Last month, my university held its Orientation Day. On that day, I met a lot of high-school students, who were interested in studying economics. As I told them that learning economics in university needed some math (this requirement is not obvious in high-school economics), some asked me how math could be used in economics. In particular, a student asked how M1/M2 would be used in economics.
M1/M2 are the extension section of mathematics in DSE, Hong Kong's high-school public examination. As far as I know, it covers some basic calculus. Hence, I need to explain to the student how some basic calculus can be used in economics.
High-school calculus does not allow students to do much. Nonetheless, at least it enables students to find the maximum point of a curve (or a function) with or without some constraints. One use of derivatives (dy/dx) is that the maximum point can be found at dy/dx = 0, given certain assumptions (say, when a curve is convex). This mathematical method is indeed very useful for economics.
Why? It is because economics studies human behaviours from a specific viewpoint. It considers rational choice as a basic model for understanding human behaviours. Perhaps there are other aspects in human behaviours. But at least we recognize that rational choice is an important aspect, if not the only aspect.
Rational choice is this. People aims at achieving the best outcome for what they can do. In other words, if you can do better, you will do it. If you can do better, but you do not, you are irrational. Economists do not think people are (at least not very often) irrational. Sometimes someone seemingly have not attained the best for them. This is only an interpretation from an outsider's perspective. In fact, the person can't improve further but we, as outsiders, do not know the constraints facing this person. This person perhaps lacks the relevant knowledge or skill. An easy job (from an observer's view) may not be conducted because the actors himself do not think it is easy. Economists will not easily say people are irrational.
If people are rational in making choice, then what? The answer is that they will maximize their benefit subject to some constraint (the "what they can do" part). For example, consumers maximize the satisfaction derived from consumption (choosing quantity bought for different goods) subject to budget constraint (what they can buy). Firms maximize profit subject to the technology that they can get access to, and the prices of hiring production factors.
As such, mathematically, rational choice can be represented as a maximization problem, or, more precisely, a constrained maximization problem. Economists use this type of mathematical models to study behaviours. For example, a firm want to maximize profit. It knows that some factors can increase or decrease profit in different situations. A higher price decreases the quantity that a firm can sell but increases the profit that it earns for each unit sold. Thus, price may increase profit up to a point, and will decrease profit beyond this point. We need a mathematical model to find out the point where profit is maximized. A successful mathematical model predicts correctly what a profit-maximizing firm will choose.
Mathematics, and M1/M2, provides the technique to solve these maximization problems. Since economics involve many these problems, mathematics is a useful tool for us. Of course, economics also involves other problems that require mathematics to help. Since I have to explain only by some math concepts that high-school students understand, I simply touch on maximization in our conversations with these students.
