Consider an economy with two goods. food (F) and music (M). The price of M is 4. The price of F is 4. Carol has an income of 500 and her preferences are represented by the utility function in A.
A. Find optimal bundle of M and F given the utility function U(M,F)= sqrt M + 2sqrt F
B. Suppose a new club opens which carol can join for a fee (x). The advantage is that once she joins the club, she can purchase (M) at a price of 2 (membership doesn't effect the price of F). For what values of x would carol prefer to join the club? Provide both algebraic and graphical solutions please. * for graphical solution---use x so carol is indifferent between joining and not joining.