Question

A consumer has a utility function of the type U(x1, x2) = max (x1, x2). What is the consumer’s

demand function for good 1?

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...

Consider a consumer who consumes two goods and has utility
function
u(x1,x2)=x2 +√x1.
The price of good 2 is 1, the price of good 1 is p, and income is
m.
(1) Show that a) both goods are normal, b) good 1 is an ordinary
good, c) good 2 is a gross substitute for good 1.

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...

1. A consumer has an utility function given by U(x1, x2) = ?
log(x1) + (1 ? ?) log(x2), with0<?<1.
HerincomeisgivenbyM,andthepricesshefacesarep1 andp2, respectively.
What is the optimal choice of x1 and x2? Follow the steps outlined
in the math refresher notes. How does this result compare to the
one in the notes? Explain.

3. Suppose that a consumer has a utility function
u(x1, x2) =
x1 + x2. Initially the
consumer faces prices (1, 2) and has income 10. If the prices
change to (4, 2), calculate the compensating and equivalent
variations. [Hint: find their initial optimal consumption
of the two goods, and then after the price increase. Then show this
graphically.]
please do step by step and show the graph

Suppose a consumer has quasi-linear utility: u(x1,x2 ) = 3x1^2/3
+ x2 . The marginal utilities
are MU1(x) = 2x1^−1/3 and MU2 (x) = 1. Throughout this problem,
assume p2 = 1
1.(a) Sketch an indifference curve for these preferences (label
axes and intercepts).
(b) Compute the marginal rate of substitution.
(c) Assume w ≥ 8/p1^2 . Find the optimal bundle (this will be a
function of p1 and w). Why do
we need the assumption w ≥ 8/p1^2 ?...

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...

Consider the following utility function: U(x1,x2)
X11/3 X2
Suppose a consumer with the above utility function faces prices
p1 = 2 and
p2 = 3 and he has an income m = 12. What’s his optimal
bundle to consume?

A consumer has the Cobb-Douglas utility function
u(x1,x2)=x3.51x42u(x_1, x_2) = x_1^{3.5}x_2^{4}
The price of good 1 is 1.5 and the price of good 2 is 3. The
consumer has an income of 11.
What amount of good 2 will the consumer choose
to consume?

Consider a utility function u(x1,x2)u(x_1, x_2) where:
MU1=2x11x42MU_1 = 2x_1^{1} x_2^{4}
MU2=4x21x32MU_2 = 4x_1^{2} x_2^{3}
The consumer with this utility function is consuming an optimal
bundle (x∗1,x∗2)=(4,6)(x_1^*, x_2^*) = (4, 6) when the price of
good 1 is p1=2p_1 = 2. What is the consumer’s income?

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