Question

1.Suppose there are two consumers, A and B.

The utility functions of each consumer are given by:

UA(X,Y) = X^1/2*Y^1/2

UB(X,Y) = 3X + 2Y

The initial endowments are:

A: X = 4; Y = 4

B: X = 4; Y = 12

a) (10 points) Using an Edgeworth Box, graph the initial allocation (label it "W") and draw the

indifference curve for each consumer that runs through the initial allocation. Be sure to label your graph

carefully and accurately.

b) What is the marginal rate of substitution for consumer A at the initial allocation?

c) What is the marginal rate of substitution for consumer B at the initial allocation?

d)is the initial allocation Pareto Efficient?

2. For Each of the following situations,

i) Write the Indirect Utility Function

ii) Write the Expenditure Function

iii) Calculate the Compensating Variation

iv) Calculate the Equivalent Variation

a) U(X,Y) = X^1/2 x Y^1/2. M = $288. Initially, PX= 16 and PY

= 1. Then the Price of X changes to PX= 9.

i) Indirect Utility Function: __________________________

ii) Expenditure Function: ____________________________

iii) CV = ________________

iv) EV = ________________

b) U(X,Y) = MIN (X, 3Y). M = $40. Initially, P

X= 1 and PY= 1. Then the Price of X changes to PX= 3.

i) Indirect Utility Function: __________________________

ii) Expenditure Function: ____________________________

iii) CV = ________________

3. Suppose A consumer's utility function is given by U(X,Y) = 3X + Y. The consumer has

$120 to spend (M = $120). Sketch the graph of the consumer's demand function for Good X. Please put

the Price of X, PX, on the vertical axis, and the quantity of Good X, X, on the horizontal axis. Scale the

Price axis up to $12, and scale the quantity axis up to 120

iv) EV = ________________

Answer #1

2. For Each of the following situations,
i) Write the Indirect Utility Function
ii) Write the Expenditure Function
iii) Calculate the Compensating Variation
iv) Calculate the Equivalent Variation
a) U(X,Y) = X^1/2 x Y^1/2. M = $288. Initially, PX= 16 and
PY
= 1. Then the Price of X changes to PX= 9.
i) Indirect Utility Function: __________________________
ii) Expenditure Function: ____________________________
iii) CV = ________________
iv) EV = ________________
b) U(X,Y) = MIN (X, 3Y). M = $40. Initially,...

Suppose there are two consumers, A and B. The utility functions
of each consumer are given by: UA(X,Y) = X2Y UB(X,Y) = X*Y
Therefore: For consumer A: MUX = 2XY; MUY = X2 For consumer B: MUX
= Y; MUY = X The initial endowments are: A: X = 120; Y = 6 B: X =
30; Y = 14 a) (20 points) Suppose the price of Y, PY = 1. Calculate
the price of X, PX that will lead...

Suppose there are 2 consumers, A and B. The utility functions of
each consumer are given by:UA(X, Y) =X^1/2 Y^1/2 UA(X, Y) = 3X+
2Y
The initial endowments are:W X/A= 10, W Y/A= 10, W X/B= 6, W
Y/B= 6
a) Using graph the initial allocation (label it W) and draw the
indifference curve for each consumer that runs through the initial
allocation. Be sure to label your graph carefully and
accurately.
b) (4 points) What is the marginal rate...

1. Suppose there are two consumers, A and B. The utility
functions of each consumer are given by: UA(X,Y) = X*Y UB(X,Y) =
X*Y3 Therefore: • For consumer A: MUX = Y; MUY = X • For consumer
B: MUX = Y3; MUY = 3XY2 The initial endowments are: A: X = 10; Y =
6 B: X = 14; Y = 19 a) (40 points) Suppose the price of Y, PY = 1.
Calculate the price of X, PX...

8) Suppose a consumer’s utility function is defined by
u(x,y)=3x+y for every x≥0 and y≥0 and
the consumer’s initial endowment of wealth is w=100. Graphically
depict the income and
substitution effects for this consumer if initially Px=1 =Py and
then the price of commodity x
decreases to Px=1/2.

If a consumer's budget constraint has a slope that is less than
-1:
A.
the consumer gets less utility from good X than from good
Y.
B.
the price of good X is less than the price of good
Y.
C.
the consumer gets more utility from good X than from
good Y.
D.
the price of good X is greater than the price of good
Y.
A consumer has U =
X0.5Y0.5 for a utility function,
with MUx =...

Suppose a consumer has the utility function U (x, y) = xy + x +
y. Recall that for this function the marginal utilities are given
by MUx(x,y) = y+1 and MUy(x,y) = x+1.
(a) What is the marginal rate of substitution MRSxy?
(b)If the prices for the goods are px =$2 and py =$4,and if the
income of the consumer is M = $18, then what is the consumer’s
optimal affordable bundle?
(c) What if instead the prices are...

Suppose a consumer’s utility function is given by U(X,Y) = X*Y.
Also, the consumer has $360 to spend, and the price of X, PX = 9,
and the price of Y, PY = 1.
a) (4 points) How much X and Y should the consumer purchase in
order to maximize her utility?
b) (2 points) How much total utility does the consumer
receive?
c) (4 points) Now suppose PX decreases to 4. What is the new
bundle of X and...

Consider a consumer with the utility function U(x, y) = min(3x,
5y). The prices of the two goods are Px = $5 and Py = $10, and the
consumer’s income is $220. Illustrate the indifference curves then
determine and illustrate on the graph the optimum consumption
basket. Comment on the types of goods x and y represent and on the
optimum solution.

Jane’s utility function has the following form: U(x,y)=x^2
+2xy
The prices of x and y are px and py respectively. Jane’s income
is I.
(a) Find the Marshallian demands for x and y and the indirect
utility function.
(b) Without solving the cost minimization problem, recover the
Hicksian demands for x and y and the expenditure function from the
Marshallian demands and the indirect utility function.
(c) Write down the Slutsky equation determining the effect of a
change in px...

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