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 $s(x, y)=x y=c$ 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