Optimization of bivariate and multivariate functions
In Chapter 5 we have considered optimization of single-variable functions. Most economic quantities, however, depend not on a single variable, but on several. Such dependences lead to analysis of functions of several variables (multivariate functions). Because of the many variables involved, the usual scalar quantities like derivative and second derivative are replaced, correspondingly, with the gradient vector and the Hessian matrix. After having introduced the necessary technical matrix tools in Chapters 6 and 7, we now have all the necessary prerequisites to deal with the calculus of several variables.