Some Economic Applications

In this chapter, we introduce some basic terms and properties related to cost, revenue and profit functions. We use differential calculus to derive some basic relationships among them. From the necessary condition for a point to be a local maximum point of the profit function we obtain the basic relationship that the maximum profit occurs at the point where marginal revenue equals marginal cost. Another important problem in economics is to determine how strongly a change in one economic variable will affect a change in another that is related to it. For example, we are interested in how intensively a change in price will affect a change in demand, a change in total revenues, etc. As we have seen so far, the term derivative allows us to determine what happens to the value of a dependent variable if we increase the value of an independent variable by one unit. However, clearly it is not the same whether the price of an ice cream increases by $1 or the price of a car increases by $1, given that the relative share of this increase in the total price of the product is significantly different. Therefore, it is often much more important to observe what will happen to the dependent variable (e.g. demand) when the independent variable (e.g. price) increases by 1%. This change is described by the term elasticity, which we consider in the last part of the chapter.