Please provide a step-by-step solution for #1.67. I included #1.66 in case the information is needed to solve #1.67.

#1. 66 & #1.67 MICRO (SEPT. 19) 1.66 A consumer with income yo faces prices po and enjoys utility w = v(p, y'). When prices change to p' , the cost of living is affected. To gauge the impact of these price changes, we may define a cost of living index as the ratio "(po, p', 40) = (p', u') e(p', wo) (a) Show that /(po, p' , u") is greater than (less than) unity as the outlay necessary to maintain base utility, w, rises (falls). 1.67 A cost of living index is introduced in the previous exercise. Suppose the consumer's direct utility function is u(x1, *2) = vx1 + x2. (a) Let base prices be po = (1, 2), base income be yo = 10, and suppose p' = (2, 1). Compute the index I. (b) Let base and final period prices be as in part (a), but now let base utility be u". Show that the value of the index / 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 p" and pl. Can you show it? and her a lalain w*11/2 In(or)