Question

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.

Answer #1

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-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?

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. 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....

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 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...

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 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.

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.

Consider the utility function U ( x,y ) = min { x , 2y }.
(a) Find the optimal consumption choices of x and y when I=50,
px=10, and py=5.
(b) The formula for own-price elasticity of x is
εx,px = (−2px/2px +
py) For these specific values of income, prices, x and
y, what is the own-price elasticity? What does this value tell us
about x?
(c) The formula for cross-price elasticity of x is
εx,py = (py/2px +...

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