top of page
Search

Finding the Pricing Sweet Spot🎯

How to maximize revenue and profit



Finding the optimal price for profit and /or revenue is the holy grail for most businesses.

But it’s far less straightforward than it seems.

Let’s break it down.


Revenue is (relatively) simple


We know the basics:


  • If a product is inelastic (e > -1), increasing the price increases revenue

  • If it’s elastic (e < -1), increasing the price decreases revenue


So, in theory, if you know elasticity, you can estimate the price change that maximizes revenue.


And in fact, you can.


Profit is where things get interesting


Profit optimization is more complex, and intuitively, we expect optimal price changes to be higher than revenue because we also need to account for costs.

So the question becomes: given elasticity (e) and margin (m), how much should the price change to maximize revenue vs. profit, and how different are the two optimum prices?


Finding the pricing sweet spot


We can derive both revenue and profit responses directly from elasticity and margin:


Profit

➡️ pr = (e/m).p.(p-2.Popt) - profit change
➡️ Δpr/Δp = 2.(e/m).(p-Popt) - sensitivity
➡️ Popt = -(m+1/e)/2 

where pr, p is the % change of profit and price respectively

Revenue change over price change

➡️ r = e.p.(p-2.Popt) - revenue change
➡️ Δr/Δp = 2.e.(p-Popt) - sensitivity
➡️ Popt = -(1+1/e)/2 

where r, p is the % change of revenue and price respectively

Based on that, the optimum price changes for profit and revenue are: 


Optimum price change

For profit maximization = -(m+1/e)/2
For revenue maximization = -(1+1/e)/2

Key insights


  • Profit optimum price is always higher than the revenue optimum price: their difference is 1-m, which is always positive

  • Revenue rule: Increase price if inelastic (e > -1) or decrease price if elastic (e < -1)

  • Profit rule is more nuanced: Increase price if 𝑚 < -1/e or decrease otherwise

  • Elastic ≠ lower optimal price for profit: Even for elastic products, we often need to increase prices to optimize profit

  • Edge case: If e > 0 for rare situations, such as luxury signaling or constrained supply, the “optimum” becomes a minimum, not a maximum


What the curve tells us


  • Revenue and profit both follow a hill-shaped curve over price changes

  • Profit is typically more sensitive to price changes than revenue

  • Revenue peaks earlier and profit peaks at a higher price point


👉 This is why pricing is often the most powerful lever for profit growth.


What the table reveals


Optimum price change for different margins and elasticities


Across different elasticities and margins:


  • Price increases improve profit in most scenarios for both elastic and inelastic products

  • Price decreases are only optimal for highly elastic products with high margins


In other words:


👉 Raising prices is usually the right first move for profit optimization

👉 But the magnitude depends heavily on both elasticity and margin


Practical next steps


So… can we just plug in elasticity and margin and move on?


Tempting, but no.


Two major issues:


  1. Elasticity is hard to estimate because real-world demand is messy:

    1. Customer segments behave differently

    2. External factors (seasonality, competition, macro or market trends) interfere


  2. Elasticity is not constant

    1. It changes with price

    2. It changes with customer or product characteristics and other factors


⚠️ So, assuming constant elasticity only works for very small price changes.


The real answer


If you want indicative, directional insights → formulas work

If you want accurate, actionable pricing → you need:


  • Demand modeling

  • Supply dynamics (shortages, approval constraints)

  • Econometric intelligence

  • AI-driven optimization

  • Continuous elasticity estimation across price points


In other words:


👉 You don’t optimize price from a single elasticity number

👉 You optimize it from a full response curve

👉 Elasticity becomes a byproduct, not the input


Final takeaway


  • Pricing is the most powerful profit lever

  • The optimum price for profit is always higher than for revenue

  • Most businesses underprice due to oversimplified assumptions

  • True optimization requires modeling reality, not simplifying it away






Interested in learning more about AI-Powered Price Optimization and Strategic Forecasting?



Comments

bottom of page