Suppose the following equations represent an individual’s utility maximization problem: U(X,Y) = X0.5 + Y0.5 And the bu...
Suppose the following equations represent an individual’s utility maximization problem: U(X,Y) = X0.5 + Y0.5 And the budget constraint is: I = PxX + PyY (a) Set up the individual’s maximization problem using the Lagrange technique. (b) Find the individual’s demand function for X and Y (Derive from first order condition). (c) Find the indirect utility function. (d) Find the expenditure function. (e) Find the share of X and Y on expenditure. (f) Find the marginal utility of income.
Homework Answers
![] - I = x P + P * 2. * (PxPy tra Yo Te pyta ta?) a taifa y](http://img.homeworklib.com/questions/f562ae60-f949-11e9-a40e-e5f6de610fdc.png?x-oss-process=image/resize,w_560)
Add Answer to:
Suppose the following equations represent an individual’s utility maximization problem: U(X,Y) = X0.5 + Y0.5 And the bu...
Solve the following Utility Maximization Problem for x* and y* that Max U(x,y)= ln(x) subject to...
Solve the following Utility Maximization Problem for x* and y* that Max U(x,y)= ln(x) subject to Pxx + pyy = I ----.-.(2) where In denotes the natural logarithm (base e) and x and y>0. a) (25 points) by Substitution and show that your values of x* and y* max U (x*,y*). Problem 1. b) (20 points) by the Lagrange Multiplier Method
M 4. Consider the utility maximization problem max U(x,y) = x +y s.t. x + 4y...
M 4. Consider the utility maximization problem max U(x,y) = x +y s.t. x + 4y = 100. (a) Using the Lagrange method, find the quantities demanded of the two goods. (b) Suppose income increases from 100 to 101. What is the exact increase in the optimal value of U(x, y)? Compare with the value found in (a) for the Lagrange multiplier. (C) Suppose we change the budget constraint to px + y = m, but keep the same utility...
1. A consumer is faced with the Utility function U = InX + InY. The budget...
1. A consumer is faced with the Utility function U = InX + InY. The budget I constraint is given as: I = PxX + PyY. Derive the various individual demand functions if: a) The consumer maximizes his utility subjected to the budget constraint b) The consumer minimizes his expenditure subjected to his utility function
L I L I JUNULUI! SM 4. Consider the utility maximization problem max U(x,y) = (x...
L I L I JUNULUI! SM 4. Consider the utility maximization problem max U(x,y) = (x + y s.t. x+4y= 100. (a) Using the Lagrange method, find the quantities demanded of the two goods. (1) Suppose income increases from 100 to 101. What is the exact increase in the optimal value of U(x,y)? Compare with the value found in (a) for the Lagrange multiplier (c) Suppose we change the budget constraint to px + 4y=m, but keep the same utility...
An individual’s utility is expressed by the function u(x,y) = xy The person’s income is ten...
An individual’s utility is expressed by the function u(x,y) = xy The person’s income is ten dollars (I = $10) The price of item x is $1. The price of item y is $1. Maximize this consumer’s utility subject to a budget constraint using the Lagrange Multiplier method. At what point does the marginal rate of substitution equal the price ratio?
Derive the demand for x for a person with income (I) and Utility=min(x,y) with budget constraint I= pxX+pyY. Find the...
Derive the demand for x for a person with income (I) and Utility=min(x,y) with budget constraint I= pxX+pyY. Find the own price elasticity of demand for x and the income elasticity of demand for x.
1. Suppose a consumer has the utility function over goods x and y u(x, y) =...
1. Suppose a consumer has the utility function over goods x and y u(x, y) = 3x}}} (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x (Px, py,m) and y* (Px, Py,m). Show all of your work and circle your final...
Suppose an individual’s utility function for two goods X and Y is givenby U(X,Y) = X^(3/4)Y^(1/4)...
Suppose an individual’s utility function for two goods X and Y is givenby U(X,Y) = X^(3/4)Y^(1/4) Denote the price of good X by Px, price of good Y by Py and the income of the consumer by I. a) (2 points) Write down the budget constraint for the individual. b) (4 points) Derive the marginal utilities of X and Y. c) (3 points) Derive the expression for the marginal rate of substitution of X for Y. Write down the tangency...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x3...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x3 yž (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x* (Px, Py,m) and y* (Px, Py,m). Show all of your work and circle your final...
Consider the utility function u(x) = √x1 + √x2 ; and a standard budget constraint: p1x1+p2x2=I
1. (Consumer theory) Consider the utility function u(x) = √x1 + √x2 ; and a standard budget constraint: p1x1+p2x2=I. a. Are the preferences convex? (1 pt) b. Are the preferences represented by this function homothetic? (1 pt) c. Formally write the utility maximization problem, derive the first order conditions and find the Marshallian demand function. (2 pt) d. Verify that the demand function is homogeneous of degree 0 in prices and income. (1 pt) e. Find the indirect utility function. (1 pt) f. Find the expenditure function by...
Solve the following Utility Maximization Problem for x* and y* that Max U(x,y)= ln(x) subject to Pxx + pyy = I ----.-.(2) where In denotes the natural logarithm (base e) and x and y>0. a) (25 points) by Substitution and show that your values of x* and y* max U (x*,y*). Problem 1. b) (20 points) by the Lagrange Multiplier Method
M 4. Consider the utility maximization problem max U(x,y) = x +y s.t. x + 4y = 100. (a) Using the Lagrange method, find the quantities demanded of the two goods. (b) Suppose income increases from 100 to 101. What is the exact increase in the optimal value of U(x, y)? Compare with the value found in (a) for the Lagrange multiplier. (C) Suppose we change the budget constraint to px + y = m, but keep the same utility...
1. A consumer is faced with the Utility function U = InX + InY. The budget I constraint is given as: I = PxX + PyY. Derive the various individual demand functions if: a) The consumer maximizes his utility subjected to the budget constraint b) The consumer minimizes his expenditure subjected to his utility function
L I L I JUNULUI! SM 4. Consider the utility maximization problem max U(x,y) = (x + y s.t. x+4y= 100. (a) Using the Lagrange method, find the quantities demanded of the two goods. (1) Suppose income increases from 100 to 101. What is the exact increase in the optimal value of U(x,y)? Compare with the value found in (a) for the Lagrange multiplier (c) Suppose we change the budget constraint to px + 4y=m, but keep the same utility...
1. Suppose a consumer has the utility function over goods x and y u(x, y) = 3x}}} (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x (Px, py,m) and y* (Px, Py,m). Show all of your work and circle your final...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x3 yž (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x* (Px, Py,m) and y* (Px, Py,m). Show all of your work and circle your final...
Most questions answered within 3 hours.
-
Using MARS simulator, write MIPS programs according to
the following scenarios: Receive a positive integer number...
asked 1 hour ago -
An object in front of a concave mirror has a real image that is
11.5 cm...
asked 1 hour ago -
Consider the reaction, C3 H8 + O2 --> CO2 + H2O. How many
moles of O2...
asked 3 hours ago -
You and your opponent both roll a fair die. If you both roll the
same number,...
asked 3 hours ago -
In a study of the accuracy of fast food drive-through orders,
Restaurant A had 257 accurate...
asked 3 hours ago -
Identify and describe in detail the four categories of
institutions that could be included in a...
asked 3 hours ago -
In python
class Customer:
def __init__(self, customer_id, last_name, first_name, phone_number, address):
self._customer_id = int(customer_id)
self._last_name =...
asked 4 hours ago -
What is an example of a limitation in implementing a new
ERP system and how it...
asked 4 hours ago -
In a section of 9.7cm of an artery with a radius of 2.6mm there
is a...
asked 4 hours ago -
the two carboxylic acid groups of aspartic acid have different
acidities with pKa values of 2.1...
asked 4 hours ago -
Would CuCO3 aqueous salt combined with calcium chloride
form a solid precipitate? If so, what would...
asked 4 hours ago -
How do ECM Solutions assist in embedding a culture of continuous
improvement in an organization? (Project...
asked 4 hours ago