34. (2010 ZA Q 11 OR 2015 ZA Q13) Consider an economy with two goods: food (F) and music (M). The price of M is 4 and the price of F is 1. Harvey has an income of 800. Suppose F and M are good substitutes (but not perfect substitutes) for Harvey, and his preferences are such that he optimally con- sumes 100 units of M. (a) Suppose a new club opens which Harvey can join for a fee of 300. The advan- tage is that once he joins the club, he can purchase M at a relative price of 1. Would Harvey join the club? (b) Suppose Carol has the same income as Harvey, but her preferences are repre- sented by the utility function Uc(M, F) = min(&M, F). For what values of a would Carol prefer to join the club