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. Casper’s budget equation, therefore, is x² + 2y =16 where x is his consumption of cocoa and y is his consumption of cheese. Casper’s utility function is U(x, y) = 3x + y.

(a) On the graph below, draw the boundary of Casper’s budget set in blue ink. Use red ink to sketch two or three of his indifference curves. 

(b) Write an equation that says that at the point (x, y), the slope of Casper’s budget “line” equals the slope of his indifference “curve.” ________. Casper demands _______ units of cocoa and _______ units of cheese.