Question

. Suppose utility is given by the following function:

u(x, y) = min(2x, 3y) Suppose P_{x} = 4, P_{y} =
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 x and y?

(d) Suppose that these goods can not be purchased in fractional amounts. If income increased by $6, could this consumer increase their utility? Why or why not?

Answer #1

b) The consumers utility function is given by U(X,Y) = MIN(2X,
3Y), and the given bundle is X = 3 and Y = 1.
i) MRS = __________________________________________________
ii) Draw your graph in this space:

Suppose the utility function is given by U(x1,
x2) = 14 min{2x, 3y}. Calculate the optimal consumption
bundle if income is m, and prices are p1, and
p2.

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) = 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?

1) For a linear preference function u (x, y) = x + 2y, calculate
the utility maximizing consumption bundle, for income m = 90,
if
a) px = 4 and py = 2
b) px = 3 and py = 6
c) px = 4 and py = 9

Suppose that your utility function is 7x+3y. The market prices
are px=20 and
py=14. Assuming that your wealth is
$10,000, calculate the utility-maximizing commodity bundle.

1. A consumer has the utility function U = min(2X, 5Y ). The
budget constraint isPXX+PYY =I.
(a) Given the consumer’s utility function, how does the consumer
view these two goods? In other words, are they perfect substitutes,
perfect complements, or are somewhat substitutable? (2 points)
(b) Solve for the consumer’s demand functions, X∗ and Y ∗. (5
points)
(c) Assume PX = 3, PY = 2, and I = 200. What is the consumer’s
optimal bundle?
(2 points)
2....

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...

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...

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.

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