A consumer of two goods has Hicksian demand (h₁ (p, u), h₂(p, u)) = (u, 2u). (a) Find the Marshallian demand. Solution: The expenditure function is given by e(p,u) = p.h(p, u) = p₁u+2p₂u. Using the identity e(p, v(p, w)) = w, we obtain W
A consumer of two goods has Hicksian demand (h₁ (p, u), h₂(p, u)) = (u, 2u). (a) Find the Marshallian demand. Solution: The expenditure function is given by e(p,u) = p.h(p, u) = p₁u+2p₂u. Using the identity e(p, v(p, w)) = w, we obtain W
Chapter1: Making Economics Decisions
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![A consumer of two goods has Hicksian demand
(h₁ (p, u), h₂(p, u)) = (u, 2u).
(a) Find the Marshallian demand.
Solution: The expenditure function is given by
Therefore,
e(p, u) = p.h(p,u) = p₁u+2p₂u.
Using the identity e(p, v(p, w)) = w, we obtain
v(p, w) =
=
x(p,w) = h(p, v(p, w))
W
P₁+2p₂
=
W
2w
P₁+2p2 P1+2p2/
(b) Suppose prices change from (2, 1) to (2, 3), and, at the same time, wealth changes from
6 to 10. Calculate the equivalent variation associated with this change.
Solution: The equivalent variation is
10
2+2.3
e ((2, 1), v((2, 3), 10) - 6 = (2+2-1);
= -1.
6](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc5f3af6a-2abe-4d35-9076-d60b28159552%2F889ad477-c9e9-463b-a0ae-62b09531ef69%2Fmfjtgeh_processed.png&w=3840&q=75)
Transcribed Image Text:A consumer of two goods has Hicksian demand
(h₁ (p, u), h₂(p, u)) = (u, 2u).
(a) Find the Marshallian demand.
Solution: The expenditure function is given by
Therefore,
e(p, u) = p.h(p,u) = p₁u+2p₂u.
Using the identity e(p, v(p, w)) = w, we obtain
v(p, w) =
=
x(p,w) = h(p, v(p, w))
W
P₁+2p₂
=
W
2w
P₁+2p2 P1+2p2/
(b) Suppose prices change from (2, 1) to (2, 3), and, at the same time, wealth changes from
6 to 10. Calculate the equivalent variation associated with this change.
Solution: The equivalent variation is
10
2+2.3
e ((2, 1), v((2, 3), 10) - 6 = (2+2-1);
= -1.
6
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