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27 Apr 2018
A cost of living index is introduced in the previous exercise. Suppose the consumerâs direct utility function is u(x1, x2) = âx1 + x2.
(a) Let base prices be p0 = (1, 2), base income be y0 = 10, and suppose p1 = (2, 1). Compute the index I.
(b) Let base and final period prices be as in part (a), but now let base utility be u0. Show that the value of the index I will vary with the base utility.
(c) It can be shown that when consumer preferences are homothetic, I will be independent of the base utility for any prices p0 and p1. Can you show it?
A cost of living index is introduced in the previous exercise. Suppose the consumerâs direct utility function is u(x1, x2) = âx1 + x2.
(a) Let base prices be p0 = (1, 2), base income be y0 = 10, and suppose p1 = (2, 1). Compute the index I.
(b) Let base and final period prices be as in part (a), but now let base utility be u0. Show that the value of the index I will vary with the base utility.
(c) It can be shown that when consumer preferences are homothetic, I will be independent of the base utility for any prices p0 and p1. Can you show it?
Jarrod RobelLv2
29 Apr 2018
