Question

Emily's preferences can be represented by u(x,y) =
x^{1/2} y^{1/2} . Emily faces prices
(p_{x},p_{y}) = (2,1) and her income is $60. (some
formulas in chapter 5 might help)

**Her optimal consumption bundle is**:
______________ (write in the form of (x,y) with no space)

Now the price of x increases to $3 while price of y remains the same

**Her new** **optimal consumption bundle is:
______________** (write in the form of (x,y) with
no space)

**Her Equivalent Variation** **is**:
$_______________

**Her Equivalent Variation** **is**:
$

Answer #1

Emily's preferences can be represented by u(x,y)=x1/4
y3/4 . Emily faces prices (px,py)
= (2,1) and her income is $120.
Her optimal consumption bundle is: _______
(write in the form of (x,y) with no space)
Now the price of x increases to $3 while price of y remains the
same
Her new optimal consumption bundle
is:_______ (write in the form of (x,y) with no
space)
Her Equivalent Variation is:
$__________

Emily's preferences can be represented by u(x,y)=x1/4
y3/4 . Emily faces prices (px,py)
= (2,1) and her income is $120.
a) Her optimal consumption bundle is:________
(write in the form of (x,y) with no space)
Now the price of x increases to $3 while price of y remains the
same
b) Her new optimal consumption bundle
is:_______ (write in the form of (x,y) with no
space)
c) Her Equivalent Variation
is: $________

Emily's preferences can be represented by u(x,y)=x^1/4 y^3/4 .
Emily faces prices (px,py) = (2,1) and her income is $120.
Her optimal consumption bundle is: __________ (write in the form
of (x,y) with no space)
Now the price of x increases to $3 while price of y remains the
same Her new optimal consumption bundle is: ____________ (write in
the form of (x,y) with no space)
Her Equivalent Variation is: $ ____________

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...

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. Emily has preferences for two goods x, y while her marginal
rate of substitution (MRS) between x and y is given by 3y/x. Her
budget constraint is m ≥ pxx + pyy, where m = income and px, py are
prices of x, y respectively. (a) Emily's expenditure on y (i.e.,
pyy) is 1/3 of her expenditure on x (i.e., pxx). Is this true Are x
and y normal goods? (b) Andrew has different preferences: his
marginal rate of...

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?

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...

Suppose x represents weekly meat consumption and y represents
weekly vegetables consumption. Their prices are px and py. Paul’s
utility function is U1(x,y) = x2y3 and Peter’s utility function is
U2(x,y) = 2x + 3y.
a. Derive the utility level for both at the bundle (4,4)
respectively. Does one enjoy the bundle (4,4) more than the
other?
b. If the meat price px = 5, vegetables price py = 1, and each
of them has a budget of 100. What...

A consumer's preferences are given by the utility function
u=(107)^2+2(x-5)y and the restrictions x>5 and y>0 are
imposed.
1. Write out the Lagrangian function to solve the consumer's
choice problem. Use the Lagrangian to derive the first order
conditions for the consumer's utility maximizing choice problem.
Consider only interior solutions. Show your work.
2. Derive the Optimal consumption bundles x*(px,py,w) and
y*(px,py,w)
3. Use the first order condition from 1 to calculate the
consumer's marginal utility of income when w=200,...

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