3. Casper consumes cocoa and cheese. He has an income of $16. Cocoa is sold in an unusual way. There is only one supplier and the more cocoa one buys from him, the higher the price one has to pay per unit. In fact, x units of cocoa will cost Casper a total of x² dollars. Cheese is sold in the usual way at a price of $2 per unit.

(a) What is Casper's budget equation?

(b) Assume that Casper's utility function is U (x; y) = 3x+y: How many units of x and y will Casper purchase?

(c) What if the price of cheese increases from $2 to $4?