Joint work with: Sami Dakhlia (Department of Economics and Finance, College of Business, University of Southern Mississippi, USA) and Peter Gothen (Centro de Matemática and Faculdade de Ciências, Universidade do Porto, Portugal). A main concern in economics is the study of the set of equilibria in an economy, that is, the set of prices for which supply equals demand in the economy. Supply and demand are best modelled by the excess demand function defined to be the difference between demand and supply, that is, equilibrium prices are zeros of the aggregate excess demand. In 1970, Debreu ["Economies with a finite set of equilibria," Econometrica 38, 387-392] showed that regular economies (those represented by a regular aggregate excess demand) have finitely many isolated equilibria. It is however known that critical economies may have an infinite number, even a continuum, of equilibrium prices. By showing that the aggregate excess demand of an economy is generically (that is, for an open and dense subset of the set of smooth maps) a Boardman map, we are able to perturb the economy so as to transform any smooth aggregate excess demand function into a function with isolated zeros. Clearly, the challenge of this type of exercise is that the perturbations must be `legal': the perturbed function must also be an admissible aggregate excess demand function and satisfy its canonical properties. In order to do this, we use a particular topology for the space of preferences and geometric arguments to deal with the perturbation of the indifference level surfaces of agents, leading to a `legal' perturbation of aggregate excess demand. We show that the aggregate excess demand being a Boardman map is a sufficient condition for local isolation of all price equilibria. Finiteness then follows when we show that, under generic assumptions on the economy, the set of price equilibria is compact. After a brief description of the concepts and problems in economics, I shall present the results in Castro and Dakhlia, "Finiteness of Walrasian equilibria" and in Castro, Dakhlia and Gothen, "Direct perturbations of aggregate excess demand" that lead to the proof of finiteness of equilibria.