Question

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?

Answer #1

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?

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 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...

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...

Ginger's utility function is U(x,y)=x2y with associated marginal
utility functions MUx=2xy and MUy=x2. She has income I=240 and
faces prices Px= $8 and Py =$2.
a. Determine Gingers optimal basket given these prices and her
in.
b. If the price of y increase to $8 and Ginger's income is
unchanged what must the price of x fall to in order for her to be
exactly as well as before the change in Py?

A consumer has utility function U(x, y) = x + 4y1/2 .
What is the consumer’s demand function for good x as a function of
prices px and py, and of income m, assuming a
corner solution?
Group of answer choices
a.x = (m – 3px)/px
b.x = m/px – 4px/py
c.x = m/px
d.x = 0

. 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...

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.

Consider a consumer with preferences represented by the utility
function:
U(x,y) = 3x + 6 √ y
Are these preferences strictly convex?
Derive the marginal rate of substitution
Suppose, the utility function is:
U(x,y) = -x +2 √
y
Are there any similarities or differences between the two
utility functions?

Suppose a consumer has a utility function U(X,Y) = MIN (X,Y) + X
+ Y. Using a graph, illustrate the indifference curve that goes
through the bundle X = 3, Y = 3.
I have the answer but could someone explain to me how to
approach the solution and what each part means.

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