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 percent chance of being able to get vacation time to attend the festival. If she gets the vacation time, then she would be willing to pay up to $S to attend the festival. If she does not get the vacation time, then she is unwilling to pay anything for the festival.
a. What is her expected surplus from the cultural festival?
b. Write an expression for her expected utility if the festival does not take place.
c. Write an expression incorporating her option price, OP, for the festival if the festival takes place. (To do this, equate her expected utility if the festival takes place to her expected utility if the festival does not take place. Also, assume that if the festival does take place, then she makes a payment of OP whether or not she is able to attend the festival.)
d. Manipulate the expression for option price to show that the option price must be smaller than her expected surplus. (In doing this, begin by substituting 0.5S e for OP in the equation derived in part
e. Also keep in mind that because the person is risk averse, her marginal utility declines with income.) e. Does this exercise suggest any generalizations about the benefits of recreational programs when individuals are uncertain as to whether they will be able to participate in them?