Part 2 solution needed urgent Problem 2: Time and monetary constraints with optionsThere are two goods, X and Y, available in arbitrary non-negative quan-tities (so the consumption set is R²).Beenish has preferences over consumption bundles that can be representedby a differentiable, strictly increasing and strictly quasi-concave utilityfunction u: R2R+, given byu(2,y) = r®yl-awhere is the quantity of good X, y is the quantity of good Y, anda € (0, 1) is a preference parameter.1. Suppose Beenish has 80 AED. In a nearby store (called "Store A"),the price of good X is p = 2 AED per unit of good X, and the priceof good Y is q = 8 AED per unit of good Y. However, Beenish alsohas a time constraint. At Store A, it takes tx = 4 minutes per unitto purchase good X and ty = 1 minutes per unit to purchase good Y.That means, purchasing a consumption bundle (x, y) = R² at StoreA would take 4x + y minutes. Beenish has only 80 minutes to do hershopping.(a) In an appropriate diagram, illustrate Beenish's constraint set, giventhat she has both a monetary constraint and time constraint.(b) Describe Beenish's demand for good X and her demand for good Yas a function of her preference parameter a € (0, 1), and illustrateher demand for good X, i.e., x(a), in an appropriate diagram.(c) For what values of a does Beenish not spend all of her wealth? Forwhat values of a does Beenish spend all of her wealth and use upall of her available time?2. Now suppose that there is another store (called "Store B"), which is further away, where Beenish could do her shopping instead. At StoreB, the goods are half-price: good X only costs 1 AED per unit andgood Y only costs 4 AED per unit. At Store B, it still takes tx = 4minutes per unit to purchase good X and ty = 1 minutes per unit topurchase good Y. However, it also takes 40 minutes to drive to Store Band back, and so Beenish's total time for shopping is only 40 minutesif she travels to Store B.(a) In an appropriate diagram, illustrate Beenish's constraint set, giventhat she has both a monetary constraint and a time constraint butnow has the option between two stores.(b) Describe Beenish's demand for good X and her demand for goodY as a function of her preference parameter a, and illustrate herdemand for good X, i.e., x(a), in an appropriate diagram.(c) For what values of a does Beenish shop in Store A, and for whatvalues of a does she travel to Store B?

Answered: Image /qna-images/answer/e09d41eb-d400-488e-a432-8f8088a40b1d.jpg

There are two goods, X and Y, available in arbitrary non-negative quan- tities (so the consumption set is R2). Beenish has preferences over consumption bundles that can be represented by a differentiable, strictly increasing and strictly quasi-concave utility function u: R2 → R+, given by

There are two goods, X and Y, available in arbitrary non-negative quan- tities (so the consumption set is R2). Beenish has preferences over consumption bundles that can be represented by a differentiable, strictly increasing and strictly quasi-concave utility function u: R2 → R+, given by

ENGR.ECONOMIC ANALYSIS

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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

Part 2 solution needed urgent

Problem 2: Time and monetary constraints with options
There are two goods, X and Y, available in arbitrary non-negative quan-
tities (so the consumption set is R²).
Beenish has preferences over consumption bundles that can be represented
by a differentiable, strictly increasing and strictly quasi-concave utility
function u: R2R+, given by
u(2,y) = r®yl-a
where is the quantity of good X, y is the quantity of good Y, and
a € (0, 1) is a preference parameter.
1. Suppose Beenish has 80 AED. In a nearby store (called "Store A"),
the price of good X is p = 2 AED per unit of good X, and the price
of good Y is q = 8 AED per unit of good Y. However, Beenish also
has a time constraint. At Store A, it takes tx = 4 minutes per unit
to purchase good X and ty = 1 minutes per unit to purchase good Y.
That means, purchasing a consumption bundle (x, y) = R² at Store
A would take 4x + y minutes. Beenish has only 80 minutes to do her
shopping.
(a) In an appropriate diagram, illustrate Beenish's constraint set, given
that she has both a monetary constraint and time constraint.
(b) Describe Beenish's demand for good X and her demand for good Y
as a function of her preference parameter a € (0, 1), and illustrate
her demand for good X, i.e., x(a), in an appropriate diagram.
(c) For what values of a does Beenish not spend all of her wealth? For
what values of a does Beenish spend all of her wealth and use up
all of her available time?
2. Now suppose that there is another store (called "Store B"), which is

further away, where Beenish could do her shopping instead. At Store
B, the goods are half-price: good X only costs 1 AED per unit and
good Y only costs 4 AED per unit. At Store B, it still takes tx = 4
minutes per unit to purchase good X and ty = 1 minutes per unit to
purchase good Y. However, it also takes 40 minutes to drive to Store B
and back, and so Beenish's total time for shopping is only 40 minutes
if she travels to Store B.
(a) In an appropriate diagram, illustrate Beenish's constraint set, given
that she has both a monetary constraint and a time constraint but
now has the option between two stores.
(b) Describe Beenish's demand for good X and her demand for good
Y as a function of her preference parameter a, and illustrate her
demand for good X, i.e., x(a), in an appropriate diagram.
(c) For what values of a does Beenish shop in Store A, and for what
values of a does she travel to Store B?

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