Hyperbolic Coordinates - Economic Applications

Economic Applications

There are many natural applications of hyperbolic coordinates in economics:

• Analysis of currency exchange rate fluctuation:

The unit currency sets . The price currency corresponds to . For

we find, a positive hyperbolic angle. For a fluctuation take a new price

.

Then the change in u is:

.

Quantifying exchange rate fluctuation through hyperbolic angle provides an objective, symmetric, and consistent measure. The quantity is the length of the left-right shift in the hyperbolic motion view of the currency fluctuation.

• Analysis of inflation or deflation of prices of a basket of consumer goods.
• Quantification of change in marketshare in duopoly.
• Corporate stock splits versus stock buy-back.