How can I find the optimal price that maximizes profits, given past sales data? I thought I could do this, but I've been running into problems.
Price, Quantity Sold, Unit Cost $90, 1100, $10 $100, 1000, $10
I can find elasticity (-0.82) and I've been reading some things that say that you can find the optimal price, but I've only been able to tell the direction the price should be moved. This answer says use the Lerner condition, but that just shows if elasticity < -1 decrease and if elasticity > -1 increase price. And this article says
what is much harder to do (although there are structural techniques to do so) is to work out what the optimal price should be
edit to add: I can find the linear equation for demand based on these 2 data points and find the point that maximizes revenue. I also found a demand function equation Qd=Qh*((P/Ph)^Ed), where Qd is the predicted Quantity Demand, Qh is observed Quantity, Ph is observed Price, Ed is Elasticity of Demand, and P is the independent variable price. But are any of these the best method to use?