Find the partial derivatives of the demand functions

Assignment Help Mathematics
Reference no: EM131139129

Consider the utility maximization problem

max  xa + y          subject to px + y = m

for x, y ≥ 0 and where all constants are positive and a ∈ (0, 1).

The optimal choices of x and y are denoted x and y and can be expressed as demand functions of the variables p and m; that is, x = x (p, m) and y = y (p, m). Similarly, the maximal utility function (often called the value function or indirect utility function) is given by

U (p, m):= U(x(p, m), y(p, m))

(a) Verify that any stationary point of the Lagrangian L will yield a global maximum of the optimization problem (Hint: Use the convexity/concavity of the Lagrangian).

(b) Find the demand functions x(p, m) and y(p, m).

(c) Find the partial derivatives of the demand functions with respect to p and m, and check their signs.

(d) How does the optimal expenditure on the good x vary with p? (That is, compute the elasticity of px (p, m) with respect to p).

(e) Interpret your work above when a = 1/2. What are the demand functions in this case? Verify that, in this case,

∂U/∂p = -x(p, m).

Reference no: EM131139129

Questions Cloud

Find the area between the curves : Find the area between the curves
What are some physiological aspects of cognitive processes : What role do the principles of cognitive neuropsychology play in developing coping mechanisms and prevention strategies for children and/or adolescents who are at risk or are experiencing these cognitive issues?
Explain how might company build more of an online presence : How might the company build more of an online presence". Analysis of their website. What was favorable about their website? What are some of their website attributes that customers may find unappealing?
Explain why the results differ between the two cases : Show that licensing can be beneficial for firm 1 in this case and therefore increase innovation incentives. Explain why the results differ between the two cases.
Find the partial derivatives of the demand functions : Find the demand functions x∗(p, m) and y∗(p, m). Find the partial derivatives of the demand functions with respect to p and m, and check their signs. How does the optimal expenditure on the good x vary with p? (That is, compute the elasticity of px∗ ..
Share our insights about ethical principles in psychology : Read one of the Ethics Case Studies by Specialization applicable to your future career vision in the field.- What do you see as the ethical issue or issues involved in the case study you reviewed?
What key points would you address concerning issue and why : Some in your department at work are arguing that accounting changes are the same thing as accounting errors. Based on your study of accounting changes, what key points would you address concerning this issue and why?
Write the assignment on given topic : Explain whether you think an autobiographical or fictional account by a slave is more persuasive than a biographical or fictional account by a white author.
How can you as a therapist avoid becoming stuck : How can you, as a therapist, avoid becoming "stuck" in a particular theoretical framework? Identify specific ways that you can ensure you continue to grow.

Reviews

Write a Review

 

Mathematics Questions & Answers

  Ace novelty manufactures giant pandas and saint bernards

ace novelty manufactures giant pandas and saint bernards. each giant panda requires 1.5 yd2 of plush 30 ft3 of stuffing

  Find the x-coordinate of the absolute maximum for function

Find the x-coordinate of the absolute maximum for the function f(x)=(3+9ln(x))/x x>0

  Closed-loop system is under-damped

Consider the unity feedback of P(s) where k is a scalar gain. (please check the attached file) Determine k such that the closed-loop system is under-damped with a damping factor of 0.5.

  Binary operations-monoids

Let S be a set with an associative binary operation but with no identity. Choose an element 1 not belonging to S, write M = {1} or S, and define an operation on M by using the operation of S and 1s=s=s1 for all s belonging to S.

  Write down the corresponding differential equation

Use the method of separation of variables, with Θ(x,t) = X(x)T(t), to show that the function X(x) satisfies the differential equation X′′ - μX = 0 for some constant μ. Write down the corresponding differential equation that T (t) must satisfy

  What interest rate would the investment have to yield

Patrick Seeley has $2,400 that he is looking to invest. His brother approached him with an investment opportunity that could double his money in four years. What interest rate would the investment have to yield in order for Patrick's brother to de..

  Find the rate of increase in revenue

Find the rate of increase in revenue when production is 1000 switches per day. Find the rate of increase in profit when production is 1000 switches per day. dollars/day.

  Decision regarding the null hypothesis and interpret

At the 0.05 significance level, can a claim be made that it takes longeron average than 20 hours to side a house?

  Find the points on the given graph

Find the points on the graph of y = x3/2 -x1/2 at which the tangent line is parallel to y -x = 3. Use the general power rule to find f'(x) if f(x) = (4x2 + 6x+ 8)-3 and f(x)=3√(x+1)/(x+2).

  What are the dimensions of the door

The height of a door is 15 inches more than three times its width. What are the dimensions of the door if the perimeter is 246 inches?

  What is the constant of variation?

What is the constant of variation?

  Explain information about poisson distribution

Information about "Poisson Distribution". During cross country pipeline construction, day production rates of more than 120 girth welds are not unusual. On pipe laying barges operating around the clock,

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd