Assignment help-ECON 361 – Intermediate Microeconomics
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Chapters 3 & 4 Homework #2 Due: September 14th, 2017
ECON 361 – Intermediate Microeconomics Page 1 of 1
1. Jan has the following utility function for broccoli:
U(B) = 54B 0:5B3
a) What is Jan’s marginal utility function?
b) Plot the utility and the marginal utility functions on two
separate graphs. Be sure to label the axes and the curves
c) Suppose that Jan is allowed to consume as much broccoli
as she likes and that broccoli costs her nothing. Show,
both algebraically and graphically, the value of B at which
she would stop consuming broccoli.
2. Consider the utility function U (x; y) = 12×3=2y1=2.
a) What are MUx and MUy?
b) Does the consumer believe that more is better for each
good? Explain using your answer from a).
c) Do the consumer’s preferences exhibit a diminishing
marginal utility of x? Is the marginal utility of y dimin-
3. Draw indierence curves to represent the following types of
consumer preferences. Make sure to include arrows to indicate
direction of preference. (Hint: Start with a bundle (say 10
units of each), and think about other bundles that give the
consumer the same utility.)
a) I like Soda, but neither like nor dislike Coee.
b) I dislike Soda, but neither like nor dislike Coee.
c) I like Soda, but dislike Coee.
d) I like both Soda and Coee, and always get the same ad-
ditional satisfaction from 1 ounce of Soda as I do from 2
ounces of Coee.
e) I like Soda and Coee, but I only want 2 ounces of Soda
for every 1 ounce of Coee.
4. The utility that Mary receives by purchasing E units of enter-
tainment and purchasing F units of food is given by,
U (E; F) = E1=2F
a) What are the marginal utility functions?
b) On a graph with E on the horizontal axis and F on the
vertical axis, draw indierence curves for U = 12, U = 18,
and U = 24.
c) Do the shapes of these indierence curves suggest that
Mary has a diminishing marginal rate of substitution of
entertainment for food? Explain.
d) Using the marginal utilities, determine the MRSE;F .
e) Calculate the slope of the indierence curve U = 12 at
the points (E; F) = (4; 6); (1; 12). Do these slopes suggest
diminishing marginal rate of substitution?
Now, assume that entertainment costs $4 per unit and the
food cost $2 per unit. Mary has $24 to spend on entertainment
f) Using algebra (the tangency condition and budget line),
nd the optimal choice of entertainment and food.
g) Using a new graph with entertainment on the horizontal
axis and food on the vertical axis, draw the budget line,
the utility maximizing basket, and the indierence curve
that contains the utility maximizing basket.
h) Now, assume that Mary has $I and the prices are PE and
PF , solve for the optimal basket as a function of I; PE;
and PF .
5. Alex is currently spending all of his income and consumes 10
hamburgers and 3 salads each week. At his current consump-
tion basket, his marginal utility for hamburgers is 5 and his
marginal utility for salads is 2. If the price of one hamburger
is $3 and the price of one salad is $1.50, is Alex currently
maximizing his utility? If not how should he reallocate his
spending in order to increase his utility?
6. Tom is trying to decide whether or not to buy Arizona season
tickets for basketball. There are a total of 20 home games dur-
ing the 2017-2018 basketball season. If Tom buys individual
game tickets they cost $25 each. A season ticket which allows
Tom to go to all the games costs $325. If for some reason Tom
can’t go to a game, then he can sell the tickets to his friend
for $10 per game.
a) On a graph with games attended on the horizontal axis
and \other goods” on the vertical axis draw Tom’s budget
b) On the graph from part (a) draw a set of indierence curves
that illustrates why Tom may be better o without season
c) On a new graph draw the same budget line you found in
part (a). Now draw a set of indierence curves that illus-
trates why Tom might not be better o with season tickets.
7. A consumer buys two goods, food and housing, and likes both
goods. When she has budget line BL1, her optimal choice is
basket A. Given budget line BL2, she chooses basket B, and
with BL3, she chooses basket C. Examine the following graph
in order to answer the following questions: (Hint: use revealed
preference, transitivity and more is better)
BL1 BL2 BL3
a) What can you infer about how the consumer ranks baskets
A, B, and C? If you can infer a ranking, explain how. If
you cannot infer a ranking, explain why not.
b) On the graph, shade in (and clearly label) the areas that
are revealed to be less preferred to basket B, and explain
why you indicated these areas.
c) On the graph, shade in (and clearly label) the areas that
are revealed to be (more) preferred to basket B, and ex-
plain why you indicated these areas.
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