Question

Imran consumes two goods, X_{1} and X_{2}. his
utility function takes the form: u(X_{1}, X_{2})=
4(X_{1})^3+3(X_{2})^5. The price of X_{1}
is Rs. 2 and the price of X_{2} is Rs. 4. Imran has
allocated Rs. 1000 for the consumption of these two goods.

(a) Fine the optimal bundle of these two goods that Imran would consume if he wants to maximize his utility. Note: write bundles in integers instead of decimals.

(b) What is Imran's expenditure on X_{1}? On
X_{2}?

(c) Do you find more than one bundle satisfying the first order conditions? Why?

Answer #1

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 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?

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

7.
Suppose you have the following utility function for two
goods:
u(x1, x2) = x
1/3
1 x
2/3
2
. Suppose your initial income is I, and prices are p1 and
p2.
(a) Suppose I = 400, p1 = 2.5, and p2 = 5. Solve for the
optimal bundle. Graph the budget
constraint with x1 on the horizontal axis, and the
indifference curve for that bundle.
Label all relevant points
(b) Suppose I = 600, p1 = 2.5, and...

Change the Humphrey and Lauren example such that Lauren’s
utility function is uL(x1,x2) = min{x1, x2} and Humphrey’s utility
function is uH (x1, x2) = 2√x1 + √x2. Their endowments are eL =
(4,16) and eH = (2,24).
1)Suppose Humphrey and Lauren are to simply just consume their
given endowments. State the definition of Pareto efficiency. Is
this a Pareto efficient allocation? As part of answering this
question, can you find an alternative allocation of the goods that
Pareto dominates...

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?)

Suppose Alex only consumes 3 units of x1 with 8 units of x2.
That is, if he is consuming more x1 or x2 in a different ratio, it
does not increase his utility
a) Write down Alex’s utility function. What kind of utility
function does he have?
b) Suppose Alex wants to have a utility 48. If he desires to
make the best use of his money, based on your utility function in
a) how many units of x1 and...

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*)?

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?

Suppose the utility function is given by U(x1,
x2) = 14 min{2x, 3y}. Calculate the optimal consumption
bundle if income is m, and prices are p1, and
p2.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 10 minutes ago

asked 24 minutes ago

asked 27 minutes ago

asked 29 minutes ago

asked 30 minutes ago

asked 36 minutes ago

asked 41 minutes ago

asked 44 minutes ago

asked 55 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago