Consider a change in price that is accompanied by a change in wealth that returns the consumer to his original level of utility. That is, starting from prices p and wealth w, the consumer obtains exactly the same utility after the change to prices p' and wealth w' as he had before the change. (a) Express the wealth w' in terms of the original wealth w and either the compensating or equivalent variation of a change from prices p to p' keeping the wealth w fixed. Solution: Since CV = w' - w, we have w=w-CV. (b) Use your answer to part (a) to find, as a function of p, p', and w, the value of w' for a consumer with expenditure function e(p, u) = u² (2√PI + √P₂) ². If you are unable to answer part (a), you will get most of the points for this question if you calculate either the compensating or equivalent variation of a change in prices from p to p' (as a function of p, p', and w). Solution: From part (a), w' = w-CV = e(p', v(p, w)). Using the identity e(p, v(p, w)) = w, we obtain Therefore, v(p, w) = + 2√P1 + √P2 2 2 u^² = e(1², v(x,x)) = (2√ √5)² (2√rh + √5)². w e(p',v(p, P₂ √P1+ √P2,

Consider a change in price that is accompanied by a change in wealth that returns the consumer to his original level of utility. That is, starting from prices p and wealth w, the consumer obtains exactly the same utility after the change to prices p' and wealth w' as he had before the change. (a) Express the wealth w' in terms of the original wealth w and either the compensating or equivalent variation of a change from prices p to p' keeping the wealth w fixed. Solution: Since CV = w' - w, we have w=w-CV. (b) Use your answer to part (a) to find, as a function of p, p', and w, the value of w' for a consumer with expenditure function e(p, u) = u² (2√PI + √P₂) ². If you are unable to answer part (a), you will get most of the points for this question if you calculate either the compensating or equivalent variation of a change in prices from p to p' (as a function of p, p', and w). Solution: From part (a), w' = w-CV = e(p', v(p, w)). Using the identity e(p, v(p, w)) = w, we obtain Therefore, v(p, w) = + 2√P1 + √P2 2 2 u^² = e(1², v(x,x)) = (2√ √5)² (2√rh + √5)². w e(p',v(p, P₂ √P1+ √P2,

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.7P

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Consider a change in price that is accompanied by a change in wealth that returns the consumer to his original level of utility. That is, starting from prices p and wealth w, the consumer obtains exactly the same utility after the change to prices p' and wealth w' as he had before the change. ( Express the wealth w' in terms of the original wealth w and either the compensating or equivalent variation of a change from prices p to p' keeping the wealth w fixed. Use your answer to part (a) to find, as a function of p, p', and w, the value of w' for a consumer with expenditure function e(p, u) = u² (2√P1 + √P₂) ².
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