9458

Cobb-Douglas Utility Function

This Demonstration examines the Cobb–Douglas utility function. Figure 1 shows the consumer's optimal choice and wealth expansion paths. Figures 2 and 3 show demand curves. By modifying prices and wealth levels you can see how the consumer reacts to these changes. By modifying the parameter (and holding prices and wealth fixed) you can compare the choices of two different consumers and the resulting demands.

THINGS TO TRY

SNAPSHOTS

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

DETAILS

Figure 1 depicts the optimal choice of a consumer whose preferences are represented by a Cobb–Douglas utility function. The purple indifference curve and the red budget line represent the initial situation ( and ). By changing prices and wealth you can see how the consumer adjusts her decisions to the new environment. By leaving initial prices and wealth unchanged and modifying the parameter , you can see how two consumers with different preferences change from their optimal choices. In Figures 2 and 3, these changes in translate into changes in the consumer's willingness to pay for goods 1 and 2. (The effects always move in opposite direction: when willingness to pay for good 1 increases (falls), it falls (increases) for good 2.) From these figures you can also see that: (1) demands derived from a Cobb–Douglas utility function have no cross-price effects and (2) good 1 and good 2 are both normal goods for the consumer (and, because of this, both are also ordinary goods). Finally, you can notice that as long as the wealth level changes, optimal bundles are related by proportional expansion along rays from the origin.
Additional references:
    • 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.
Powered by Wolfram Mathematica © 2014 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+