5. (10 points) Suppose a consumer's demand for good 1 is given by $x_1(p_1, p_2, m) = \frac{m}{2(p_1 + p_2)}$, and she spends all her income on these two goods.
(a) (3 points) Find the consumer's demand for good 2. (Hint: use the
budget equation.)
Now, let the initial prices be $p_1 = 2$ and $p_2 = 2$, and let $m = 48$.
Suppose the price of good 1 drops to $p_1' = 1$.
(b) (3 points) Is good 1 a normal good or inferior good? Ordinary or
Giffen? Is good 2 a complement or substitute for good 1?
(c) (2 points) Are the consumer's preferences homothetic?
(d) (4 points) Calculate the change in the consumption of good 1 due to
the income effect and substitution effect. (Hint: read the example in
the textbook.)
