What is price elasticity, and how does price optimization work?
By: Roy Swisa
Tags: Financial Planning, Price Analysis, Banking Technology, Data Science, Fintech

Have you ever wondered how product prices are determined? How do large corporations (i.e. Hotel.com, Amazon, or American Airlines) decide on the right price for their products? Whether that product is an airline ticket, an insurance policy, or a loan. Companies have to use price optimization, as a vital tool for your pricing process.

Credit: Michael Byers

To best understand price optimization, we first need to understand a core concept of microeconomics: Price Elasticity.

What is price elasticity?

As the price increases, your demand for the orange juice decreases. If we plot this behavior the trend would appear as below:

The price elasticity for purchasing the orange juice is different for every point in the graph.

It can be calculated using the following formula:

We can see that the price elasticity at a price of $3 is -1. Then, for every 1% of price increase, the demand will drop by 1%. And at a price of $4.5 is -3. Then, for every 1% of price increase, the demand will drop by 3%.

What can we understand from the Price elasticity of demand?

When the customer has a high price elasticity, they are very sensitive to the change in price. Therefore, if we can set the price, we would aim towards the area where the price elasticity is lower in absolute terms. In our example: around $3. Based on the price elasticity and other factors, we can build a demand model that estimates the probability of buying the product. Now that we have a grasp of what price elasticity is, we have a solid foundation to dive into price optimization…

What is price optimization?

Price optimization will help us to understand how much to charge in order to maximize the profits of a given product.

Price optimization is based on two factors:

1. The behavior factor, also known as the demand model based on “Price Elasticity” — the customer’s sensitivity to change in price.

2. The profitability factor: how much potential profit the company can earn from selling this product at a given price.

Let us look at the following example: Rebecca is 30 years old, and she wants to take a $10,000 loan to replace her car. She went to shop around for a loan from different banks and settled on her local branch.

Rebecca’s demand vs APR

The upper graph represents Rebecca’s change in demand for the change in the price of the loan (APR). We observe that her demand decreases at different rates as the price of the loan increases; this relative change in demand represents her price elasticity.

The bank’s profit vs in profit APR

This graph represents the bank’s change in profit as a result of the change in the price of the loan (APR). The bank’s profit increases for every increase in APR.

Back to our story, the bank’s initial offer was a loan with an 8 % annual interest rate for ten years. If Rebecca closes this deal, the bank will make a $2180 profit (in the diagrams above: the purple circle represents this initial offer).

We can observe that there is a trade-off between these two factors: on the one hand, as we increase the annual interest rate the probability for Rebecca to close the deal decreases, but on the other hand, as the interest rate increases the expected profit for the bank increases.

How do we solve this trade-off?

First, the bank evaluated Rebeca’s Price elasticity of demand at 8% APR. Her price elasticity was considered very high [-5], in other words, she was not likely to take the loan. therefore the bank decided to lower the price of the loan. But for how much should they lower the price?

The bank will formulate it’s expected profit. The bank will do this by multiplying Rebecca’s probability of closing the deal by the bank’s profit.

If the bank wants to maximize the profit from Rebecca, it will be better to offer her a loan with a lower interest rate of 6.5 %, as opposed to 8%.

The bank’s expected profit vs APR

If the bank offers her a loan with 6.5%, her probability of closing the deal will rise, and the bank’s profit will decrease to $1,760 from $2,180, but the bank’s expected profit will increase to from $872 to $1,068.

Now the bank needs to repeat this process and calculate the expected profit for every customer. Therefore, for some customers, the bank will increase the APR, and for other customers, the bank will reduce the APR, as we saw in Rebecca’s case.

If the bank builds a robust “demand model” it will increase it’s profits.

Summary: