Demand Functions with Inferior Goods: The Implicit Function Approach

In this article, we propose a numerically computable utility function that can apply to inferior goods. The implicit function and its optimization technique are fully used. Since the implicit function is carefully formulated, it works well as a standard utility function. This technique ensures tractability and extendability. We propose the following: (1) a simple utility function of an inferior good which contains only two parameters; (2) a total cost function and its extension to the Cobb-Douglas production function with an inferior input; (3) a generalized utility function whose Engel-curve always stems from the origin.