Cory has the utility function U(X,Y) = X + 16*root(Y) , where X is the quantity of water consumed, and Y is the quantity of coffee consumed. Let the price of water be Px = 1 and the price of coffee be Py = 4. Let I represent income.
a) If I = 8 what are the quantities of water and coffee that maximize Cory's utility subject to his budget constraint?
b) What is the marginal utility of income when I = 8?
c) If I = 32, what are the quantities of water and coffee that maximize Cory's utility subject to his budget constraint?
d) What is the marginal utility of income when I = 32?