Question

Let the Utility Function be U = X1/2Y PX = $1; PY = $2; I = $15 a. What are X and Y if there is an increase in the price of good X to $2? (0.5 Points) b. Use the slutsky equation to show this impact and what is attributed to the: a. Income Effect (0.5 Points) b. Substitution Effect (0.5 Points) c. What is the reduction in Utility caused by this increase in price? (0.5 Points)

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...

Consider a consumer with the following utility function: U(X,
Y ) = X1/2Y 1/2
(a) Derive the consumer’s marginal rate of substitution
(b) Calculate the derivative of the MRS with respect to
X.
(c) Is the utility function homogenous in X?
(d) Re-write the regular budget constraint as a function of PX
, X, PY , &I. In other words, solve the equation for Y .
(e) State the optimality condition that relates the marginal
rate of substi- tution to...

Let U=X1/2Y2,
dU/dX=(1/2)X-1/2Y2,
dU/dY=2X1/2Y
Px=$15, Py=$3 and I=$300
1.(2 pts)_______________________ What is the level of happiness
at X=16, Y=6?
2. (2 pts)_______________________What is the marginal utility of
X at this point?
3.(2 pts)________________________ What is the slope of the
indifference curve at this point?
4.(2 pts)_______________________ At this point, which is larger:
the marginal utility of the last dollar spent on X or the marginal
utility of the last dollar spent on Y? (You must show both marginal
utilities per...

Let income be I = $90, Px = $2, Py = $1, and utility U = 4X½Y.
a.[12] Write down and simplify the two conditions required for
utility maximization. b.[6] Compute the optimal consumption bundle
for the consumer. What is the level of utility at the optimum?

Alice’s preferences over two goods are described by the utility
function u(x1, x2) = 2x1+ 4x2. Her income is m= 100 and p1= 4, p2=
5. Assume now that the price of good 1 falls to p01= 2.
a) Find the substitution, income, and total effect for good
1.
b) Find the substitution, income, and total effect for good
2.
c) Verify that the Slutsky equation holds for both goods

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...

Consider the utility function U(x,y) = xy Income is I=400, and
prices are initially
px =10 and py =10.
(a) Find the optimal consumption choices of x and y.
(b) The price of x changes, to px =40, while the price of y remains
the same. What are
the new optimal consumption choices for x and y?
(c) What is the substitution effect?
(d) What is the income effect?

1) For a linear preference function u (x, y) = x + 2y, calculate
the utility maximizing consumption bundle, for income m = 90,
if
a) px = 4 and py = 2
b) px = 3 and py = 6
c) px = 4 and py = 9

Suppose the preferences of an individual are represented by a
quasilinear utility func- tion: U (x, y) = 3 ln(x) + 6y (a)
Initially, px=1, py=2 and I=101. Then, the price of x increases to
2 (px=2). Cal- culate the changes in the demand for x. What can you
say about the substitution and income effects of the change in px
on the consumption of x? (Hint: since the change in price is not
small, you cannot use the Slutsky...

Assume that Sam has following utility function: U(x,y) =
2√x+y
MRS=(x)^-1/2, px = 1/5, py = 1 and her income I = 10. price
increase for the good x from px = 1/5 to p0x = 1/2.
(a) Consider a price increase for the good x from px = 1/5 to
p0x = 1/2. Find new optimal bundle under new price using a graph
that shows the change in budget set and the change in optimal
bundle when the price...

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