Suppose for a given consumer X is an inferior good and Y is a normal good.
a. Focusing on the income effect, show that an increase in the price of X will cause the consumer to “buy more” X (that is, show that the income effect is positive when the price of X increases).
b. Focusing on the income effect, show that an increase in the price of Y will cause the consumer to buy more X (that is, show the income effect for Y is negative when the price of Y increases, resulting in more X being purchased).