The following is intended to explore what kinds of income-demand relationships are logically possible.
A: For each of the following, indicate whether the relationship is possible or not and explain:
(a) A good is a necessity and has a positive income-demand relationship.
(b) A good is a necessity and has a negative income-demand relationship.
(c) A good is a luxury and has a negative income-demand relationship.
(d) A good is quasilinear and has a negative income-demand relationship.
(e) Tastes are homothetic and one of the goods has a negative income-demand relationship.
B: Derive the income-demand relationships for each good for the following tastes:
(a) where α and β lie between zero and 1 and sum to less than 1.
(b) u(x1,x2) = α ln x1 + x2. Graph the income demand curves for x1 and x2 —carefully labeling slopes and intercepts.