Question

Christine has the following utility function:

U=100x–0.5x2 +y,

where x is rounds of golf at the local private golf club. Only members can play at this golf club, and one must pay a membership fee to join the club. The price, Px, of a round of golf is $60 and the price of good y is Py = $1. Christine has an income of $40,000. [Note: Christine cannot play golf anywhere, except at this private club].

(i) What is the maximum membership fee that Christine would pay to belong to this club?

(ii) Suppose she is already a member of the club. What is the minimum amount she will accept to give up her membership?

(iii) Are your answers in (i) and (ii) the same or different? Explain why.

I have answers 1 and 2 and they are both 800. I do i explain they are the same

Answer 1

III)

In this case, the preference of the consumer is quasilinear. Therefore, the consumption of x is independent of the money income of the consumer. That is as long as the price of the good remains the same the consumer will demand the same amount of x. Therefore, the amount of money she would be willing to give up will be equal to the money she would be ready to receive. Hence, both Cv and EV will be the same.

Proof:

Let the consumer initially consumes y* amount of Y with money income m. Then,

Therefore, the utility of the consumer is

Let the consumer is willing to pay C amount of money to consume x. Then

Therefore, the utility of the consumer is

At equilibrium,

....(1)

Similarly, let the consumer willing to accept amount E to give up the membership

At equilibrium,

....(2)

then from (1) and (2)