Question

1. Suppose Jill has a utility function U=x^1/3 y^2/3with income 100. Jill is not as unique

as she thinks she is, there are 1000 people with the exact same

preferences.

(a)What is Jill’s demand for good x as a function of px? (The answer

will only be partial credit, you must show the maximization p

roblem for full

credit.)

(b)What is the inverse aggregate demand function ?

(c) What is the price elasticity for the whole market?

Answer #1

Suppose a consumer has the utility function u(x, y) = x + y.
a) In a well-labeled diagram, illustrate the indifference curve
which yields a utility level of 1.
(b) If the consumer has income M and faces the prices px and py
for x and y, respectively, derive the demand functions for the two
goods.
(c) What types of preferences are associated with such a utility
function?

Suppose a consumer has the utility function u(x,y)=x+y -
(a) In a well labelled diagram illustrate the indifference curve
which yields a utility level of 1
(b) If the consumer has income And faces the prices Px and Py
for x and y, respectively, derive the demand function for the two
goods
(c) What types of preferences are associated with such a utility
function?

A consumer has utility function U(x, y) = x + 4y1/2 .
What is the consumer’s demand function for good x as a function of
prices px and py, and of income m, assuming a
corner solution?
Group of answer choices
a.x = (m – 3px)/px
b.x = m/px – 4px/py
c.x = m/px
d.x = 0

Assume that we have following utility maximization problem with
quasilinear utility function:
U=2√ x + Y
s.t. pxX+pyY=I
(a)derive Marshallian demand and show if x is a normal good, or
inferior good, or neither
(b)assume that px=0.5, py=1, and I =10. Then the price x
declined to 0.2. Use Hicksian demand function and expenditure
function to calculate compensating variation.
(c)use hicksian demand function and expenditure function to
calculate equivalent variation
(e) briefly explain why compensating variation and equivalent
variation are...

An agent has preferences for goods X and Y represented by the
utility function U(X,Y) = X +3Y
the price of good X is Px= 20, the price of good Y is
Py= 40, and her income isI = 400
Choose the quantities of X and Y which, for the given prices and
income, maximize her utility.

1. Suppose utility for a consumer over food(x) and clothing(y)
is represented by u(x,y) = 915xy. Find the optimal values of x and
y as a function of the prices px and py with an income level m. px
and py are the prices of good x and y respectively.
2. Consider a utility function that represents preferences:
u(x,y) = min{80x,40y} Find the optimal values of x and y as a
function of the prices px and py with an...

1. Consider the following information:
Jessica’s utility function is U(x,
y) = xy.
Maria’s utility function is U(x, y)
= 1,000xy.
Nancy’s utility function is U(x,y) =
-xy.
Chawki’s utility function is U(x,y) = xy -
10,000.
Marwan’s utility function is U(x,y)= x(y +
1).
Which of these persons have the same preferences as Jessica?
2. Suppose the market demand for a product is given by
Qd = 1000 −10P
and the market supply is given by
Qs= −50...

A consumer has preferences represented by the utility function
u(x, y) = x^(1/2)*y^(1/2). (This means that
MUx=(1/2)x^(−1/2)*y^(1/2) and MUy =1/2x^(1/2)*y^(−1/2)
a. What is the marginal rate of substitution?
b. Suppose that the price of good x is 2, and the price of good
y is 1. The consumer’s income is 20. What is the optimal quantity
of x and y the consumer will choose?
c. Suppose the price of good x decreases to 1. The price of good
y and...

(A). Find the maximum of the following utility function with
respect to x;
U= x^2 * (120-4x).
The utility function is U(x,y)= sqrt(x) + sqrt(y) . The price of
good x is Px and the price of good y is Py. We denote income by M
with M > 0. This function is well-defined for x>0 and
y>0.
(B). Compute (aU/aX) and (a^2u/ax^2). Is the utility function
increasing in x? Is the utility function concave in x?
(C). Write down...

Let
the Utility Function be U=X^2/3·Y^1/3. Find the uncompensated
demands for X and Y by solving the Utility Maximization
Problem.

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