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Economics Problem Set: Indifference Curves & Utility

This document contains 8 problem sets related to concepts in financial management and economics. Problem set 1 involves drawing indifference curves to represent different levels of risk aversion. Problem set 2 involves constructing indifference curves for 5 individuals with different preferences over pineapples and coconuts. Problem set 3 asks about the marginal rate of substitution between store and brand name sugar. Problem set 4 involves plotting a utility function and determining if it satisfies the principle of diminishing marginal utility. Problem set 5 involves solving a utility maximization problem. Problem sets 6 and 7 involve additional utility maximization problems. Problem set 8 asks for an opinion on whether online gift cards are a fad.

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Manas Ghosh
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140 views2 pages

Economics Problem Set: Indifference Curves & Utility

This document contains 8 problem sets related to concepts in financial management and economics. Problem set 1 involves drawing indifference curves to represent different levels of risk aversion. Problem set 2 involves constructing indifference curves for 5 individuals with different preferences over pineapples and coconuts. Problem set 3 asks about the marginal rate of substitution between store and brand name sugar. Problem set 4 involves plotting a utility function and determining if it satisfies the principle of diminishing marginal utility. Problem set 5 involves solving a utility maximization problem. Problem sets 6 and 7 involve additional utility maximization problems. Problem set 8 asks for an opinion on whether online gift cards are a fad.

Uploaded by

Manas Ghosh
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© © All Rights Reserved
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ME-2018

Problem Set-I
1. In the field of financial management it has been observed that there is a trade-off
between the rate of return that one earns on investments and the amount of risk that
one must bear to earn that return.
a. Draw a set of indifference curves between risk and return for a person that is risk
averse (a person that does not like risk).
b. Draw a set of indifference curves for a person that is risk neutral (a person that does
not care about risk one way or the other).
c. Draw a set of indifference curves for a person that likes risk.

2. An island economy produces only two goods, coconuts and pineapples. There are
five people (A, B, C, D, and E) living on the island with these preferences:

A has a strong preference for pineapples.


B has a strong preference for coconuts.
C doesn't care for pineapples (assigns no value to them).
D doesn't care for coconuts (assigns no value to them)
E will only consume pineapples and coconuts in the fixed proportion of
one pineapple to one coconut.
For each of these five individuals, construct a representative indifference curve with
pineapples on the vertical axis and coconuts on the horizontal axis. Discuss the shape of the
indifference curves and relate them to the MRS.

3. It is common for supermarkets to carry both generic (store-label) and brand-name


(producer-label) varieties of sugar and other products. Many consumers view these
products as perfect substitutes, meaning that consumers are always willing to
substitute a constant proportion of the store brand for the producer brand. Consider a
consumer who is always willing to substitute 4 pounds of a generic store-brand sugar
for 2 pounds of brand-name sugar. Do these preferences exhibit a diminishing
marginal rate of substitution between store-brand and producer-brand sugar?

4. Consider the single-good utility function U(x) = 3x2, with a marginal utility given by
MUx = 6x. Plot the utility and marginal utility functions on two separate graphs. Does
this utility function satisfy the principle of diminishing marginal utility? Explain.

5. A consumer has the utility function U = xy, with the marginal utilities MUx = y and
MUy = x. The price of x is 2, the price of y is Py, and his income is 40. When he
maximizes utility subject to his budget constraint, he purchases 5 units of y. What
must be the price of y and the amount of x consumed?
6. Consider a consumer with the utility function U(x, y) = min(3x, 5y), that is, the two
goods are perfect complements in the ratio 3:5. The prices of the two goods are Px =
Rs. 5 and Py = Rs.10, and the consumer’s income is Rs. 220. Determine the optimum
consumption basket.

7. Robinson Crusoe lives alone on a deserted island. He can spend his time gathering
coconuts or bananas. He has 16 hours available each day and can gather 4 coconuts in
an hour or 8 bananas in an hour. Draw Robinson's budget constraint. Given that
Robinson's Marginal Utility of bananas is always 25 and his Marginal utility of
coconuts is always 100, what is his optimal consumption?
One day an individual from a neighbouring island arrives by boat and offers to
exchange any number of fruits at a rate of 1 coconut for 1 banana. Draw Robinson's
budget constraint at this exchange rate assuming he will now spend all his time
gathering bananas. Is Robinson better off? What does he consume?

8. A recent study by Web Mystery Shoppers International indicates that holiday gift cards
are becoming increasingly popular at online retailers. Two years ago, online shoppers
had to really hunt at most e-retailers’ sites to purchase a gift certificate, but today it is
easier to purchase gift cards online than at traditional retail outlets. Do you think online
gift cards are merely a fad?

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