Natasha Derives Utility from Attending Rock Concerts (R) and from Drinking

Essay

Natasha derives utility from attending rock concerts (r) and from drinking colas (c) as follows:
U(c,r) = c^.9r^.1
The marginal utility of cola (MUc) and the marginal utility of rock concerts (MUr) are given as follows:
MUc = .9c^-.1r^.1 MUr = .1c^.9r^-.9
a. If the price of cola (Pc) is $1 and the price of concert tickets (Pr) is $30 and Natasha's income is $300, how many colas and tickets should Natasha buy to maximize utility?
b. Suppose that the promoters of rock concerts require each fan to buy 4 tickets or none at all. Under this constraint and given the prices and income in (a), how many colas and tickets should Natasha buy to maximize utility?
c. Is Natasha better off under the conditions in (a) or (b)? Explain your answer.