Suppose a consumer’s demand for good 1 is given by x1(p1,p2,m) = m/(2(p1 + p2), and she spends all her income on these two goods.

(a) (3 points) Find the consumer’s demand for good 2.

Now, let the initial prices be p1 = 2 and p2 = 2, and let m = 48. Suppose the price of good 1 drops to p1 = 1.

(b) (3 points) Is good 1 a normal good or inferior good? Ordinary or Gi?en? 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 e?ect and substitution e?ect.

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