

Your utility function is of the form U = ln(W). Your initial wealth is $30. You are offered a lottery, which gives $50 with probability ½ and $10 with probability ½. What is the maximum amount of money he is willing to participate?


    23.94

    22.12

    24.89

    26.76

(correct ans= 23.94; mine is coming as 26.68)

[Nikkita]

Also, guys, how we find exact value of log in paper( like in uncertainty type of ques.)?
by manual calculator, we get appox. value.. are we supposed to use those?

[Nikkita]

2. Suppose there is a 50% chance that the next season is going to be draught. You are a farmer and you are expected utility maximizer , with U(w) = ln(w) and your initial wealth is $0.  You can grow crop C1 and/or C2. Payoffs are as follows : Payoff(C1|Normal rain) = $5000, Payoff(C2|Normal rain) = $20,000, Payoff(C1|Draught) = $40,000 and Payoff(C2|Draught) = $12,000.
Suppose you decide to plant half your land with each crop. You are offered an insurance for crop C2. This insurance costs $5,000 and pays $10,000 in the event of drought. What is your utility in this case? Will you buy an insurance?


    9.81 , yes

    9.72, no

    9.82, yes

    9.78, no

(Correct Ans.= 9.72, no)

[Abhitesh]

Initial wealth = 30 => initial utility = ln(30)
Let us bet m.
Wealth if I win = 80-m.
Wealth if I lose = 40-m.
Expected utility <U>=0.5*(ln(80-m)+ln(40-m))
The amount money I will be willing to bet will be given by
<U> >= ln(30)
=> (80-m)(40-m) >= 900
=> m^2 -120m +2300 >=0.
Now we have to find maximum m(<=30) which satisfies above inequality.
The solution of this equation in 60+/- 10\root(13)
Solve it to get the answer.

[Abhitesh]

Since one type of crop is planted on only half of the land. So payoff from each type will be half.

Without insurance.
In case of normal rain (P=.5)
Payoff = 2500 + 10000 = 12500
In case of draught (P=.5)
Payoff = 20000 + 6000 = 26000
Expected utility <U0> = 0.5(ln12500 + ln26000)

With insurance
In case of normal rain (P=.5)
Payoff = 2500 + 10000 - 5000 = 7500
In case of draught (P=.5)
Payoff = 20000 + 6000 - 5000 + 10000 = 31000
Expected utility <U1> = 0.5(ln7500 + ln31000) = 9.63
Check that U1 < U0

[Nikkita]

Thankyou Abhitesh