Question

Given the following utility function: U (X,Y) = 2X½ + Y and given that U = 40

Part 1: Find Y1 for X = 4

Part 2: Find Y1 for X = 9

Part 3: Find Y1 for X = 16

Part 4: Find Y1 for X = 36

Part 5: Find Y1 for X = 49

Using graph paper construct the graph for indifference curve for U = 40 Given : Py = 20, Px = 5 and I = 720

Using the same set of axis as used above graph the budget line.

Part 6: Find the optimal quantity of good X

Part 7: Find the optimal quantity of good Y

Answer #1

. Suppose utility is given by the following function:
u(x, y) = min(2x, 3y) Suppose Px = 4, Py =
6, and m = 24.
Use this information to answer the following questions:
(a) What is the no-waste condition for this individual?
(b) Draw a map of indifference curves for these preferences. Be
sure to label your axes, include the no-waste line, and draw at
least three indifference curves.
(c) Given prices and income, what is the utility-maximizing
bundle of...

Given the following utility function and budget
contraints:
U(X,Y) = XY
I = Px (X) + Py(Y)
and given that: Py = 10 , Px=12 and I = 360
Fill in the blanks in the following table (round to two
decimal places):
Part 1: What is the Value of
Qx?
Part 2: What is the Value of
Qy?
Part 3: What is the Optimal
level of utility?

Tamer derives utility from goods X and Y, according to
the following utility function: U(X,Y)= 3 X radical y . His budget
is $90 per period, the price of X is PX=$2, and the
price of Y is PY=$6.
1. Graph the indifference curve when U=
36
2. What is the Tamer’s MRS between goods X
and Y at the bundle (X=8 and Y=2 )? What does the value of MRS
means? (أحسب القيمة واكتب بالكلمات ماذا تعني القيمة)
3....

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...

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...

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,...

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.

5. Harry Mazola [4.7] has preferences u = min (2x + y, x + 2y).
Graph the u = 12 indifference curve. Mary Granola has preferences u
= min (8x + y, 3y + 6x). Graph the u = 18 indifference curve.
6. A consumer with m = 60 is paying pY = 2. They must pay pX = 4
for the first 5 units of good x but then pay only pX = 2 for
additional units. The horizontal...

(15) A representative consumer’s utility is given by:
U=min(2X,
Y). Income is 2400. The prices are:
PX=2, PY=1.
X is the consumption of gasoline and Y is the
consumption of composite good.
(3) Write the budget constraint. Compute the optimal
consumption bundle.
(4) Now the government imposes 100% tax on the consumption of
gasoline. Write the new budget constraint. Compute the optimal
consumption bundle.
(4) Now, in addition to the tax in part (B), suppose that the
government gives the...

(15) A representative consumer’s utility is given by:
U=min(2X,
Y). Income is 2400. The prices are:
PX=2, PY=1.
X is the consumption of gasoline and Y is the
consumption of composite good.
(3) Write the budget constraint. Compute the optimal
consumption bundle.
(4) Now the government imposes 100% tax on the consumption of
gasoline. Write the new budget constraint. Compute the optimal
consumption bundle.
(4) Now, in addition to the tax in part (B), suppose that the
government gives the...

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