also possesses a technology that allows him to costlessly convert any quantity of grapes into he 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 tility from consuming a units of grapes and y units of wine is u(x, y) = x²y. For each of the ollowing 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.,

also possesses a technology that allows him to costlessly convert any quantity of grapes into he 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 tility from consuming a units of grapes and y units of wine is u(x, y) = x²y. For each of the ollowing 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.,

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Concept explainers

Form Utility

The term utility in general refers to the satisfaction earned from usage of a particular product or service. Utility always plays an important role because it influences various important elements like demand & thereby the price of the good or service as well. Though utility is not easy to measure, various types of economic models can be used indirectly. There can be various types of utilities like economic utility, marginal utility, cardinal utility, form utility.

Question

please only do: if you can teach explain steps of how to solve each part

why p1= pother

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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