Question

Suppose that a consumer gains utility from apples and bananas according to the utility function: U(A,B)=A^2 ×B

a)Suppose A = 2 and B = 1. What is the marginal utility of each
good?

b)For the consumer’s utility, how valuable are apples relative to
bananas? That is, what is the MRS?

c)Suppose PA = 2 and PB = 1. How valuable are apples relative to bananas in the marketplace? That is, what is the price ratio?

d)Suppose A = 2, B = 1, PA = 2, and PB = 1. Which good provides the consumer with more utility per dollar? How should the consumer change consumption from the current levels?

e)On a graph, draw an indifference curve for a utility level of Ū = 16. Use at least 4 different consumption bundles.

Answer #1

George is making a consumption choice over apples (a) and
bananas (b). George’s preferences are represented by u (a, b)
=(2a^2)b where a > 0 and b > 0. Denote by f = (a, b) a fruit
bundle.
1. In terms of preference relations, how does George rank the
three bundles f1 = (3, 1), f2 = (1, 3), and f3 = (2, 2) relative to
each other?
2. State George’s marginal rate of substitution (MRS) function,
MRS(a, b) (where...

Evelyn eats only apples and bananas. Suppose Evelyn has the
following utility function: ?(??, ??) = ????.
a. Evelyn currently has 40 apples and 5 bananas. What is
Evelyn’s utility at this bundle? Graph the indifference curve
showing all bundles that Evelyn likes exactly as well as the bundle
(40, 5).
b. Norah offers to trade Evelyn 15 bananas if she will give her
25 apples. Would Evelyn take this trade? Explain.
c. What is the largest number of apples...

Suppose Sophie receives utility from bananas and apples. If A =
# of apples Sophie consumes and B = # of Bananas she consumes,
Sophie's utility function can be described as U (A, B) = ln(A) +
2ln(B). Sophie is also able to purchase fractions of fruit instead
of having to buy whole amounts.
a) Income = Y, price of apples = p(a) and price of bananas =
p(b). Derive the demand for apples.
b) Say that apples only cost...

T/F/U: Garrett's utility function is U(a,b) = a*b, where a is
his consumption of apples and b is his consumption of bananas. If
prices and income change in such a way that Garrett's old
consumption lies on his new budget line, then Garrett will not
change his consumption bundle. (Draw Garrett's budget line and some
indifference curves to illustrate your answer.)

3. Suppose that Karen’s utility function is given by U = 2A +
5B. a. Calculate Karen’s marginal utility of good A and her
marginal utility of good B. b. Suppose that the prices of the goods
PA and PB are such that Karen is (optimally) consuming positive
quantities of both goods. What is the price of good A in terms of
the price of good B? c. How will her consumption change if PA
doubles, while PB does not...

Scenario 5
Charlie has the utility function U ( X A , x B ) =
X1/2A X1/2B
where XA stands for the number of apples and
XB stands for the number of bananas consumed.
Refer to Scenario 5.
- Putting apples on the x-axis, and bananas on the y-axis, what
is the equation for the Marginal Rate of Substitution (MRS)?
Refer to Scenario 5.
- His indifference curve passing through 36 apples and 4 bananas
will also pass through...

Suppose your utility is given by U(A,B)=10A+B
a) Find the marginal utility of each good
b) What is the marginal rate of substitution?
c)If I(income)=20, pa=5, pb=2 what is the optimal consumption of
products A and B?

Angela's fruit options at the convenience store are apples and
bananas. Angela's utility function over apples, A, and bananas, B,
is given by: U(A,B)=A+B a. Describe Angela's preferences over
apples and bananas and explain her optimal decision rule b. What is
the optimal bundle if price of apples is $1 a pound and the price
of bananas is $2 a pound, and she has $100 a month to spend on
apples and bananas. c. This convenience store is closing for...

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...

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...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago