Question

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 x2 should he consume? When his utility is 48, draw an indifference curve for Alex (with x1 on the horizontal axis). Label two points on this indifference curve.

c) Suppose Alex’s income is m. If price of x1 is $8 (p1 = 8) and price of x2 is $3 (p2 = 3), using the utility function that you chose in a), draw Alex’s Engel curve for x1 (Hint: the Engel curve should have x1 on the horizontal axis and income m on the vertical axis). Make sure to label the axes and indicate the slope of the line

d) Now, suppose Alex’s income is $320. If price of x1 is $16 (p1 = 16) and price of x2 is $6 (p2 = 6), what is

Alex’s optimal consumption bundle? What is Alex’s utility at this bundle?

Answer #1

A) as fixed ratio between x1 & x2

X1/x2 = 3/8

8x1 = 3x2

**so, U(x1, x2) = Min(8x1, 3x2)**

**Utility function is perfectly Complements
type**

**B) U =
48,**

*48= 8x1=
3x2*

*x1*= 48/8 =
6*

*x2*= 48/3=
16*

*c) from BC , P1X1 + P2X2 =
m*

**8X1 + 3X2=
m**

**at eqm, from utility
function**

**8x1 =
3x2**

**so, 8x1 + 8x1=
m**

**m = 16x1
:** **Engel
curve**

**d) m = 320, p1= 16 ,
p2= 6**

**Optimal
bundle**

**BC: 16x1 + 6x2=
320**

**put, 8x1=
3x2**

**16x1 =
6x2**

**32x1=
320**

**x1"= 10, x2"=
80/3**

**U= Min(80,
3*80/3)**

**=
80**

Graphs

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...

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?

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 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*)?

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.

Imran consumes two goods, X1 and X2. his
utility function takes the form: u(X1, X2)=
4(X1)^3+3(X2)^5. The price of X1
is Rs. 2 and the price of X2 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 X1? On
X2?...

Consider the utility function U(x1,x2) = ln(x1) +x2. Demand for
good 1 is: •x∗1=p2p1 if m≥p2 •x∗1=mp1 if m < p2 Demand for good
2 is: •x∗2=mp2−1 if m≥p2 •x∗2= 0 if m < p2 (a) Is good 1
Ordinary or Giffen? Draw the demand curve and solve for the inverse
demand curve. (b) Is good 2 Ordinary or Giffen? Draw the demand
curve and solve for the inverse demand curve. (c) Is good 1 Normal
or Inferior? Derive and...

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...

4. Suppose a consumer has perfect substitutes preference such
that good x1 is twice as valuable as to the consumer as good
x2.
(a) Find a utility function that represents this consumer’s
preference.
(b) Does this consumer’s preference satisfy the convexity and
the strong convex- ity?
(c) The initial prices of x1 and x2 are given as (p1, p2) = (1,
1), and the consumer’s income is m > 0. The prices are changed,
and the new prices are (p1,p2)...

Let Antonio and Kate’s preferences be represented by the utility
functions, uAntonio(x1, x2) = 9((x1)^2)(x2) and uKate(x1, x2) =
17(x1)((x2)^2), where good 1 is Starbursts and good 2 is M&M’s.
Antonio’s endowment is eA = (24, 0) and Kate’s endowment is eK =
(0, 200). Antonio and Kate will exchange candy with each other
using prices p1 and p2, where p1 is the price of one starburst and
p2 is the price of one M&M.
a) Determine Antonio’s and Kate’s...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 33 minutes ago

asked 38 minutes ago

asked 39 minutes ago

asked 46 minutes ago

asked 46 minutes ago

asked 50 minutes ago

asked 57 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago