# Price elasticity of demand and time lags

This is probably a very basic question so apologies in advance, but we are stuck.

We currently change prices by varying amounts (both positively and negatively)every 3 months,and would like to calculate the price elasticity of demand.

Questions:

1) Should we eliminate a period of time immediately after the price change to allow time for people to adjust behavior?

2)Should we include the entire time between quarters (i.e. the three months before the price change (so everything right after the previous price change all the way up to the current price change) and the 3 months after the price change (so everything after the current price change all the way up to the next price change)?

Any help would be greatly appreciated!!!!

Although you talk about "calculation", in order to justify the presence of your question in this forum I will treat your problem as one of "statistical estimation".

Moreover, I understand that this is not a supply-demand interaction framework, since it seems that you change prices and then "wait to see what happens", fulfilling whatever demand appears. Given these preliminaries:

$1$) The fact that people may exhibit some degree of inertia is an integral part of their behavior, so trying to "eliminate" it is not useful since what you will then be estimating would perhaps be the "true" price elasticity of demand, but one which will never materialize, since inertia will always be present, and will affect the total demand response. More over, how would you determine the length of time to ignore?

What you need is to obtain a separate estimate of both effects. This calls for a specification like the following:

$$\frac {\Delta q_t}{q_{t-1}} = a\frac {\Delta q_{t-1}}{q_{t-2}} + b\frac {\Delta p_{t}}{p_{t-1}} + u_t$$

wher $a$ captures the degree of inertia, expected positive, and $b$ is expected negative, while $u_t$ is assumed white noise. The inclusion of the error term, and the whole statistical approach permits to allow for other "unpredictable", "uncontrollable" factors that may affect demand in each quarter.
The estimate $\hat b$ will be the estimated average price elasticity of demand, "cleansed" from any inertia effects and other "random" factors.

$2$) Yes you should use as your time period the whole quarter. Hopefully you have data for many quarters.

As Alecos stated you should take into account all things which might affect time lag between change in the input series and resulting output series.

Formally you can think you have a somekind of stochastic control problem, where you assume some market reaction schedule for your input series (price) assuming that ability to produce do not hinder supplying realized demand.

One consideration might be seasonality and possibility to use storage/warehouses/inventories as a buffer to adjust changing demand. But inventories keep capital tied to them so there is a cost element there.

Regards,

Analyst