# Optimal Price Calculator

By Bogna Szyk
Last updated: Nov 03, 2020

Whether your business provides customers with physical products, intangible goods, or a service, your main goal is always the same: maximum profit. This optimal price calculator will help you maximize your profit by analyzing the patterns of price vs. demand relationship.

In this article, we will explain to you how to find the optimal price and accompanying quantity of units sold. Once you'll get a result, you can immediately use it to adjust the prices and enjoy maximized total profit!

## What is the optimal price?

By definition, optimal price is the price per unit at which the overall profit (calculated as quantity multiplied by unit price) is maximized.

Let's consider two shops selling notebooks, located at two sides of the same street. One of them sells high-quality notebooks at a price of \$15 per unit. The other one sells very basic notebooks at \$3 per unit.

As you can expect, the shop with luxury notebooks will sell fewer notebooks per month. Still, their revenue per unit is high enough to allow for selling only a small quantity. The second shop, on the other hand, needs to sell a lot of notebooks to make a profit. Low price causes more customers to buy in their shop.

Each of the two shops makes a certain profit. The question they both could be asking - and that gets answered by our calculator - is:

At what price should I sell my product to optimize the profit?

## How to find the optimal price

If you want to use this maximum profit calculator to determine the optimal price, you need to provide it with the following values:

1. Marginal cost: this is the cost of producing one additional unit of your product. Typically, this cost is lowered with every item produced.

2. Marginal revenue: revenue generated by selling one additional unit. For an optimal price, the marginal revenue is equal to the marginal cost.

3. Initial price and quantity: the initial behavior of the sales process - the price at which the product was sold, and the quantity that you managed to sell.

4. Final price and quantity: the price of the product after a price change and the corresponding demand.

Basing on this input, our optimal price calculator will determine the results:

1. Price elasticity of demand: optimal price is highly dependent on the elasticity of demand. In short, this value describes the relationship between price and demand for a certain product.

2. Optimal price: the price that you should sell your product at. It is calculated with the following formula:

`OP = MC * (PED / (PED + 1))`

where OP is the optimal price, MC is the marginal cost, and PED stands for price elasticity of demand.

1. Optimal quantity: the actual number of units you will be able to sell at the optimal price.

2. Profit at initial and final price: the profit generated when selling your product at the initial or final price.

3. Profit at optimal price: the profit generated when selling your product at the optimal price. It is calculated with the use of the following equation:

`profit = (OP - MC) * OQ`

where OP is the optimal price, MC is the marginal cost, and OQ is the optimal quantity.

Remember that the profit calculation does not show you the actual profit, as it assumes that every unit is produced at the same cost. If you want to analyze your profit in more detail, check the margin calculator and markup calculator.

Bogna Szyk
Marginal costs
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Marginal revenue
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Price elasticity of demand
Initial price
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Initial quantity
Final price
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Final quantity
Price elasticity of demand
Optimum
Optimal price
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Optimal quantity
Profit
Profit at initial price
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Profit at final price
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Profit at optimal price
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