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-s,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.
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-s,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.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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please only do: if you can teach explain each
What does it mean?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-s, 3+ s) why the s ? What does mean?
with s € [0,4]
how to know what to look at: If p₁ < p2 or p1 ≥ p2, why these?
Please how to solve:
x(p, w) = (2w/3p1, w/3p1) (2w/3p1, w/3p2)
![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-s, 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)
(2w/3p1, w/3p2)
if p₁ < p2,
if p1 ≥ p2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc5f3af6a-2abe-4d35-9076-d60b28159552%2Fcb7ce4bb-c06e-4a5e-9d1f-f46d4e0c0374%2Fblh28g9_processed.png&w=3840&q=75)
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-s, 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)
(2w/3p1, w/3p2)
if p₁ < p2,
if p1 ≥ p2.
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