Differentiation of Multivariate Functions

Abstract

We have so far used simple economic models which express a relationship between just two variables, say price and quantity or profit and output. Unfortunately, the real world is not that simple. We have to therefore consider functions of several variables. For example, the output of a firm depends upon many factors such as the size of the labour force, amount of machinery, cost of capital etc. Also, the supply and demand of a commodity will not only depend upon its price, but also on the prices of other related goods, the level of income, the time of year or week, etc. In the latter case, we could have the multi-variable demand function: