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).
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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how to know what are p w p' w' show steps what is p1, w1, which how to map the values
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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