Question

A consumer has an income of $120 to buy two goods (X, Y). the price of X is $2 and the price of Y is $4. The consumer utility function is given by ?(?, ?) = ? 2/3 ∗ ? 1/3 You are also told that his marginal utilities are ??? = 2 3 ( ? ? ) 1/3 ??? = 1 3 ( ? ? ) 2/3

1. Find the slope of the budget constrain. (1 point)

2. Calculate the optimal quantity of good X and Y for this consumer (Point A). (2 points)

Assume that the price of good X increases to ?? ′ = $8, and holding everything else constant:

3. Graph all your findings by showing the change in price if good X along the points A and B. (2 points)

Hint: Do not compute and graph point C. Research studies found the demand for good X as follow: ? = 8 −0.4 ∗ ?? + 0.2 ∗ ?? +0.05 ∗ ? where, ?? is the price of good X, ?? is the price of good Y, and M is consumer’s income.

4. Based on this research finding and holding everything else constant, can the consumer afford to buy 12 units of good X. Explain. (2 points)

Answer #1

A consumer has preferences represented by the utility function
u(x, y) = x^(1/2)*y^(1/2). (This means that
MUx=(1/2)x^(−1/2)*y^(1/2) and MUy =1/2x^(1/2)*y^(−1/2)
a. What is the marginal rate of substitution?
b. Suppose that the price of good x is 2, and the price of good
y is 1. The consumer’s income is 20. What is the optimal quantity
of x and y the consumer will choose?
c. Suppose the price of good x decreases to 1. The price of good
y and...

Suppose there are two goods, X and
Y. The price of good X is $2 per unit and the price of
good Y is $3 per unit. A given consumer with an income
of $300 has the following utility function:
U(X,Y) = X0.8Y0.2
which yields
marginal utilities of:
MUX= 0.8X-0.2Y0.2
MUY= 0.2X0.8Y-0.8
a. What
is the equation for this consumer’s budget constraint in terms of X
and Y?
b. What
is the equation for this consumer’s marginal rate of substitution
(MRSXY)? Simplifyso you only have...

Consider a consumer with Cobb-Douglas preferences over two
goods, x and y described by the utility function u(x, y) = 1/3ln(x)
+ 2/3n(y) 1. Assume the prices of the two goods are initially both
$10, and her income is $1000. Obtain the consumer’s demands for x
and y.
2. If the price of good x increases to $20, what is the impact
on her demand for good x?
3. Decompose this change into the substitution effect, and the
income effect....

A basket of goods for a given consumer includes two goods, X
and Z. Consumer income is equal to $1,500 and the prices of these
two goods are as follows: Px = $25 Pz = $50 This consumer is
consuming 10 units of good X. Suppose that over the course of a
year, the price of good X changes by −10% and the price of good Z
changes by 10%. How much income would be required for the consumer
to...

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...

1. A consumer has the utility function U = min(2X, 5Y ). The
budget constraint isPXX+PYY =I.
(a) Given the consumer’s utility function, how does the consumer
view these two goods? In other words, are they perfect substitutes,
perfect complements, or are somewhat substitutable? (2 points)
(b) Solve for the consumer’s demand functions, X∗ and Y ∗. (5
points)
(c) Assume PX = 3, PY = 2, and I = 200. What is the consumer’s
optimal bundle?
(2 points)
2....

Consider the budget set for a consumer with income of 100 facing
the following prices. The price for the first five units of good 1
is $10 (per unit) If the consumer buys more than five units, the
price is $5 for any subsequent unit purchased. If the consumer
spends all of her money on good 1, how many units of good 1 can she
buy?
10
12
15
20
25
Well-behaved preferences are
convex
monotonic
reach the consumer’s bliss...

Suppose a consumer’s utility function is given byU(X, Y) =X^1/2
Y^1/2. Also, the consumer has $30 to spend. The price of X,PX= $3,
and the price of Y,PY= $5.
a) (4 points) How much X and Y should the consumer purchase in
order to maximize their utility?
b) (4 points) How much utility does the consumer receive?
c) (4 points) Now suppose PX increases to$6. What is the new
bundle of X and Y that the consumer will demand?
How...

Consider a consumer whose utility function is
u(x, y) = x + y (perfect substitutes)
a. Assume the consumer has income $120 and initially faces the
prices px = $1 and py = $2. How much x and y would they buy?
b. Next, suppose the price of x were to increase to $4. How
much would they buy now?
c. Decompose the total effect of the price change on demand
for x into the substitution effect and the...

Suppose that a consumer has a 10$ budget. The price of Good X is
$2 and the price of Good Y is $1. Which of the following bundles
would the consumer be able to purchase with a voucher for Good X of
$8 (The consumer may still have some of the cash or voucher left
unused)
a. X = 3. Y= 10
b. X = 5. Y= 10
c. X = 1. Y= 14
d. X = 6. Y= 6...

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