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.


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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.
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