Question

**(1) Explain why the assumption of convex preferences
implies that “averages are preferred to extremes.” Make both a
formal argument and an intuitive one (that is, an explanation that
can be understood by the “man on the street.”)**

**(2) What does the negative slope of an indifference
curve imply about a consumer’s tastes for the two goods? How would
this change if one of the goods wasn’t a “good” at all (but instead
a “bad”…something people do not like)?**

**(3) For the following sets of goods draw two
indifference curves, U1 and U2, with U2 > U1. Draw each graph
placing the amount of the first good on the horizontal axis and the
second good on the vertical axis.**

a) Hot dogs and chili (the consumer likes both and has diminishing marginal rate of substitution of hot dogs for chili).

b) Sugar and Splenda (the consumer likes both and will accept an ounce of Splenda or an ounce of sugar with equal satisfaction).

c) Peanut butter and jelly (the consumer likes exactly 2 ounces of peanut butter for every ounce of jelly).

d) Nuts (which the consumer neither likes nor dislikes) and ice cream (which the consumer likes).

e) Apples (which the consumer likes) and liver (which the consumer dislikes).

**(4) The utility that Julie receives by consuming food
(F) and clothing (C) is given by U(F, C) = FC. For this utility
function, the marginal utilities are given by MUF = C and MUC =
F.**

a) On a graph with F on the horizontal axis and C on the vertical, draw indifference curves for U = 12, U = 18, and U = 24.

b) Do the shapes of these indifference curves suggest that Julie has diminishing MRSFC ? Explain.

c) Using the marginal utilities, find the MRSFC. What is the slope of the indifference curve U=12 at the basket with 2 units of food and 6 units of clothing? What is the slope at (4, 3)? Does this support your answer to b?

**(5) Consider the utility function U(x, y) = x – 2y2, MUx
= 1, MUy= -4y. a) Graph some typical indifference curves and show
the direction of increasing utility. b) Which of the three basic
assumptions of consumer preferences does this function
violate?**

Answer #1

Q1. Averages are preferred to extremes because indifference curves are convex. This means that to keep the individual's utility constant decrease in the quantity of one good must be compensated with greater quantity of another good. Now intutively, averages are preferred to extremes because averages represent a balance of both goods, for instance if an individual can choose one of three bundles;

a. 100 shoe and 0 socks

b. 0 shoe and 100 socks

c. 50 shoe and 50 socks

Now from the point of view of a 'rational' individual, one can easily conclude that 99% of the people( if not 100%) will prefer option C as both goodsa are available in suficient / average quantity in this bundle.

For the following sets of goods draw two indifference curves, U1
and U2, with U2 > U1. Draw
each graph placing the amount of the first good on the
horizontal axis. Clearly label U1 and U2.
a)Hot dogs and
chili (the consumer likes both and has a diminishing marginal
rate of
substitution for hot dogs with chili).
b)Sugar and Sweet ’N Low (the consumer likes both and will
accept an ounce of Sweet ’N
Low or an ounce of sugar...

Consider the utility function U(x, y) =
x0.4y0.6, with MUx = 0.4
(y0.6/x0.6) and MUy = 0.6
(x0.4/y0.4).
a) Is the assumption that more is better satisfied for both
goods?
b) Does the marginal utility of x diminish, remain constant, or
increase as the consumer buys more x? Explain.
c) What is MRSx, y?
d) Is MRSx, y diminishing, constant, or increasing as the consumer
substitutes x for y along an indifference curve?
e) On a graph with x on...

Julie has preferences for food, f, and clothing, c, described by
a Cobb-Douglas utility function u(f, c) = f · c. Her marginal
utilities are MUf = c and MUc = f. Suppose that food costs $1 a
unit and that clothing costs $2 a unit. Julie has $12 to spend on
food and clothing.
a. Sketch Julie’s indifference curves corresponding to utility
levels U¯ = 12, U¯ = 18, and U¯ = 24. Using the graph (no algebra
yet!),...

Consider the following cases where preferences are characterized
by some unusual utility functions. For each utility, carefully draw
a set of 3 indifference curves withU1 <U2<U3.
a) Peter consumes good apples together with bad, poisonous ones
that she dislikes.
b) Bob consumes herbal products regularly. However, some herbs
become ineffective when being taken in conjunction. Regarding two
herbal products, A and B, Winnie’s utility function is given by
U(A, B) = max (A, 3B). Given PX = 0.4, PY =...

I. Chapter 3: Question 3.17 on page 104 from Besanko and
Braeutigam 5th ed.
Answer all parts of Problem 3.15 for the utility function U(x,
y) = xy + x. The marginal utilities are MUx = y + 1 and MUy = x. a)
Is the assumption that more is better satisfied for both goods? b)
What is MRSx, y? Is MRSx, y diminishing, constant, or increasing as
the consumer substitutes x for y along an indifference curve? How
do...

1.) For this exercise you will need to first build a graph to
these specifications: Draw a budget constraint with vertical
intercept (0,8) and horizontal intercept (4,0). Zach’s indifference
curves are downward sloping straight lines with a slope of -1 i.e.
they all have vertical intercept (0,N) and horizontal intercept
(N,0) for some number N. Draw Zach’s indifference curves. Label the
bundle(s) that Zach will consume when optimizing.
2.) Now suppose the price of the “x-good” falls to become 4...

Suppose that Ken cares only about bathing suits (B) and
flip-flops (F). His utility function is U = B^0.75*F^0.25. The
price of bathing suits are $12, and the price of flip-flops are $6.
Ken has a budget of $240.
(a) (4 points) Draw and label a graph containing Ken’s budget
line with bathing suits (B) on the x-axis and flip-flops (F) on the
y-axis. Graph the x and y intercepts and determine the slope of the
budget line.
(b) (4...

Question 1
If you are trying to make yourself as happy as you can be given
the constraints that you face, you are effectively:
Select one:
a. trying to find the intersection point between two budget
constraints.
b. trying to find the point on the budget constraint that is on
the highest indifference curve.
c. trying to find the point where the budget constraint and an
indifference curve intersect.
d. trying to find the point on an indifference curve that...

1.Suppose there are two consumers, A and B.
The utility functions of each consumer are given by:
UA(X,Y) = X^1/2*Y^1/2
UB(X,Y) = 3X + 2Y
The initial endowments are:
A: X = 4; Y = 4
B: X = 4; Y = 12
a) (10 points) Using an Edgeworth Box, graph the initial
allocation (label it "W") and draw the
indifference curve for each consumer that runs through the
initial allocation. Be sure to label your graph
carefully and accurately....

Question 1
The line that connects the combinations of goods that leave you
indifferent is called:
Select one:
a. the indifference curve.
b. the budget constraint.
c. the indifference constraint.
d. the indifference line.
Question 2
An increase in income will cause:
Select one:
a. the budget constraint to become flatter, so that it includes
more combinations.
b. the budget constraint to become steeper, so that it includes
more combinations.
c. a parallel shift inward of the budget constraint.
d....

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