Casper consumes cocoa and cheese. Cocoa is sold in an unusual way. There is only one supplier, and the more cocoa you buy from him, the higher the price you have to pay per unit. In fact y units of cocoa will cost Casper y2 dollars. Cheese is sold in the usual way at a price of 2 dollars per unit. Casper's income is 20 dollars and his utility function is U(x, y) = x + 2y, where x is his consumption of cheese and y is his consumption of cocoa.
a. Sketch Casper's budget set and shade it in.
b. Sketch some of his indifference curves and label the point that he chooses.
c. Calculate the amount of cheese and the amount of cocoa that Casper demands at these prices and this income.