# Finbarr Timbers

Setting prices is hard. Really, really hard. If you’re like most people, you just sit down, think really hard, and guess, using all the knowledge you’ve acquired over time. Maybe you use a margin calculation- you take the amount it cost you, and add, say, 20% to cover your costs and add some profit.

If you’re a larger company, you might have someone whose job it is to analyse data. How do they use data to figure out prices? (Or how should they be using data?)

The core problem is that, if you increase prices, you decrease the amount of goods you sell, and, after all, what you care about is profit, not individual prices. So if you raise prices, you need to make sure that you don’t just lose sales to compensate for it.

When calculating profits, the basic equation is:

$\text{Profit} = \text{Price} \cdot \text{Number of goods sold} - \text{Cost per good} \cdot \text{number of goods purchased} - \text{fixed costs}.$

Fixed costs are those costs that don’t change with the number of goods sold.

The key thing to realize is that none of the costs matter once you have the goods (the exception is marginal costs- the cost to fulfill the order, e.g. shipping- and we’re going to assume you can’t really change those costs). So all we need to do is look at the price you’re charging per good, and the number of goods you sell.

Let’s look at this again:

$\text{Profit} = \text{Revenue} - \text{Costs}$

Let’s dive into the Revenue side of things:

$\text{Revenue} = \text{Price per good} \cdot \text{Number of goods sold.}$

So if you increase your price by 1%, as long as your volume goes down by less than 1%, you make more revenue! Vice versa, if you decrease your price by 1%, as long as your volume goes up by more than 1%, you make more money!

In economics, we call this elasticity:

$\text{Elasticity} = \text{Change in price (%)} / \text{change in volume (%)}$

Elasticity is the key indicator to figure out how to change your prices. If you have an elasticity that’s greater than 1, then a change in price of 1% will lead to a less than 1% change in volume.

Conversely, if you have an elasticity that’s less than 1%, you should lower prices, as a decrease in price will lead to an increase in volume.

## Estimating elasticity

How can we estimate this number?

Running online sales with coupons can let you estimate this pretty easily. You can do the following:

1. Randomly show some % of your users (say, 10%) a coupon, say for 10% off. Then, see how this affects sales.
2. Track the price each buyer pays.
3. Compare how many sales you got from the users with the coupon vs the users that didn’t get a coupon. The change in volume is (number of sales with coupon) / (number of sales without coupon / 9).

You end up with this equation:

$\text{Elasticity} = 10\% / \text{Change in volume (%)}.$

Then, you can figure out if you should bump up your prices!

You can also do this geographically- show everyone in BC a higher price, and show everyone in Alberta a lower price. That way, you have consistency, and people won’t be shown random prices.

You can also use data to estimate this for various goods- e.g. if you sell coffee machines, you can probably run this experiment on only one coffee machine, and estimate the elasticity for other coffee machines using statistics. I’ll have a future blog post about this.

If you want to chat more about this, give me an email at [email protected] I love chatting to people about their businesses, as I’m a huge geek. And if you’re a business that wants to try this, please let me know how it goes- I’d love to know what sort of impact this can have.