Question

Jane's utility function is **U(x, y) = x + 63y -
3y ^{2}**. Her income is $184. If the price of x is
$1 and the price of y is $33, how many units of Good x will Wanda
demand?

- 25 units.
- 22 units.
- 24 units.
- 21 unit.
- 19 units.

Answer #1

A person spends all his/her $400 weekly income on goods, X and
Y. His/her utility function is U(X,Y)=XY.
a) What is the marginal rate of substitution (MRS) for consuming
4 units of X and 8 units of Y?
b) How much of each good would be purchased if the price of X is
4 and the price of Y is 8?

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?

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.

Sharon has the following utility function: U (X,Y)=
sqrt(X)+sqrt(Y) where X is her consumption
of candy bars, with price Px=$1 , and Y is her consumption of
espressos, with price Py= $4 .
a. Derive Sharon’s demand for candy bars and espressos.
A. X=0.906I and Y=1.456I
B. X=1.352I and Y=1.456I
C. X=0.800I and Y=0.050I
D. X=1.241Iand Y=1.929I
E. X=0.157I and Y=0.050I
b. Assume that her income is I=$100 . How many candy bars and
espressos will Sharon consume?
c. What...

Julie’s utility function is U(x, z) = xz x+z . Solve for her
optimal values of good x and good z as a function of the price of
good x, px, the price of good z, pz, and income, Y . For
simplicity, assume that pz = 1.

Suppose that there are two goods, X and Y. The utility function
is U = XY + 2Y. The price of one unit of X is P, and the price of
one unit of Y is £5. Income is £60. Derive the demand for X as a
function of P.

Anna’s utility function is U(x,z) = x? + z?. Solve for her
optimal values of good x and good z as a function of the price of
good x, px, the price of good z, pz, and income, Y . For
simplicity, assume that pz = 1. step by step

9. AJ has a utility function: u(x,y) = x2y3. The price of x is
px = 1 and the price of y is py = 2, and AJ has income m = 15 to
spend on the goods. To maximize his utility, how many units of y
will AJ consume?

Let U (x ,y) = x ,y represent the consumer's utility function.
If the consumer's income (M) is $1,000, the price of Good X is $10,
and the price of Good Y is $20, what is the slope of the budget
line or market rate of substitution between Goods X and Y?

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