10170

# Two-Period Consumer Model with Different Interest Rates

This Demonstration shows how the variation of different parameters of the two-period model changes the utility maximizing solution for a consumer deciding what to consume in the first period ( axis) and in the second period ( axis), constrained to a piecewise, two-period budget. The maximizing process is performed with a standard Cobb–Douglas utility function and decides whether the consumer is a saver or a borrower (given by the distance between the blue dashed line and the green dotted line).
You can vary these parameters: the consumer's first and second period income, the savings interest rate, a parameter to represent the additional interest rate charged for needing money rather than saving it, the price level in the first period, the inflation rate the consumer sees or expect in the second period, and the utility parameter that represents the importance the consumer gives to consuming in the present rather than in the future.

### DETAILS

Snapshot 1: net borrower
Snapshot 2: net saver
Snapshot 3: neither saver or borrower
The utility function used in this model is Cobb–Douglas: .
The budget constraint is: , with if the consumer is a saver rather than a borrower.
If the green dotted line is located on a value of greater than the blue dashed line, the consumer saves; otherwise, the consumer borrows.

### PERMANENT CITATION

 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 » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.