# Intermediate Microeconomics With Calculus

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As an economics professor with several years of experience, I have been asked this question repeatedly: What subject, besides economics, should I study if I want to major in economics?  My answer has always been: “Mathematics, mathematics, and more mathematics, especially calculus.”  For introductory courses in microeconomics, the presentation is usually graphical for illustrative purposes, with occasional use of elementary algebra, but a more in-depth study of microeconomics requires a good knowledge of differential and integral calculus.

Fundamentally, calculus studies function.  Basically, a function expresses the relationship among variables.  Let us consider two variables, X and Y.  If changes in X cause Y to change, we say that Y depends on X or Y is a function of X, written as

Y= f(X)

For example, we know that when the price (P) of an item changes, other things being equal, the quantity (Q) that people will buy will also change.  So the quantity that people will buy is a function of the price, written as

Q = f(P)

The calculus concept of a function has numerous applications in microeconomics, such as demand function, supply function, cost function, production function, utility function, etc.

In economics in general, and in microeconomics in particular, the concept of marginal looms high in importance.  In fact, it has been said that economists make decisions at the margin.  The calculus equivalent of the marginal concept is what mathematicians refer to as the first derivative.  In microeconomics, we seek to maximize satisfaction or utility, and profits for example, and to minimize cost, for example.

Via calculus, we know that:

• A firm maximizes its profits when its marginal revenue equals its marginal cost
• If marginal revenue is greater than marginal cost, the firm’s profits will increase if it increases its output
• If marginal revenue is less than marginal cost, the firm should reduce the level of its output
• A household consuming two goods will be maximizing its satisfaction when the ratio of the marginal utilities of the two goods equals the ratio of their prices.

In sum, a sound knowledge of calculus will enable us to have a deeper understanding of microeconomics and will help us to solve many microeconomic problems.

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