ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN: 9780190931919
Author: NEWNAN
Publisher: Oxford University Press
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![Armando consumes two goods: grapes and wine. He can purchase both at the market and
also possesses a technology that allows him to costlessly convert any quantity of grapes into
the same number of units of wine. This technology is not reversible: there is no quantity
of wine that he can convert to grapes. Thus, for example, if he purchases 4 units of grapes
and 3 units of wine, he could consume any bundle (4-8,3+s) with s = [0,4]. Armando's
utility from consuming a units of grapes and y units of wine is u(x, y) = x²y. For each of the
following questions, you may use, without proof, any results from the lectures for this course.
(a) Find Armando's Marshallian demand expressed in terms of the bundle he consumes (i.e.,
after any conversion of grapes into wine).
Solution: Let på denote the price of grapes and p2 the price of wine. If P₁ <p2, he can
produce wine at lower cost than he can buy it, so will only buy grapes. In this case, it
is as if both goods are priced at p₁, which gives demand (2w/3p1, w/3p1). If p₁ ≥ p2, he
has no need to convert grapes to wine and will demand (2w/3p1, w/3p2). Therefore, his
demand is
x(p, w) =
(2w/3p1, w/3p1) if P₁ < P2,
(2w/3p1, w/3p2) if p₁ ≥ p2.
(b) Suppose a researcher who is not aware of Armando's technology for converting goods
observes, for each price vector, the bundle that Armando consumes (but not the bundle
he purchases). If this researcher assumes that Armando always spends all of his wealth,
will she think that his choices satisfy the Weak Axiom of Revealed Preference?
Solution: Yes. Armando's choices look the same as those of someone who has utility
x²y for bundles with x ≤ 2y and receives no benefit from additional units of x beyond 2y
(that is, utility 4y³ for bundles with x > 2y).](https://content.bartleby.com/qna-images/question/cc93dd3a-e660-4464-bc8c-e382a2c34aae/72eb1e90-f70a-40ce-8beb-4a45ee12b03e/lb6kay3_processed.png)
Transcribed Image Text:Armando consumes two goods: grapes and wine. He can purchase both at the market and
also possesses a technology that allows him to costlessly convert any quantity of grapes into
the same number of units of wine. This technology is not reversible: there is no quantity
of wine that he can convert to grapes. Thus, for example, if he purchases 4 units of grapes
and 3 units of wine, he could consume any bundle (4-8,3+s) with s = [0,4]. Armando's
utility from consuming a units of grapes and y units of wine is u(x, y) = x²y. For each of the
following questions, you may use, without proof, any results from the lectures for this course.
(a) Find Armando's Marshallian demand expressed in terms of the bundle he consumes (i.e.,
after any conversion of grapes into wine).
Solution: Let på denote the price of grapes and p2 the price of wine. If P₁ <p2, he can
produce wine at lower cost than he can buy it, so will only buy grapes. In this case, it
is as if both goods are priced at p₁, which gives demand (2w/3p1, w/3p1). If p₁ ≥ p2, he
has no need to convert grapes to wine and will demand (2w/3p1, w/3p2). Therefore, his
demand is
x(p, w) =
(2w/3p1, w/3p1) if P₁ < P2,
(2w/3p1, w/3p2) if p₁ ≥ p2.
(b) Suppose a researcher who is not aware of Armando's technology for converting goods
observes, for each price vector, the bundle that Armando consumes (but not the bundle
he purchases). If this researcher assumes that Armando always spends all of his wealth,
will she think that his choices satisfy the Weak Axiom of Revealed Preference?
Solution: Yes. Armando's choices look the same as those of someone who has utility
x²y for bundles with x ≤ 2y and receives no benefit from additional units of x beyond 2y
(that is, utility 4y³ for bundles with x > 2y).
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