Question
In: Economics
When maximizing the utility function subject to budget constraint, does the value of the Lagrange multiplier...
When maximizing the utility function subject to budget constraint, does the value of the Lagrange multiplier (λ) equal the marginal utility of income? Justify your answer
Solutions
Expert Solution
A function being maximized with a specific constraint is quite common in economy. Consumer theory of maximization of the function of utility deals with a certain amount of income for spending on the commodities. For maximizing the utility with the wealth constraints three commodities are considered.
Rahul Sunny answered 1 year agoRelated Solutions
Suppose an individual has the following utility function: U(X,Y) = 2XY. Draw the budget constraint when...
Suppose an individual has the following utility function: U(X,Y)
= 2XY. Draw the budget constraint when the price of each unit of X
and Y are 5 and 4, and income is 120. Find the choice that
maximizes utility.
An individual consumer’s utility function and the budget constraint are described below. (ch. 5). U =...
An individual consumer’s utility function and the budget
constraint are described below. (ch. 5). U = x1x2 s.t. m = p1x1 +
p2x2 where, m = $100, p1 = $5, and p2 = $2. (i) Find the marginal
rate of substitution between x1 and x2. [Show your work] (ii) Find
the slope of the budget constraint. [Show your work] (iii) Given
the answers to (i) and (ii), find the optimal amount of each good,
x⇤ 1 and x⇤ 2. [Show...
QUESTION ONE A Consumer seeks to maximize a utility function Ux,y subject to his income constraint...
QUESTION ONE
A Consumer seeks to maximize a utility
function Ux,y
subject to his income constraint given by:
P1x+P2y=M.
What is meant by a duality problem in constrained optimization?
Please provide
examples.
[6 marks]
Set up a Lagrange function for this
optimization.
[3
marks]
State the First order conditions and explain how you would
solve for the critical values.
[6
marks]
Explain the meaning of the Lagrange multiplier as it related to
this optimization problem.
[4
marks]...
Use the Lagrange multiplier method to identify the stationary point(s) of the function ?(?, ?, ?)=10?...
Use the Lagrange multiplier method to identify the stationary
point(s) of the function ?(?, ?, ?)=10? + 5? + ? + 2?^2 + 4?? + ?^2
+ 2?? - ?^2 - ??, subject to the constraint 5? + 3? + ? = 27.
Subsequently determine the nature of the stationary point(s) using
the bordered Hessian matrix.
Given the following utility function U(X,Y)=X0.4 Y0.6 subject to the constraint I=XPx+YPy find: a the marshallian...
Given the following utility function U(X,Y)=X0.4
Y0.6 subject to the constraint
I=XPx+YPy
find:
a the marshallian demand functions for X and Y
b the indirect utility function
c the expenditure function
d the compensated demand functions for X and Y
e from 1 and 2 establish whether x and y are inferior or normal
goods
f discuss the compensating variation, and distinguish it from
equivalent variation, for a normal and inferior good. give real
life examples
For each of the following, draw the indifference curves and budget constraint, and find the utility...
For each of the following, draw the indifference curves and
budget constraint, and find the utility maximizing demands.
Remember, don’t plug in the given prices and income until the
end.
u(x1,x2)=(x1)^2(x2), (p1,p2,m)=(1,2,10)
find the absolute minimum and absolutely maximum value of function f(x,y)= e^xy subject to the constraint...
find the absolute minimum and absolutely maximum value of
function f(x,y)= e^xy subject to the constraint x^2+y^2= 18
The function f(x,y,z)=4x−9y+7z has an absolute maximum value and absolute minimum value subject to the constraint...
The function
f(x,y,z)=4x−9y+7z
has an absolute maximum value and absolute minimum value subject
to the constraint
x^2+y^2+z^2=146.
Use Lagrange multipliers to find these values.
Define the concepts of utility, indifference curve, and budget constraint. Discuss how these concepts relate to...
Define the concepts of utility, indifference curve, and budget
constraint. Discuss how these concepts relate to consumer
choice.
Explain the following concepts: demand schedule, demand curve,
supply schedule, supply curve. Then, list the determinants of
demand and explain how a change in each determinant affects the
demand curve. Do the same for the supply.
Define the concepts of utility, indifference curve, and budget constraint. Discuss how these concepts relate to...
Define the concepts of utility, indifference curve, and budget
constraint. Discuss how these concepts relate to consumer
choice.
Explain the following concepts: demand schedule, demand curve,
supply schedule, supply curve. Then, list the determinants of
demand and explain how a change in each determinant affects the
demand curve. Do the same for the supply.
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