A shopper buys x units of item A and y units of item B, obtaining satisfaction s(x, y) from the purchase. (Satisfaction is called utility by economists.) The contours s(x, y) = xy = c are called indifference curves because they show pairs of purchases that give the shopper the same satisfaction.
(a) A shopper buys 8 units of A and 2 units of B. What is the equation of the indifference curve showing the other purchases that give the shopper the same satisfaction? Sketch this curve.
(b) After buying 4 units of item A, how many units of B must the shopper buy to obtain the same satisfaction as obtained from buying 8 units of A and 2 units of B?
(c) The shopper reduces the purchase of item A by k, a fixed number of units, while increasing the purchase of B to maintain satisfaction. In which of the following cases is the increase in B largest?
• Initial purchase of A is 6 units
• Initial purchase of A is 8 units