Question

Suppose an individual consumers two goods, with utility function U (x1; x2) = x1 + 6(x1x2)^1/2 + 9x2. Formulate the utility maximization problem when she faces a budget line p1x1 + p2x2 = I. Find the demand functions for goods 1 and 2.

(b) Now consider an individual consumers with utility function U (x1; x2) = x1^1/2 + 3x2^1/2. Formulate the utility maximization problem when she faces a budget line p1x1 + p2x2 = I. Find the demand functions for goods 1 and 2.

Answer #1

2. A consumer has the utility function U ( X1,
X2 ) = X1 + X2 +
X1X2 and the budget constraint
P1X1 + P2X2 = M ,
where M is income, and P1 and P2 are the
prices of the two goods. .
a. Find the consumer’s marginal rate of substitution (MRS)
between the two goods.
b. Use the condition (MRS = price ratio) and the budget
constraint to find the demand functions for the two goods.
c. Are...

Given a utility function for perfect complements: U(x1,x2) =
min{x1,βx2}, where β is a positive num- ber, and a budget
constraint: p1x1 + p2x2 = Y , where p1 and p2 are prices of good 1
and good 2 respectively, Y is the budget for the complements. Find
the demand functions for good 1 and good 2.

1. Using the following utility function, U(x1,x2) =
x1x2+x1+2x2+2 Find the demand functions for both x1 and x2 (as
functions of p1, p2, and m).
Thank you!

Consider utility function u(x1,x2)
=1/4x12
+1/9x22. Suppose the prices of good
1 and
good 2 are p1 andp2, and income is
m.
Do bundles (2, 9) and (4, radical54) lie on the same
indifference curve?
Evaluate the marginal rate of substitution at
(x1,x2) = (8, 9).
Does this utility function represent
convexpreferences?
Would bundle (x1,x2) satisfying (1)
MU1/MU2 =p1/p2 and (2)
p1x1 + p2x2 =m be an
optimal choice? (hint: what does an indifference curve look
like?)

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 an individual utility function is (i) U = min (X1, X2)
and (ii) U = 2X1 + X2. Show the indifference curves in both cases.
Calculate and explain cross elasticity of X1 and X2 in (i) and
(ii).

1. Al Einstein has a utility function that we can describe by
u(x1, x2) = x21 +
2x1x2 + x22
. 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 utility function a...

The utility function is given by u (x1,x2) = x1^0.5 + x2^0.5
1) Find the marginal rate of substitution (MRSx1,x2 )
2) Derive the demand functions x1(p1,p2,m) and x2(p1, p2,m) by
using the method of Lagrange.

The utility function is given by u (x1, x2) = x1^0.5+x2^0.5
1) Find the marginal rate of substitution (MRSx1,x2 )
2) Derive the demand functions x1(p1, p2, m) and x2(p1,p2, m) by
using the method of Lagrange.

Ted’s utility function over goods 1 and 2 is given by:
U(x1,x2) =
4x11/2x21/4. What is
Ted’s demand for goods 1 and 2 if the price of good 1 is 1, the
price of good 2 is 2, and Ted has $18 to spend?
Group of answer choices
A.) (x1, x2) = (12,3)
B.) (x1, x2) = (4,7)
C.) (x1, x2) = (6,6)
D.) (x1, x2) = (2,8)

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