Question

A consumer has utility function U(x, y) = x + 4y^{1/2} .
What is the consumer’s demand function for good x as a function of
prices p_{x} and p_{y}, and of income m, assuming a
corner solution?

Group of answer choices

a.x = (m – 3p_{x})/p_{x}

b.x = m/p_{x} – 4p_{x}/p_{y}

c.x = m/p_{x}

d.x = 0

Answer #1

Suppose a consumer has the utility function U (x, y) = xy + x +
y. Recall that for this function the marginal utilities are given
by MUx(x,y) = y+1 and MUy(x,y) = x+1.
(a) What is the marginal rate of substitution MRSxy?
(b)If the prices for the goods are px =$2 and py =$4,and if the
income of the consumer is M = $18, then what is the consumer’s
optimal affordable bundle?
(c) What if instead the prices are...

Suppose a consumer has the utility function u(x, y) = x + y.
a) In a well-labeled diagram, illustrate the indifference curve
which yields a utility level of 1.
(b) If the consumer has income M and faces the prices px and py
for x and y, respectively, derive the demand functions for the two
goods.
(c) What types of preferences are associated with such a utility
function?

8) Suppose a consumer’s utility function is defined by
u(x,y)=3x+y for every x≥0 and y≥0 and
the consumer’s initial endowment of wealth is w=100. Graphically
depict the income and
substitution effects for this consumer if initially Px=1 =Py and
then the price of commodity x
decreases to Px=1/2.

Suppose a consumer’s Utility Function
U(x,y) = X1/2Y1/2. The consumer wants to
choose the bundle (x*, y*) that would maximize utility.
Suppose Px = $5 and Py = $10 and the
consumer has $500 to spend.
Write the consumer’s budget constraint. Use the budget
constraint to write Y in terms of X.
Substitute Y from above into the utility function U(x,y) =
X1/2Y1/2.
To solve for the utility maximizing, taking the derivative of U
from (b) with respect to X....

Consider a consumer with the utility function U(x, y) = min(3x,
5y). The prices of the two goods are Px = $5 and Py = $10, and the
consumer’s income is $220. Illustrate the indifference curves then
determine and illustrate on the graph the optimum consumption
basket. Comment on the types of goods x and y represent and on the
optimum solution.

Suppose a consumer’s utility function is given by U(X,Y) = X*Y.
Also, the consumer has $360 to spend, and the price of X, PX = 9,
and the price of Y, PY = 1.
a) (4 points) How much X and Y should the consumer purchase in
order to maximize her utility?
b) (2 points) How much total utility does the consumer
receive?
c) (4 points) Now suppose PX decreases to 4. What is the new
bundle of X and...

Consider a consumer with the utility function U(x, y) =2 min(3x,
5y), that is, the two goods are perfect complements in the ratio
3:5. The prices of the two goods are Px = $5 and Py = $10, and the
consumer’s income is $330. At the optimal basket, the consumer buys
_____ units of y. The utility she gets at the optimal basket is
_____ At the basket (20, 15), the MRSx,y = _____.

Suppose a consumer has the utility function u(x,y)=x+y -
(a) In a well labelled diagram illustrate the indifference curve
which yields a utility level of 1
(b) If the consumer has income And faces the prices Px and Py
for x and y, respectively, derive the demand function for the two
goods
(c) What types of preferences are associated with such a utility
function?

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...

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...

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