# Conducting an experiment to calculate empirical elasticity with very small price changes

Let's say I want to conduct an experiment where I randomly vary the price of a product up or down by a small amount. Let's say I want to understand the price elasticity of demand for online shoppers in a given category.

When someone visits my site, I will randomly move the price up or down by some amount, x.

Does it matter how what the magnitude of x is given a large enough sample? I think theory will say that a large enough sample will overcome a really small x. But my concern is that let's say the average price in my shop is $440, x = \$0.01. Does anyone care about \$0.01 when buying a \$440 item?

Do I need x to be, for example, \$10 before I am able to detect a meaningful elasticity? ## 1 Answer You are facing a problem which is probably much more sophisticated than you may have previously thought. I guess you want to learn something about aggregate elasticity of demand. By shifting the price per individual website visitor you do not get variation in aggregate demand but only in individual demand. I guess you do not observe the individual demand of prior weeks which then does not allow you to observe the change in demand caused by the price change. Overall, I guess, individual elasticities of demand are not useful for your purposes anyway, so I move further. Now, if you would vary prices in the same way for all visitors and observe differences in aggregate demand this potentially tells you something useful. I.e., how does aggregate demand change when the price changes? I think this is what you want to study. Note that your assumption is then that nothing changed for the consumers (income, demand shocks, ...). One could actually control for that in a reduced form regression model or some structural model a la discrete choice. However, notice that you may be facing severe endogeneity problems in your future estimations if you aspire to do this. Concerning the relative magnitude of$x\$: there is an extensive literature on this out there. Just use google scholar and type something like "experimental economics elasticity of demand".

• Yeah, actually my current approach involves measuring the aggregate demand change after the price change event, but there is sufficient variability in the response that it makes it difficult to do anything but measure the elasticity at the aggregate level (you mentioned demand shocks, there's a lot of stuff happening creating volatility). We struggle to observe the elasticity with confidence of a sub-segment. For this reason, I was thinking if we can measure the individual response to price changes we can get elasticity by customer segment. – Caleb Jul 25 '18 at 6:00
• My Google scholar search didn't turn up much, @saguru, any specific ones worth checking out? – Caleb Jul 25 '18 at 6:01