18.1 Introduction

In Monday’s lecture, we derived the cost function for a firm: for any quantity of output $q$ we determined the total cost $c(q)$ of producing that quantity. From that function, in turn, we determined the firm’s average cost $AC(q) = c(q)/q$ and marginal cost $MC(q) = c’(q)$.

In Friday’s lecture, we’ll determine the firm’s optimal quantity $q^\star$ to produce. We’re going to assume that the firm is trying to maximize its profit, which we’ll write as $\pi(q)$, which is the revenue it receives from selling $q$ units, $r(q)$, minus the cost of producing those $q$ units, $c(q)$: \(\pi(q) = r(q) - c(q)\) So, in order to do this, we need to derive the revenue function $r(q)$; this is the topic for today.

A firm’s revenue function will depend on the price elasticity of the demand curve facing the firm. Therefore, before we get to talking about revenue, let’s review what elasticity is, and how it’s calculated. You’re hopefully familiar with elasticity from high school Econ and/or Econ 1; so this will be partly review and partly showing how elasticity can be calculated using calculus techniques.