Question

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).

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Answer #1

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A consumer has utility function
U(x1,x2)= x1x2 / (x1 + x2)
(a) Solve the utility maximization problem. Construct the
Marshallian demand function D(p,I) and show that the indirect
utility function is
V (p, I) = I / (p1+ 2 * sqrt (p1*p2) + p2)
(b) Find the corresponding expenditure function e(p; u). HINT:
Holding p fixed, V and e are inverses. So you can find the
expenditure function by working with the answer to part (a).
(c) Construct the Hicksian...

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.

Qin has the utility function U(x1, x2) = x1 + x1x2, where x1 is
her consumption of good 1 and x2 is her consumption of good 2. The
price of good 1 is p1, the price of good 2 is p2, and her income is
M.
Setting the marginal rate of substitution equal to the price
ratio yields this equation: p1/p2 = (1+x2)/(A+x1) where A is a
number. What is A?
Suppose p1 = 11, p2 = 3 and M...

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...

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...

Consider the utility function:
u( x1 , x2 ) = 2√ x1 +
2√x2
a) Find the Marshallian demand function. Use ( p1 ,
p2 ) to denote the exogenous prices of x1 and
x2 respectively. Use y to denote the consumer's
disposable income.
b) Find the indirect utility function and verify Roy's
identity
c) Find the expenditure function
d) Find the Hicksian demand function

Suppose x1 and x2 are perfect substitutes
with the utility function U(x1, x2) =
2x1 + 6x2. If p1 = 1,
p2 = 2, and income m = 10, what it the optimal bundle
(x1*, x2*)?

1.) Liz has utility given by u(x2,x1)=x1^7x2^8. If P1=$10,
P2=$20, and I = $150, find Liz’s optimal consumption of good 1.
(Hint: you can use the 5 step method or one of the demand functions
derived in class to find the answer).
2.) Using the information from question 1, find Liz’s optimal
consumption of good 2
3.) Lyndsay has utility given by u(x2,x1)=min{x1/3,x2/7}. If
P1=$1, P2=$1, and I=$10, find
Lyndsay’s optimal consumption of good 1. (Hint: this is Leontief
utility)....

Consider a two good economy. A consumer has a utility function
u(x1, x2) = exp (x1x2). Let p = p1 and x = x1.
(1) Compute the consumer's individual demand function of good 1
d(p).
(2) Compute the price elasticity of d(p).
Compute the income elasticity of d(p).
Is good 1 an inferior good, a normal good or neither?
Explain.
(3) Suppose that we do not know the consumer's utility function
but we know that the income elasticity of his...

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