Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Question

Answered step-by-step

Homework Assignment 7 Suppose that the output q of a firm depends on the quantities of z1 and z2 that it employs as inputs. Its output level is determined by the production function 1. q = 26z1 + 24z2 − 7z2 1 − 12z1z2 − 6z2 2 2. Write down the firm's profit function when the price of q is $1 and the factor prices are w1 and w2(per unit) respectively. 3. Find the levels of z∗ 1 and z∗ 2 which maximize the firm's profits. Note that these are the firm's demand curves for the two inputs. 4. Verify that your solution to [2] satisfies the second order conditions for a maximum. 5. What will be the effect of an increase in w1 on the firm's use of each input and on its output q? [hint: You do not have to explicitly determine the firm's supply curve of output to determine ∂q/∂w1. Instead write out the total derivative of q and make use of the very simple expressions for ∂q/∂z1 and ∂q/∂z2 at the optimum that can be obtained from the first order conditions.] 6. Is the firm's production function strictly concave? Explain

AI Recommended Answer:
1. Write down the firm's profit function when the price of q is $1 and the factor prices are w1 and w2(per unit). P = W1 + W2 ? q 2. Find the levels of z? 1 and z? 2 which maximize the firm's profits. Note that these are the firm's demand curves for the two inputs. z? 1 = 26 ? 1w1 z? 2 = 24 + 1w2 3. Verify that your solution to [2] satisfies the second order conditions for a maximum. Yes, the solution does satisfy the second order conditions for a maximum.


Best Match Video Recommendation:

Solved by verified expert

preview
Numerade Logo

Get the answer to your homework problem.

Try Numerade free for 7 days

QM
Qbs Main
We don’t have your requested question, but here is a suggested video that might help.

Best Match Question:

7 . Consider a perfectly competitive firm that produces output from capital and labor, according to the production function: q f(K,L): The production function has continuous first and second partial derivatives with the following properties: f > 0,fk > 0,fu < 0,fkk <0, fuk = fkl >0. The firm can purchase as much capital (K) and labor (L) as it wants to at their market prices: > 0 (the unit price of capital) and w > 0 (the unit price of labor), which the firm takes as given. It can sell as much output as it likes at the market price for its product: p > 0, which the firm takes as given. Find both first-order partial derivatives of the firm'$ profit function: T(K,L) = p f(K,L) (rK + wL): What two equations describe the first order, necessary conditions for a local max of the profit function? Find the total differentials of the two equations that describe the first order, necessary conditions for a local max of the profit function_ [dK Letting the vector of unknowns, X, be defined as x = write the system of two dL equations from part € as a matrix equation, Ax = b_ Use Cramer's rule to find the partial derivatives dK* /dr and dK* /dw of the capital demand function, K* g (r ,W,p), implicitly defined by the first order, necessary conditions for a local max of the profit function. What are the signs of dK* /dr and dK* /dw?

Discussion

You must be signed in to discuss.

Video Transcript

Comma l, minus n k, plus w l, find first order derivativeso to solve this question, because we have been given production function sown by pi, equal to p, cube minus w, l plus r, and I equal to p f of k. The parts are divided by de k, small p del f, divided by de k, minus del k, r, and a plus w n. The tail pi, divided by l, is equal to p tal. minus tail f, divided by tall arch, a plus w l equal to p d f, divided by tail n plus w tall divided by tail n part b. We need to find condition for local maximum 4 local and maximum d f equal to 0, so tal f, divide by tall multiply, b, l plus aLF, divided by a multiply dek equal to 0, which means tail f. Since t's equal to p f of k, l minus w l plus r o d pi equal to tail pi divided. If you divide deca by del pi, you get deca plus del pi. Minus r t k plus p de divided by tail l, minus wt, l, p y equal to p al f idyl k, t k, plus delta f, divided. W l plus arca is equal to 0 del f, divided by a l and tall. It is equal to 0 in part b. From the past questions, let x equal to t k, t n p so that the solution is equation number 1 and equation number 2. It is possible to write kisinumer, 1 and 2 in matrix form capital a equal to tal, f, divided by 10 k. The answer is equal to a x and a v.

Did you know?

Numerade has step-by-step video solutions, matched directly to more than +2,000 textbooks.



Find Your Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Try Now
Top Calculus 1 / AB Educators
Grace He

Numerade Educator

Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

Heather Zimmers

Oregon State University

Kayleah Tsai

Harvey Mudd College

Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

Joseph Lentino

Boston College

Calculus 1 / AB Courses

Lectures

Video Thumbnail

03:09

Precalculus Review - Intro

In mathematics, precalculus is the study of functions (as opposed to calculus, which is the study of change, and algebra, which is the study of operations and their application to solving equations). It is generally considered to be a part of mathematics that prepares students for calculus.

Video Thumbnail

31:55

Functions on the Real Line - Overview

In mathematics, a function (or map) f from a set X to a set Y is a rule which assigns to each element x of X a unique element y of Y, the value of f at x, such that the following conditions are met: 1) For every x in X there is exactly one y in Y, the value of f at x; 2) If x and y are in X, then f(x) = y; 3) If x and y are in X, then f(x) = f(y) implies x = y; 4) For every x in X, there exists a y in Y such that f(x) = y.

Join Course
Recommended Videos

01:31

A firm uses a single input, labor, to produce output $q$ according to the production function $q=8 \sqrt{L}$. The commodity sells for $\$ 150$ per…

Additional Mathematics questions

00:12

An open top box is to be constructed from a 7 inch by 15 inch piece of cardb…

Want better grades, but can’t afford to pay for Numerade?

Ask your parent or guardian for help.


Enter your parent or guardian’s email address:

Already have an account? Log in

Share Question

Copy Link

OR

Enter Friends' Emails

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

97% of Numerade students report better grades

Create an account to get free access

Join Numerade as a

By clicking Sign up you accept Numerade's Terms of Service and Privacy Policy

or sign up with

Already have an account? Log in

Log in to watch this video
...and 3,000,000 more!


OR

EMAIL

PASSWORD

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started