Optimal Price / Discounting Ratio

Ok, this isn't optimal because I'm not looking at gross margin dollars (that's reserved for clients), but you'll get the idea here about what I'm looking to accomplish.

I created regression models that predict the impact of prices on rebuy rates, and another model that predicts the impact of discounting on rebuy rates (again, gross margin work is done for clients).

The average price point for this category was $50.00, and the average percentage of items sold at/above the historical average price point was 75%. This yielded a 51.6% rebuy rate.

What happens if prices increase to $55.00 and discounting remains constant?  Rebuy rates decrease to 49.7%.

What happens if prices increase to $55.00 and discounting increases so that just 56.3% of the items are selling at/above their historical average price point?  Rebuy rates maintain at 51.5%.

This dynamic is coming to an omnichannel brand near you (your mileage will vary). Prices increased a year ago and continue to increase, customers balk at higher prices and purchase less often, leading "brands" to discount more to maintain response (which means that gross margin dollars decrease and the brand is less profitable).

It's hard to fight the customer. The customer is telling us how much s/he is willing to spend, and the customer does not care one bit, one bit, about how our cost-of-goods increased. Many of us are going to give up profitability, either by increasing prices / decreasing response, or by increasing prices / discounting (which decreases gross margin dollars).