Question

A consumer generally buys 2 goods, good A and a composite good B. The function that represents utility is U(A,B) = ln(3AB). The price of good A is PA and the price of good B is PB, and also income is represented by I. What is the demand equation for good A? and are A and B compliments or substitutes?

Answer #1

Suppose that a consumer has utility given by U(a,b) = ab + 10b,
her income is n, the price of a is Pa, and the price of b is
Pb.
a. Write the demand functions for both goods.
In parts b - d you assume interior solution:
b. Is each good normal or inferior? Explain.
c. Is each good a normal good or a giffen good?
d. Are the two goods (gross) complements or substitutes?
e. Prove that these preferences...

There are two goods, Good 1 and Good 2, with positive prices
p1 and p2. A consumer has the utility
function U(x1, x2) = min{2x1,
5x2}, where “min” is the minimum function, and
x1 and x2 are the amounts she consumes of
Good 1 and Good 2. Her income is M > 0.
(a) What condition must be true of x1 and
x2, in any utility-maximising bundle the consumer
chooses? Your answer should be an equation involving (at least)
these...

There are two goods, Good 1 and Good 2, with positive prices
p1 and p2. A consumer has the utility
function U(x1, x2) = min{2x1,
5x2}, where “min” is the minimum function, and
x1 and x2 are the amounts she consumes of
Good 1 and Good 2. Her income is M > 0.
(a) What condition must be true of x1 and
x2, in any utility-maximising bundle the consumer
chooses? Your answer should be an equation involving (at least)
these...

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...

Suppose the price of good A is $2 and price of good B is $3. You
have $90 to spend and your preferences over A and B are defined as:
a^2/3*b^1/3 = U(a,b).
If income changes from $100 to $84, Pa = $2, Pb = $3 calculate
and show work on how the optimal choice of A and B change and what
the total utility achieved is given the Utility Function.

A consumer likes two goods; good 1 and good 2. the consumer’s
preferences are described the by the cobb-douglass utility
function
U = (c1,c2) =
c1α,c21-α
Where c1 denotes consumption of good 1, c2
denotes consumption of good 2, and parameter α lies between zero
and one; 1>α>0. Let I denote consumer’s income, let
p1 denotes the price of good 1, and p2
denotes the price of good 2. Then the consumer can be viewed as
choosing c1 and c2...

Bilbo can consume two goods, good 1 and good 2 where
X1 and X2 denote the quantity consumed of
each good. These goods sell at prices P1 and
P2, respectively. Bilbo’s preferences are represented by
the following utility function: U(X1, X2) =
3x1X2. Bilbo has an income of m.
a) Derive Bilbo’s Marshallian demand functions for the two
goods.
b) Given your answer in a), are the two goods normal goods?
Explain why and show this mathematically.
c) Calculate Bilbo’s...

Complete parts 1 and 2:
Part 1:
Suppose the consumer believes that goods X and Y are perfect
substitutes with 5 units of X equivalent to 1 unit of Y. Which of
the following is correct?
Group of answer choices
the marginal rate of substitution is not well defined when
(X,Y)=(5,1)
the marginal utility of X is 5 and the marginal utility of Y is
1
the utility function is U(X,Y)=X+5Y
the utility function is U(X,Y)=5X+Y
Part 2:
Suppose the...

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...

Suppose there are only two goods, good X and a composite good. A
rational consumer with a weekly income of $100 consumed 5 units of
good X when the price of good X is $10 per unit. Suppose now the
price of good X has decreased to $5 per unit.
Draw the price-consumption curve (PCC) of this consumer assuming
good X is a price-elastic good. Add a brief explanation about the
shape of your PCC (that is, why it is...

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