Price elasticity differentiation

Research question: Does the price elasticity of demand for digital asset purchases differ between two groups that are distinct in terms of location and economic status?


Price elasticity of demand (PED or Ed) is a core concept in finance and economics and, unsurprisingly, a crucial indicator for any business or organisation that sells products or services for which it has some pricing flexibility. This means that neither an outside organisation nor a highly competitive environment should be able to set the price. Many executives are apprehensive about setting or changing a product's pricing, despite the fact that this is one of the most critical decisions to be made. A well-thought-out price modification can increase earnings and foster a positive environment within a business. Economists frequently use price elasticities to compare products and how consumers respond to a single price adjustment. How does the price of alcoholic beverages compare to that of vegetables, for instance? 

Underlying Theory of Price Elasticity

The price elasticity of demand, given a demand curve, is the percentage of demand decline brought on by a 1% rise in price. Demand is price elastic when elasticity exceeds 1. When demand is price elastic, lowering prices will boost sales. Price inelastic demand occurs when elasticity is less than 1. A price reduction will result in lower revenue when demand is price inelastic. For instance, a 1% reduction in air travel prices can lead to a 4% rise in demand for air travel. To choose the best price point, executives must comprehend the price elasticity at each price point. Therefore, price and quantity are inversely connected, according to the law of demand. Whenever prices fluctuate, units always move in the opposite direction. What happens to revenue, though, is the true problem. Demand must be inelastic for revenue to follow the price direction, as revenue is defined as price * units. Revenue will move in the direction of the unit if demand is elastic. Price should therefore rise under an inelastic demand curve to increase revenue. In an elastic demand curve, prices should drop to increase revenue.

Price Elasticity of Demand

Figure 1 - Price Elasticity of Demand

The Dataset

The cleaned data used corresponds to an experiment that was run in conjunction with an online vendor of creative digital assets. For this research, the price of a single asset was changed from between $2.49 and $4.99, by steps of 10c, with each different price point being tested for one week. The purchase data used has been taken from users located in two entirely different geographic areas, one with a majority of high-income households and one with mostly low-income households.

Digital Sales Dataset

Table 1 - Digital Sales Dataset


The tool for price elasticity of demand analysis available in Excel's Solver add-in was used to compute elasticities and display the results, with the dialog boxes allowing us to directly select prices and demand (units sold). Standard mathematical operations like multiplying or dividing changing cells, raising changing cells to a power, using exponential or trigonometrical functions involving changing cells, and optimisation problems where the target cell and/or some of the constraints are not linear can be calculated using Solver's GRG Nonlinear engine. 

To correctly measure the elasticity, we needed to determine how much the demand changed when the price changed from one value to another, or as previously stated, by one percent. Consequently, this would be the ratio of the differences, but it was essential to eliminate the influence of scale in order to compare elasticities for the purchased item or at different positions on the scale. As a result, we divided the price difference by the starting price and the demand difference by the starting value of demand (Q). The basic approach would have been to calculate point elasticity, as such:

Price Elasticity of Demand (PED) Formula

Figure 2 - Price Elasticity of Demand (PED) Formula

The above calculation takes the assumption that:

P0 = initial price
P1 = final price
Q0 = initial quantity
Q1 = final quantity

The problem when you write the equation this way is that PED depends on whether you change prices from P0 to P1 or from P1 to P0. Arc Elasticity is often used instead to avoid the problems and restrictions of this basic Point Elasticity. It is computed at the middle point between P0 and P1:

Price Elasticity of Demand (PED) Arc Elasticity Formula

Figure 3 - Price Elasticity of Demand (PED) Arc Elasticity Formula

Analysis and Interpretation

If the quantity is a known function of the price, elasticity is a multiple of the slope coefficient of the line that is tangent to the curve. For arc elasticity, it is a multiple of the slope coefficient of the line connecting (P1,Q1) and (P2,Q2). Remember that elasticity is the ratio between the relative change in prices and the relative change in quantities to facilitate interpretation. In other words, what is the value of PED if the price increases by 1%, and by what percentage would the quantity change?

As we can see from the visuals in Figure 4, in most cases, the price elasticity of the Location 1 group is lower than that of the Location 2 group. For the Location 1 group, the higher the price, the lower the elasticity, whereas for the Location 2 group, the elasticity range remains constant.

Elasticity vs Price / Units

Figure 4 - Elasticity vs Price / Units

An automated F-test and a t-test were conducted to ascertain statistical significance and to see whether the variance was homogeneous between groups. The F-test verifies the statistical significance of the overall strength of a model's connection with its dependent variables. If the F-test p-value is smaller than the selected α-level (0.05 in this case), we could conclude that the model is statistically significant overall.

F-Test and t-test Summary Results

Table 2 - F-Test and t-test Summary Results

A desirable F-value should be greater than one. Our model produced a critical F-statistic value of 2.979, which is higher than one, and a p-value (Prob (F-statistic)) close to zero. The probability of erroneously rejecting the null hypothesis when we should not (known as a Type I error in hypothesis testing) is less than the 5% threshold we decided to accept at the outset of the research. Since the p-value is less than 0.05, we conclude, therefore, that the model is statistically significant at the 95% confidence level.

Box plots were retrieved from the t-test outputs to confirm a significant difference in mean and variance. As the computed p-value (<0.005) is lower than the significance level α=0.05, one should reject the null hypothesis, and accept the alternative hypothesis that there are significant differences in price elasticities between these two groups.

 Arc Elasticity Box Plot and t-test

Figure 5 - Arc Elasticity Box Plot and t-test

After determining that a model is statistically significant overall, we may assess the significance of the model's individual independent variables. The t-values (denoted |t| in Table 2) for the independent variables are shown in Figure 5. The p-values were computed using the t-values that were also included in the summary findings. We compare the p-values with the α-level of 0.05. If a p-value is less than 0.05, it is a statistically significant model for explaining the variance in price elasticity.


In conclusion, understanding the price elasticity of demand for digital assets is critical for businesses to optimise their pricing strategies and maximise revenue. The study of price elasticity of demand for digital assets conducted in this article provides valuable insights into the factors that influence consumer demand for digital assets, but further research is needed to validate these findings and develop effective pricing strategies. Continued research in this area could lead to more effective pricing models, increased profitability, and improved customer satisfaction.

Recommendations for Further Study

Recommendations for further study in the area of price elasticity of demand for digital assets could include expanding the study to include a wider range of digital assets, such as software, e-books, and digital music. Further research could also investigate the impact of different pricing strategies, such as dynamic pricing, on price elasticity. Additionally, it would be valuable to examine the effect of consumer demographics, such as age and income, on price elasticity, alongside the impact of changes in product quality or features.