all that a consumer with utility Marshallian demand u(7₁, 7₂) = min{7₁, 27₂} 2w W x(p, w) = (2p₁ + p2² 2p₁ + P2) Find the indirect money-metric utility function for reference prices p. Solution: Substituting the Marshallian demand into the utility function gives 2w 2w v(p, w) = min 2w
all that a consumer with utility Marshallian demand u(7₁, 7₂) = min{7₁, 27₂} 2w W x(p, w) = (2p₁ + p2² 2p₁ + P2) Find the indirect money-metric utility function for reference prices p. Solution: Substituting the Marshallian demand into the utility function gives 2w 2w v(p, w) = min 2w
Chapter17: Capital And Time
Section: Chapter Questions
Problem 17.1P
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Transcribed Image Text:Recall that a consumer with utility
has Marshallian demand
u(x₁, x2) = min{x1,2x2}
2w
W
z (p, w) = (2p₁ + p₂² 2p₁ + P2)
(a) Find the indirect money-metric utility function for reference prices p.
Solution: Substituting the Marshallian demand into the utility function gives
v(p, w) = min
Using the identity v(p, e(p, u)) = u, we find that
e(p, u)
2w
2w
{2p₁² + P2² 2p₁² + P2} ²
=
e(p, v(p, w)) =
Therefore, the indirect money-metric utility function is
2P1 + P2
2
2p1+P2₂
2
=
-U.
= 8.
2w
2p1 + P2
(b) Calculate the equivalent variation associated with a change in prices from (4,1) to (2, 1)
when the consumer has wealth 10.
Solution: For these values,
2w
2p1 + P2
EV = e((4,1), v((2, 1), 10)) - 10
(2-4+1). 10
2.2+1
(2P₁ + P₂)w
2p1 + P2
- 10
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