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A consumer of two goods has indirect utility v(p, w) = -1/2 P₁ + P₂ (a) Find the indirect money-metric utility e(p, v(p, w)). (b) Calculate the compensating variation associated with the change from (p, w) = ((4,4), 2) to (p', w')= ((1,9), 5).

A consumer of two goods has indirect utility v(p, w) = -1/2 P₁ + P₂ (a) Find the indirect money-metric utility e(p, v(p, w)). (b) Calculate the compensating variation associated with the change from (p, w) = ((4,4), 2) to (p', w')= ((1,9), 5).

Economics (MindTap Course List)
Economics (MindTap Course List)
13th Edition
ISBN:9781337617383
Author:Roger A. Arnold
Publisher:Roger A. Arnold
Chapter20: Consumer Choice: Maximizing Utility And Behavioral Economics
Section20.1: Utility Theory
Problem 2ST
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how to know what are  what is p1,  w1, which how  to map the values

A consum sumer of two goods has indirect utility v(p, w) = √w -1/2 P₁ + P₂ (a) Find the indirect money-metric utility e(p, v(p, w)). (b) Calculate the compensating variation associated with the change from (p, w) = ((4,4), 2) to (p', w')= ((1,9), 5). can you explain the notation please break it down each part of it, please teach How do you know where to place the values? The indirect money-metric utility e(p, v(p, w)) can be calculated as follows: e(p, v(p, w)) = v(p, w) - ((p1* w1) + (p2 * w2)) plugging in the values from the problem, we get: e(p, v(p, w)) = (sqrt(w))/p1^-0.5+p2^-0.5- ((44) + (9 * 5)) e(p, v(p, w)) = 2 - 41 CV = 2 e(p, v(p, w)) = -39 The compensating variation associated with the change from (p, w) = ((4,4), 2) to (p', w')= ((1,9), 5) can be calculated as follows: CV = e(p', w')- e(p, w) plugging in the values from the problem, we get: CV-39 (-41) This means that the consu would be willing to pay up to $2 in order to maintain their original level of utility.
Transcribed Image Text:A consum sumer of two goods has indirect utility v(p, w) = √w -1/2 P₁ + P₂ (a) Find the indirect money-metric utility e(p, v(p, w)). (b) Calculate the compensating variation associated with the change from (p, w) = ((4,4), 2) to (p', w')= ((1,9), 5). can you explain the notation please break it down each part of it, please teach How do you know where to place the values? The indirect money-metric utility e(p, v(p, w)) can be calculated as follows: e(p, v(p, w)) = v(p, w) - ((p1* w1) + (p2 * w2)) plugging in the values from the problem, we get: e(p, v(p, w)) = (sqrt(w))/p1^-0.5+p2^-0.5- ((44) + (9 * 5)) e(p, v(p, w)) = 2 - 41 CV = 2 e(p, v(p, w)) = -39 The compensating variation associated with the change from (p, w) = ((4,4), 2) to (p', w')= ((1,9), 5) can be calculated as follows: CV = e(p', w')- e(p, w) plugging in the values from the problem, we get: CV-39 (-41) This means that the consu would be willing to pay up to $2 in order to maintain their original level of utility.
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