Angela derives utility from Coca-Cola (C) and attending rock concerts (R). Her utility function is U(R,C) = C0.9R 0.1, where C and R are the number of colas and rock concerts consumed per year, respectively.
A. If the price of colas is $1 and the price of concert tickets is $30, and Angela's income is $300, how many colas and concert tickets will she buy to maximize utility? Verify that MRS = MRT at the optimal solution.
B. Suppose the promoters of the rock concert make the following requirement: Either buy four rock concert tickets or none at all. Under this constraint, and given the prices and income above, how many colas and rock concerts will Angela buy to maximize utility? Verify that MRS ≠ MRT at the optimal solution.