question archive Exercise 4: Option Price Calculation Imagine that we want to value a cultural festival from the point of view of a risk-averse person
Exercise 4: Option Price Calculation Imagine that we want to value a cultural festival from the point of view of a risk-averse person
Subject:EconomicsPrice:3.86 Bought11
Exercise 4: Option Price Calculation
Imagine that we want to value a cultural festival from the point of view of a risk-averse person. The person's utility is given by U(I) where $I is her income. She has a 50% chance of being able to get vacation time to attend the festival. If she gets the vacation time, then she would derive a surplus of $X when she attends the festival. (The festival is free and does not cost her anything to attend.) If she does not get vacation time, then she cannot attend the festival.
(a) What is her expected surplus from the cultural festival?
(b) What would be an expression for her expected utility if she does not go to the festival.
(c) Show an expression that determines her option price.
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a = 0.5x
Step-by-step explanation
(a) What is her expected surplus from the cultural festival?
expected surplus
Es= (0.5) (x) + 90.5)(0)
= 0.5x
(b) What would be an expression for her expected utility if she does not go to the festival.
Option price =op
(0.5)U(I + x - op) + (0.5)U(I - op)
(c) Show an expression that determines her option price.
First term ; probability of attending times the utility of attending includes payments
second term; The probability of not attending times utility
therefor
U(I) = U(1 + x - op) + (I - op)
let op = 0.5x - e
U(I)= U(I + x - 0.5x + e) + U(I - 0.5x + e)
U(I)= U(I + x - 0.5x + e) + U(I - 0.5x + e)
since the marginal utility of the people who were most decline with, the above equation will not hold for e=0
the gain from the income increase by 0.5x would be be smaller than income loss by 0.5x.
The equation only holds when e is positive, therefor
OP < ES
OP- ES = -e
