Question

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 px = $3 and py = $3 (and income is still M = $18)?

Answer #1

Ans.

Consider a consumer whose preferences over the goods are
represented by the utility function U(x,y) = xy^2. Recall that for
this function the marginal utilities are given by MUx(x, y) = y^2
and MUy(x, y) = 2xy.
(a) What are the formulas for the indifference curves
corresponding to utility levels of u ̄ = 1, u ̄ = 4, and u ̄ = 9?
Draw these three indifference curves in one graph.
(b) What is the marginal rate of substitution...

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

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?

Donna and Jim are two consumers purchasing strawberries and
chocolate. Jim’s utility function is U(x,y) = xy and Donna’s
utility function is U(x,y) = x2y where x is
strawberries and y is chocolate. Jim’s marginal utility
functions are MUX=y and
MUy=x while Donna’s are
MUX=2xy and
MUy=x2. Jim’s income is $100,
and Donna’s income is $150.
What is the optimal bundle for Jim, and for Donna, when the
price of strawberries rises to $3?

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?

A consumer has preferences represented by the utility function
u(x, y) = x^(1/2)*y^(1/2). (This means that
MUx=(1/2)x^(−1/2)*y^(1/2) and MUy =1/2x^(1/2)*y^(−1/2)
a. What is the marginal rate of substitution?
b. Suppose that the price of good x is 2, and the price of good
y is 1. The consumer’s income is 20. What is the optimal quantity
of x and y the consumer will choose?
c. Suppose the price of good x decreases to 1. The price of good
y and...

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 the utility function U(x,y) = xy Income is I=400, and
prices are initially
px =10 and py =10.
(a) Find the optimal consumption choices of x and y.
(b) The price of x changes, to px =40, while the price of y remains
the same. What are
the new optimal consumption choices for x and y?
(c) What is the substitution effect?
(d) What is the income effect?

3. Suppose that a consumer has a utility function given by
U(X,Y) = X^.5Y^.5 . Consider the following bundles of goods: A =
(9, 4), B = (16, 16), C = (1, 36).
a. Calculate the consumer’s utility level for each bundle of
goods.
b. Specify the preference ordering for the bundles using the
“strictly preferred to” symbol and the “indifferent to” symbol.
c. Now, take the natural log of the utility function. Calculate
the new utility level provided by...

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 = _____.

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