Question

Imagine that you are moving to a new city after you graduate to start a job. You are deciding how much of your paycheck to use for housing (call this H) and how much to save for other spending (call this S). Your utility function is U ( H , S ) = H 0.5 ⋅ S. Housing is measured in square feet, and the cost per square foot is p h. Saving is measured in terms of dollars and therefore the price (p s) is $1. Just to be clear, H is the “x” good, and S is the “y” good in this problem. Your income is $6000.

a) (6 points) What is the marginal rate of substitution? What is the price ratio? What is the budget constraint?

b) (8 points) Find the utility-maximizing demand for housing, H*. It will be a function of p H. Find the utility-maximizing demand for savings, S*. Show your work using your answer from part a for full credit.

c) (10 points) Draw a graph in the (H, S) plane. Put 3 budget constraints on the graph: one with p H = 1, one with p H = 2, and one with p H = 4. Label the intercept points of these budgets. On each budget, add a dot at the (H*,S*) bundle and label those values on each axis. Put an indifference curve through each utility-maximizing point (these don’t need to be drawn to scale). Add the price-offer curve to the graph.

Answer #1

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...

2. Many people consume eggs and toast at breakfast. Assume the
typical person spends $5 per week on eggs and toast. Currently the
price of eggs is $0.50 per egg, and the price of toast is $0.25 per
piece.
(a) (10 points) Graph the budget constraint budget
constraint.
(b) Assume that some people have a utility function given by U =
min[4T, 2E] where T is the quantity of toast measured in slices,
and E is the quantity of eggs....

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....

Consider a consumer with the Utility function: U = C1/5 O 4/5
and facing a budget constraint: M ≤ PCC +POO Note: For this utility
function MUC = (1/5)C-4/5 O 4/5 and MUO = (4/5)C1/5 O -1/5 Where C
denotes the consumption of corn, and O denotes the consumption of
other goods
Consider a consumer with the Utility function: U = C1/5 O 4/5
and facing a budget constraint: M ≤ PCC +POO Note: For this utility
function MUC =...

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....

2. Many people consume eggs and toast at breakfast. Assume the
typical person spends $15 per week on eggs and toast. Currently the
price of eggs is $0.75 per egg, and the price of toast is $0.50 per
piece.
(a) Graph the budget constraint budget constraint.
(b) Assume that some people have a utility function given by U =
min[T, 2E] where T is the quantity of toast measured in slices, and
E is the quantity of eggs.
i. Explain...

Consider the demand for a public good estimated for two sets of
consumers:
P1 = -0.5Q + 10
P2 = -0.25Q + 5
where P is the price that each consumer is willing to pay at
difference levels of quantity. The cost of providing one additional
unit of this public good is $4 (e.g., marginal cost (MC) = $4)
a) Derive the equation of the market demand curve for this
public good. Hint: Remember that in this case you
have...

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...

A person's utility fromm goods A and B is U(A,B)= A x B. The
marginal utilities of each goods are MUa=B and MUb=A. The person
has $120 income to spend on the two goods and the price of both
goods equals $1.
a) Write the equation for the budget line and sketch it on a
graph – identifying relevant intercepts and slope – placing good A
on the horizontal axis.
b) Find the quantities of A and B that maximize...

a) Given the demand curve for a monopolist: Qd = 60 - 2 P and
the marginal revenue curve: MR = 30 - Q. Marginal cost equals
average cost at $14. What is the price and quantity that the
profit-maximizing monopolist will produce? Graph these curves and
label the equilibrium points. (6 pts)
b) If this were a competitive industry, what price and quantity
would be produced? Show this on the above graph and show your work
(answers) below (3...

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