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I am looking to calculate the equilibrium price, i.e an optimal price that I can set without affecting demand and maximize revenue.

I've gathered historical data: occupancy rates, asking rents for different property types by submarket / market and have a bunch of other data including local economic variables, new construction, location characteristics etc. Here's how I am thinking about estimating the demand function -

First predict demand, occupancy rates using Regression with fixed effects and historical prices for a particular property type in a given submarket. The training data for this is last 5+ years of historical data.

Approx. Model specification:

Dp = bo + b1*(Econ) + b2*Supply + b3*Loc + b4*Price t + b5*Price t-1 + b6*Price t-2

With this, I can get an estimate of how much price can change without significantly affecting quantity demanded. The assumption here is all else being equal. However, supply/vacancies changes.

So, my question is how would you model this? Are there any other analytical/ML approaches to model this and calculate equilibrium price?

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    $\begingroup$ It could be that the level of supply has little effect on quantity demanded in a poor location, but a considerable effect in a good location. To allow for this sort of effect you might consider including some interaction terms or trying a logged functional form $\endgroup$ – Adam Bailey Jun 10 at 13:17
  • $\begingroup$ Good point. Location characteristics and demographics (median income, etc) will capture some of these differences. Otherwise, I could consider classifying submarket as good, bad, average etc. and then use that interaction term? $\endgroup$ – kms Jun 10 at 13:22
  • $\begingroup$ Yes, a dummy variable classifying submarkets to use in an interaction term could be helpful. $\endgroup$ – Adam Bailey Jun 10 at 13:30
  • $\begingroup$ Any thoughts on how you'd interpret the coefficients? i.e the effect of price on demand. Given, all else being equal is not a realistic assumption, in this case. The location and demographics are fixed effects, however, competitor price and supply may vary with time. $\endgroup$ – kms Jun 10 at 13:56

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