You put a shiny new lemonade stand in front of your house in your neighborhood, selling lemonade for $1 per cup. Lots of neighbors pop by, buy your lemonade, and chat.
Then you decide to maximize your profits and increase the price to $3 per cup, and suddenly, all your neighbors disappear, and no one is buying. What’s even worse, they don’t even talk to you.
So, how do you price your lemonade to maximize profit and not ruin your relationship with neighbors?
An optimal price calculator helps you find the perfect balance between profitability and customer satisfaction.
Optimal Price Definition
Optimal pricing is finding a price point that balances maximizing sales revenue and profit.
Often, in an attempt to maximize your profit, you can hurt customer satisfaction. Optimal pricing considers this and helps you define the maximum price without damaging the demand.
You must analyze market conditions, competitor behavior, and customer willingness to pay to create strategic pricing.
Implementing periodic price changes could align with seasonal demand shifts or cost variations. Using demand elasticity insights, you can predict how price changes will impact the quantity sold and overall profit.
The Optimal Pricing Formula
To determine the optimal price for your product, you can use a straightforward formula that combines several key elements: demand and costs.
Optimal price formula:
Optimal Price = Marginal Cost * (Price Elasticity of Demand / (Price Elasticity of Demand + 1))Where:
- Marginal Cost: The cost of producing one additional unit.
- Price Elasticity of Demand (PED): A measure of how sensitive the quantity demanded is to a change in price.
- Marginal Revenue: The additional revenue generated from selling one more unit. This is the same as the marginal cost for the optimal price calculation.
The formula to calculate PED is:
PED = % Change In Quantity Demanded / % Change In PriceCalculating Optimal Price: A Step-by-Step Example
Let’s calculate the optimal price for a product using a simple example. Imagine you own a small bakery and want to determine the best price for muffins.
You have played with your pricing and monitored how the muffin demand has fluctuated at different price levels.
You know that you could sell 50 muffins per day at $4 per muffin, but when you increased the price to $7 per muffin, you only sold 15 muffins in a day.
After considering fixed and variable costs, your marginal cost of producing one additional muffin is $2.
Let’s put this all together.
- Marginal Costs: $2 per muffin
- Initial Price: $4 per muffin
- Initial Demand: 50 muffins
- Final Price: $7 per muffin
- Final Demand: 15 muffins
Now, let’s calculate our optimal price, but before, we need to calculate the price of elasticity demand.
PED = ((15 - 50) / ((50 + 15) / 2)) / (($7 - $4) / (($7 + $4) / 2)) = -0.7 / 0.75
PED = (-35 / 32.5) / ($3 / $5.5)
PED = -1.0769 / 0.5454
PED = -1.9745The price of elasticity demand is -1.9745.
Now that we have all the variables, let’s plug it into our optimal price formula:
Optimal Price = $2 * (-1.9745 / (-1.9745 + 1)
Optimal Price = $2 * 2.0262
Optimal Price = $4.05The optimal price is $4.05 per muffin, but how many muffins can you sell for that price?
First, we need to calculate the percentual price difference:
% Price Change = (($4.05 - $4) / $4) * 100 = 1.25%Now, calculate the percentage difference in quantity using PED:
% Quantity Change = PED × % Price Change
% Quantity Change = -1.9745 * 1.25%
% Quantity Change = -2.46%The expected quantity change is -2.46%.
With this information, we can now calculate the quantity we can expect to sell for the optimal price:
Optimal Quantity = 50 + (-2.46%/100 * 50) = 48.77 muffinsThe expected sold quantity for the new price is 48.77 muffins, but let’s round it to 49 since you cannot sell partial muffins.