What is Price elasticity of demand? (I)
Setting the right price for your product or service is hard. In fact, Optimising price is quite challenging in business, largely because its unpredictable effects on profit and revenue of the Company.
Understanding Price Elasticity
Price elasticity is a formula used to determine how a price change will impact the demand for a specific product. Do people buy more when prices drop? How much more do they buy? Do they buy less when prices rise — and how much less? These questions can be answered by evaluating a product’s elasticity of demand. Price elasticity of demand measures the responsiveness of demand after a change in a product’s price. One of the critical elements of pricing in this understanding what economists call price elasticity.
In this article, we will discuss about the price elasticity and how it can be calculated using machine learning. We will also explore how price elasticity can be used as a tool to optimise item selling price to maximise profit or drive revenue.
The price elasticity of demand (PED) measures the change in demand for a good in response to a change in price.
The PED is calculated by dividing the percentage change in quantity demanded by the percentage change in price. As a formula it is written thus:
PED
= %Change in Quantity Demanded / %Change in Price
= (ΔQ/Q)/(ΔP/P ) = (δQ/δP). P/Q
Where P is Price and Q is Quantity of an item. The law of demand states that there is an inverse relationship between price and demand for a good. As a result, the PED coefficient is almost always negative. Only goods that do not conform to the law of demand, such as fashion products, elite products have a positive PED. Its good to have in mind that consumers are relatively insensitive in price changes of habitually demanded products like bread, tobacco, and alcohol. Since they are necessities, their consumption will be barely reflected by price drop or increase. Here are some key observations related to the elasticity of demand.
- When the price elasticity is negative, then an increase in price will decrease the quantity sold.
- When the demand is price inelastic (i.e., 0 > PED > -1.0), then a small price increase will make the quantity sold almost unchanged and hence increase the total revenue.
- When the demand is price elastic (i.e. PED < -1.0), then a small price increase will decrease the quantity sold significantly and hence decrease the revenue.
- When the price elasticity of demand is equal to -1.0, then the current price will maximise total revenue.
How to calculate Price Elasticity using historical data?
One question relevant to industry is that How elasticity can be estimated with the past sales information of the item. A very common demand model for elasticity is Log-Linear model.
The log-linear demand model is of the following form:
ln Q = a + b · ln P
where Q and P are Quantity and Price of the item, a and b are parameters to be estimated.
The log-linear demand model is a very simple one. In the real world, there may be many additional complexities that need to be considered in the model. For example, prices of some other closely related items may have a significant effect on the quantity demanded for item; hence, they may also enter the right-hand side of the demand equation. On a store level, there may also be occasions when sales remain zero regardless of how much the price is; for example, when the good is out of stock. For demonstration purposes these complexities will be ignored in this post. We will learn and implement those in the upcoming post.
The log-linear demand function implies that the price elasticity of demand is constant:
PED = (δQ/δP). P/Q = d(ln P)/d(ln Q) = b
Thus, to obtain an estimate of the price elasticity of demand, you just need an estimate of b. We can simply use statsmodel to regress ln P and other independent variables over ln Q and get the estimated value of b.
With the elasticity in hand for each item in the portfolio, we can go ahead and optimise the price to increase the revenue/profit of the company. How to do that? We will learn this in the next blog with some practical data analysis in Python.
Until Then!
