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• Print publication year: 2012
• Online publication date: December 2012

# 4 - Differential calculus 1

## Summary

This chapter deals with differential calculus. Recall that we dealt with market supply curves in previous chapters. They were generally assumed to be upward sloping (the law of supply). In this chapter, we will derive an upward sloping supply schedule of a firm both intuitively and mathematically. To this end, we will focus on a firm's profit maximisation problem that underlies it.

A firm is an institution that hires factors of production (inputs) and transforms them into goods and services (outputs) using its production technology. Here we consider a firm whose objective is to maximise its profits. Therefore we are interested in obtaining the level of output that maximises the firm's profits. In the course of obtaining the profit maximising level of output, we will introduce differentiation, which is the process of finding the derivative of a function, and will also foreshadow some of the important mathematical notions related to curve sketching that will be covered in the next chapter.

Chapter goals By studying this chapter you will

(1) be able to explain various notions regarding costs;

(2) be able to interpret what it means by differentiating a function; and

(3) be able to set up and solve the firm's profit maximisation problem.

Cost function

As mentioned before, a firm is an institution that hires factors of production (inputs), such as labour, machines and raw materials, and transforms them into goods and services (outputs) by using their production technologies. Our focus will be profit maximising firms, i.e. those whose objective is to maximise their profits.