# How can calculus be used in economics?

Jul 31, 2014

Calculus is at the backbone of economics because it provides an analytically efficient way to understand the intricacies of decision-making and optimal choices.

For example, if you are a firm, then one of the decisions you will probably make is choosing how much quantity to produce. Usually, you would want to choose the quantity that helps you maximize profits. Mathematically , we can write the profit function as :

profit = total revenue - total costs

where total revenue = price * quantity = p * q

and total costs is written as c(q), where the total costs are a function of how much you produce. Thus the profit function becomes:

$p r o f i t = p \cdot q - c \left(q\right)$

Now assuming the firm does not have control over the price and is only choosing quantity we can use calculus to now take a derivative of the profit function with respect to quantity.

$\frac{\partial p r o f i t}{\partial q} = p - c ' \left(q\right)$

Calculus tells us that setting the first derivative to zero of a concave function helps us find the optimum. Thus, the first order condition is :

$p = c ' \left(q\right)$

meaning that the amount of quantity produced is that it which price is equal to marginal cost, the derivative of total cost with respect to quantity.

We can see that calculus was used to solve this decision problem by the firm, and was also used to understand the concept of marginal cost. This required some amount of abstraction because the quantities the firm produced had to be thought of us a continuous variable (as oppose to a discrete one) in order to be able to take a derivative. This is not too unreasonable an assumption/abstraction for a firm choosing quantities.

Hope this helps!