Question

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 points) Define and show mathematically the two conditions that need to be met for a consumption allocation {B ∗ , F ∗} to maximize utility.

(c) (4 points) What is the marginal utility of good B (MUB) and of good F (MUF) for Ken.

(d) (8 points) What is the optimal choice of B and F for Ken to maximize his utility? Label this point A on your graph from part (a).

(e) (5 points) What is the utility generated by Ken from his optimal consumption of B and F from part (d)? Find another bundle that also achieves this utility, label this new bundle point B on your graph from part (a) and draw an indifference curve between points A and B.

Answer #1

Chester consumes only bread (b) and cheese (c); his utility
function is U(b,c) = bc. In Chester’s town, cheese is sold in an
unusual way. The more cheese you buy, the higher the price you have
to pay. In particular, c units of cheese cost Chester c2 dollars.
Bread is sold in the usual way (i.e., at a constant price) and the
per-unit price of bread is pb > 0. Chester’s income is m
dollars.
(a) Write down Chester’s budget...

3. Nora enjoys fish (F) and chips(C). Her utility function is
U(C, F) = 2CF. Her income is B per month. The price of fish is
PF and the price of chips is PC. Place fish
on the horizontal axis and chips on the vertical axis in the
diagrams involving indifference curves and budget lines.
(a) What is the equation for Nora’s budget line?
(b) The marginal utility of fish is MUF = 2C and the
Marginal utility of chips...

Tastego comsumes only whale meat (W) and port (P). His utility
function is ? = √2? + √4?. The price of whale meat is $10 per
pound, and port is $5 per bottle. Tashtego has a weekly income of
$400 to spend on these goods. You may assume that it is possible to
consume fractional amounts of either good. a. Draw and label
Tashtego’s budget constraint. You may assume whale meat is on the
horizontal axis, because this will match...

T/F/U: Garrett's utility function is U(a,b) = a*b, where a is
his consumption of apples and b is his consumption of bananas. If
prices and income change in such a way that Garrett's old
consumption lies on his new budget line, then Garrett will not
change his consumption bundle. (Draw Garrett's budget line and some
indifference curves to illustrate your answer.)

7.
Suppose you have the following utility function for two
goods:
u(x1, x2) = x
1/3
1 x
2/3
2
. Suppose your initial income is I, and prices are p1 and
p2.
(a) Suppose I = 400, p1 = 2.5, and p2 = 5. Solve for the
optimal bundle. Graph the budget
constraint with x1 on the horizontal axis, and the
indifference curve for that bundle.
Label all relevant points
(b) Suppose I = 600, p1 = 2.5, and...

Charlie likes buying shoes and going out to sing. His utility
function for pairs of shoes, S, and the number of times he goes
singing per month, T, is U(S,T)=2S^2T^2 . It costs Charlie $50 to
buy a new pair of shoes or to spend an evening out singing. Assume
that he has $500 to spend on shoes and singing.
a. What is the equation for her budget line? Draw the budget
constraint with the T on the vertical axis,...

Suppose that Bruce cares only about barbecued chicken (B) and
fish (F). His utility function is U = B^0.4 F^0.6. The price of
fish is $10 and price of barbecued chicken is $5. Bruce has a
budget of $100. What is the solution to Bruce's maximization
problem?
6 units of fish and 8 units chicken
7.3 units of fish and 5.5 units chicken
4 units of fish and 3 units chicken
3 units of fish and 4 units of chicken

1. A consumer has the utility function U = min(2X, 5Y ). The
budget constraint isPXX+PYY =I.
(a) Given the consumer’s utility function, how does the consumer
view these two goods? In other words, are they perfect substitutes,
perfect complements, or are somewhat substitutable? (2 points)
(b) Solve for the consumer’s demand functions, X∗ and Y ∗. (5
points)
(c) Assume PX = 3, PY = 2, and I = 200. What is the consumer’s
optimal bundle?
(2 points)
2....

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!),...

Evelyn eats only apples and bananas. Suppose Evelyn has the
following utility function: ?(??, ??) = ????.
a. Evelyn currently has 40 apples and 5 bananas. What is
Evelyn’s utility at this bundle? Graph the indifference curve
showing all bundles that Evelyn likes exactly as well as the bundle
(40, 5).
b. Norah offers to trade Evelyn 15 bananas if she will give her
25 apples. Would Evelyn take this trade? Explain.
c. What is the largest number of apples...

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