Visualizing Multi-Dimensional Functions in Economics

Economists frequently deal with multi-dimensional functions; obvious examples include statistical optimization and simulation of all but the simplest models. However, unlike their two-dimensional cousins, multi-dimensional functions are difficult or nearly impossible to visualize. While there is an established literature in the computer visualization field for multi-dimension functions, these methods require either specialized hardware (such as 3-D glasses), or complicated software, or are designed for specific functions. The multi- dimensional visualization method described here is suitable for most any function of relatively low dimension, does not require any specialized equipment, and is relatively simple to implement. With it, economists can fairly easily visualize the functions that they use and thus gain insight into their models. After describing the method, examples are given from the literature.