a consumer has a utility function u = x^1/2y^1/2. prices are px
= 2 and py...
a consumer has a utility function u = x^1/2y^1/2. prices are px
= 2 and py = 3. she maximizes utility purchasing 6 units of good x.
her income is equal to m = ________
Solutions
Expert Solution
Given the utility function and the price of the respective
commodity x and y. Equilibrium quantity of commodity x is also
given. Here, income, m has been calculated with the help of utility
function, the price of the commodities x and y and the budget
constraint.
Suppose a consumer has preferences represented by the utility
function U(X,Y) = MIN[X,2Y]. Suppose PX = 1 and PY = 2. Draw the
Income Consumption Curve for this consumer for income values M =
100, M = 200, and M = 300. Your graph should accurately draw the
budget constraints for each income level and specifically label the
bundles that the consumer chooses for each income level. Also, for
each bundle that the consumer chooses, draw the indifference curve
that...
Consider the following utility function: U(x, y) = 10x + 2y. A consumer faces prices of px = 1 and py = 2. Assuming that graphically good x is on the horizontal axis and good y is on the vertical axis, suppose the consumer chooses to consume 5 units of good x and 13 units of good y. What is the marginal rate of substitution (MRS) equal to?
Let assume that a consumer has a
utility function u(x, y) = xy, and px = 1 dollar, py = 2 dollars
and budget=50. Derive the followings. (3 points each)
1) Marshallian demands of x and y
2) Hicksian demands of x and y
3) Indirect utility function
4) Expenditure function
5) Engel curve
Consider a quasi-linear utility function, U(X, Y) = X1/2 + Y,
with some Px and Py
a. For an interior solution, solve step-by-step for the demand
functions of X* and Y*.
b. Under what circumstance would the optimal consumption involve
a corner solution for the utility maximization problem?
c. (Now, let Py = $1, I = 24, and suppose that Px increases from
$0.5 to $2. Find the Compensating Variation (CV) and the
Equivalence Variation (EV). In this example, how...
"Suppose a consumer has preferences represented by the utility
function U(X,Y) = X(^2)Y Suppose Py = 1, and the consumer has $360
to spend. Draw the Price-Consumption Curve for this consumer for
income values Px =1, Px = 2, and Px = 5. Your graph should
accurately draw the budget constraints for each income level and
specifically label the bundles that the consumer chooses for each
income level. Also for each bundle that the consumer chooses, draw
the indifference curve...
Suppose that a consumer has the following demand function: x ∗
(px, py, m) = 3mpy/px . What type of good is good x? (Remember, m
> 0, px > 0, py > 0)
(a) ordinary, complement, normal
(b) ordinary, complement, inferior
(c) inelastic, substitute, inferior
(d) ordinary, substitute, normal
Consider the following utility function U(X,Y) = X^1/4Y^3/4
Initially
PX = 2
PY = 4
I = 120
Suppose the price of X changes to PX = 3. Perform a decomposition
and fill in the table
X
Y
Substitution Effect
Income Effect
Total Effect
For one purpose, the utility function of the consumer is
u(x,y)=4?x+2y for maximum utility.
1. For one purpose, the customer's income is I, and the price of
X is Px and the price of Y is Py. Obtain the demand function of
this person's Y ash through Px, Py, I.
2. For one purpose, the consumer has an income I = 40, and
initially the price of Px=1, and the price is Py=1.
(1) What is the difference between the...
Consider the following utility function:
U = 100X0.10 Y 0.75.
A consumer faces prices of Px = $5 and Py =$5.
Assuming that graphically good X is on the horizontal axis and good
Y is on the vertical axis, suppose the consumer
chooses to consume 7 units of good X and 15 units of good Y.
Then the marginal rate of substitution6 is equal to:
MRS = . (Enter your response rounded to two decimal places. Do
not forget to...
Suppose a consumer has preferences represented by the utility
function U(X,Y) = X2Y Suppose PY = 1, and the consumer has $300 to
spend. Draw the Price-Consumption Curve for this consumer for
income values PX = 1, PX = 2, and PX = 5. Your graph should
accurately draw the budget constraints for each income level and
specifically label the bundles that the consumer chooses for each
income level. Also, for each bundle that the consumer chooses, draw
the indifference...