Question

Bilbo can consume two goods, good 1 and good 2 where
X_{1} and X_{2} denote the quantity consumed of
each good. These goods sell at prices P_{1} and
P_{2}, respectively. Bilbo’s preferences are represented by
the following utility function: U(X_{1}, X_{2}) =
3x_{1X2}. 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 price elasticity for good 1. Explain also in words what the measure means.

d) Would the utility functionu(x_{1}, x_{2}) =
−2x_{1x2} still represent Bilbo’s preferences? Motivate
your answer!

Answer #1

A consumer’s preferences over two goods
(x1,x2)
are represented by the utility function
ux1,x2=5x1+2x2.
The income he allocates for the consumption of these two goods is
m. The prices of the two goods are p1
and p2, respectively.
Determine the monotonicity and convexity of these preferences
and briefly define what they mean.
Interpret the marginal rate of substitution
(MRS(x1,x2))
between the two goods for this consumer.
For any p1, p2,
and m, calculate the Marshallian demand functions of
x1 and...

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...

11. a. Suppose David spends his income M on goods x1 and x2,
which are priced p1 and p2, respectively. David’s preference is
given by the utility function
?(?1, ?2) = √?1 + √?2.
(i) Derive the Marshallian (ordinary) demand functions for x1
and x2.
(ii) Show that the sum of all income and (own and cross) price
elasticity of demand
b.for x1 is equal to zero. b. For Jimmy both current
and future consumption are normal goods. He has...

Suppose you consume two goods, whose prices are given by p1 and
p2, and your income is m.
Solve for your demand functions for the two goods, if
(a) your utility function is given by U(x1, x2) = ax1 + bx2
(b) your utility function is given by U(x1, x2) = max{ax1,
bx2}

1. Suppose a price-taking consumer chooses goods 1 and
2 to maximize her utility given her wealth. Her budget constraint
could be written as p1x1 + p2x2 = w, where (p1,p2) are the prices
of the goods, (x1,x2) denote quantities of goods 1 and 2 she
chooses to consume, and w is her wealth. Assume her preferences are
such that demand functions exist for this consumer: xi(p1,p2,w),i =
1,2. Prove these demand functions must be homogeneous of degree
zero.

Suppose that a consumer has preferences over bundles of
non-negative amounts of each two goods, x1 and x2, that can be
represented by a quasi-linear utility
function of the form
U(x1,x2)=x1 +√x2.
The consumer is a price taker who faces a price per unit of good
one that is equal to $p1 and a price per unit of good two that is
equal to $p2. An- swer each of the following questions. To keep
things relatively simple, focus only on...

Al Einstein has a utility function that we can describe by u(x1,
x2) = x 2 1 + 2x1x2 + x 2 2 . Al’s wife, El Einstein, has a utility
function v(x1, x2) = x2 + x1. (a) Calculate Al’s marginal rate of
substitution between x1 and x2. (b) What is El’s marginal rate of
substitution between x1 and x2? (c) Do Al’s and El’s utility
functions u(x1, x2) and v(x1, x2) represent the same preferences?
(d) Is El’s...

Find the optimal bundle (x1, x2) (two
numbers). Does Jeremy consume positive amounts of both goods?
(e) Find the optimal bundle given p1 = 2,
p2 = 4 and m = 40 assuming U(x1,
x2) = 2x1 + 3x2. Does Jeremy
consume positive amounts of both goods? Is the optimal bundle at a
point of tangency?

Consider the following Constant Elasticity of Substitution
utility function U(x1,x2) =
x1^p+x2^p)^1/p
a. Show that the above utility function corresponds to (hint:use
the MRS between good 1 and good 2. The ->refers to the concept
of limits.
1. The perfect substitute utility function at p=1
2. The Cobb-Douglas utility function as p -->0
3. The Leontiff (of min(x1,x2) as p--> -infinity
b. For infinity<p<1, a given level of income I and prices
p1 and p2.
1. Find the marshallian...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 49 minutes ago

asked 56 minutes ago

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 3 hours ago

asked 4 hours ago

asked 4 hours ago

asked 4 hours ago