How to test the hypothesis of dependency between price and demand

Question

The task is as follows: a customer of mine has been gathering statistics on purchases of a specific item (lets call it 'manna') in his shop during last year. The price of manna moved up and down a lot during that time period - sometimes in the range of only several cents per unit of volume. It seems valuable to test the hypothesis that demand for manna grows whenever the price for manna goes down a bit.

How can this be properly tested? Maybe you can provide me with the links to material describing any similar approaches?

Thanks in advance.

Answer 1

I think you need need to be careful in distinguishing between demand and quantity demanded. Quantity demanded would rise when prices fall, not the demand itself, which is merely the relationship between price and quantity demanded. It a movement along the curve (the slope of which you care about), rather than a movement of the curve itself.

A regression of price on quantity typically does not recover the slope or even its sign, because the demand curve moves over time for many reasons (competitor prices, for example). I would take a look Eric Rasmusen's intro to demand estimation for an explanation. In short, for many products, you can try using marginal costs as an instrumental variable for price in the demand equation. The details really depend on what "manna" is and that market structure looks like. There are also the NBER 2012 Summer Institute lectures and notes on demand estimation, which are more advanced.

Answer 2

Although this is a time series that might best be handled through time series modeling, let us assume that the drops are independent and only (possibly depend on manna dropping slightly). Then you could look at this like analyzing an itnervention. Take the set of paired differences between demand prior to the price drop with demand after the price drop and apply either a paired t test or a Wilcoxon signed rank test (with the choice depending on the appropriateness of the normality assumption on the paired difference).