11479

Deriving the Labor Demand Curve

This Demonstration illustrates the origin of the labor demand curve. A firm facing a fixed amount of capital has a logarithmic production function in which output is a function of the number of workers . The marginal product of labor (MPN) is the amount of additional output generated by each additional worker. In other words, MPN is the derivative of the production function with respect to number of workers, .
The tangent lines at certain points of the production function show that the MPN for any value of is simply the slope of a line tangent to the production function for that value of . The firm's profit-maximizing condition is when wage equals MPN (explained below), such that for any number of workers, the wage the firm is willing to pay is equal to the MPN associated with that value of . For this reason, the labor demand curve is simply the MPN. As productivity increases or decreases, MPN and therefore the labor demand curve respond by shifting to the right for a productivity increase and the left for a productivity decrease.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

If the firm has a fixed amount of capital, its only variable input is labor. The marginal cost (MC) of labor is the wage and the marginal revenue (MR) for labor is the MPN, because that is the amount the firm receives per unit of labor. We know that all firms maximize profit when MC = MR, or in this case when the wage = MPN. Given these conditions, the labor demand curve is simply all of these points of MPN such that for any , the firm is willing to pay the corresponding MPN as a wage because that is how the firm maximizes profit at that value. As productivity increases, MPN increases, thereby shifting the labor demand curve out, which leads to higher wages.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+