A consumer's consumption set is ? ≡ R2
+, and her (weak) preference relation % can be represented
by a (real valued) utility function u, defined by:
u(x1, x2) = x1x2 for all (x1, x2) in ?
Suppose the price of the second good is p2 = 1, and the price of the first good is p1 > 0. The
consumer's income is m > 0.
We know (using the procedure to solve Problem 4 in Problem Set 2) that the demand functions of
the two goods are given by:
x1(p1, m)=(m/2p1); x2(p1, m)=(m/2)
and the consumer's utility at the demanded bundle is given by:
u(x1(p1, m), x2(p2, m)) = (m2/4p1)
In year 2010, the price of the first good was p0
1 = 4, and in the year 2015, the price of the first good
had changed to p1
1 = 9. Assume that the consumer's income, m, is the same in both years.
(i) Obtain the change in consumer's surplus (in terms of m) between the two years as measured by the compensating variation.
(ii) Obtain the change in consumer's surplus (in terms of m) between the two years as measured by the equivalent variation.