Question

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.

Answer #1

Jane’s utility function has the following form: U(x,y)=x^2
+2xy
The prices of x and y are px and py respectively. Jane’s income
is I.
(a) Find the Marshallian demands for x and y and the indirect
utility function.
(b) Without solving the cost minimization problem, recover the
Hicksian demands for x and y and the expenditure function from the
Marshallian demands and the indirect utility function.
(c) Write down the Slutsky equation determining the effect of a
change in px...

(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...

Find the utility maximizing demands for x and y, x* and
y*, when U(x,y)=min(x,5y)
, the price of x is $1, the price of y is $15, and
income (M) is $140. The demand for x is , and the demand for y
is

The consumer’s Utility Function is
U(x,y) = X1/2Y1/2. Further Px = $5 and Py =
$10 and the consumer has $500 to spend. The values of x* = 50 and
y* = 25 maximizes utility.
The dual to the utility maximization
problem is expenditure minimization problem where the consumer
choose x and y to minimize the expenditure associated with
achieving a specified level of utility. That is,
Choose x and y to Minimize
Expenditure 5x + 10y subject to U...

Claraís utility function is u (x; y) = (x + 2) (y + 1) where x
is her consumption of good x and y is her consumption of good
y.
(a) Write an equation for Claraís indi§erence curve that goes
through the point (x; y) = (2; 8).
(b) Suppose that the price of each good is $1 and Clara has an
income of $11. Can Clara achieve a utility level of at least 36
with this budget? (
c)...

Consider the following utility function: U =
X^2 + Y^2
If P x = 3 and P y = 2.5,
and the income is I= 50. Find the optimal
consumption bundle.

Let the Utility Function be U = min { X , Y }. Income
is $12 and the Price of Good Y is $1. The price of good X decreases
from $2 to $1. What is the substitution effect and the income
effect for good X given this price change?

Suppose the utility function for goods ?? and ?? is given by:
u(x, y) = x0.5 y0.5 a) Explain the difference between compensated
(Hicksian) and uncompensated (Marshallian) demand functions. b)
Calculate the uncompensated (Marshallian) demand function for ??,
and describe how the demand curve for ?? is shifted by changes in
income , and by changes in the price of the other good. c)
Calculate the total expenditure function for ??.

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...

Jim’s utility function for good x and good y is U(x, y) =
X^1/4*Y^3/4.
1. Calculate Jim’s marginal utilities for good x and good y.
2. Calculate Jim’s Marginal rate of substation of his utility
function.

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