If you need price elasticity of demand, profit at initial price and profit at optimal price and you already have final price, final quantity, initial price, initial quantity and optimal quantity, this calculator does the substitution for you. It suits a quick check, a homework answer you want to confirm, or any figure you need to sanity test.
What Is the Optimal Price Calculator?
The optimal price calculator takes final price, final quantity, initial price, initial quantity and optimal quantity and turns them into price elasticity of demand, profit at initial price and profit at optimal price.
It is the kind of calculation you would otherwise do on the back of an envelope: mechanical, repeatable and easy to get subtly wrong without noticing.
How the Optimal Price Figure Is Built
Each result is calculated from the ones before it, so the working is fully visible. That matters when the answer is going to be quoted to somebody else and you need to be able to explain where it came from.
The figures are exactly as good as the assumptions underneath them. Check the rates, the periods and the tax treatment before you rely on the result.
Reading the Result Sensibly
A small change in an input can move the result by much more than you would expect, particularly where the calculation divides by one of the figures you supplied. That is worth understanding before you rely on a figure.
For anything that will be committed to, write the inputs down beside the result. A number you can reproduce is worth far more than one you cannot explain.
A Worked Example
Working through an example, with final price set to 10, final quantity set to 5, initial price set to 2, the calculator returns price elasticity of demand of -1.35714, and optimal price of 6.06, and marginal revenue of 1.59. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out price elasticity of demand?
Enter final price, final quantity, initial price, initial quantity and optimal quantity. The calculator then works through the relationship and reports price elasticity of demand, profit at initial price and profit at optimal price.
What does the optimal price actually calculate?
It takes final price, final quantity, initial price, initial quantity and optimal quantity and converts them into price elasticity of demand, profit at initial price and profit at optimal price using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter final price?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Can I use this for a quick estimate as well as a precise answer?
Yes. The calculator is built for quick checks, so round your inputs to a sensible number of significant figures and the result will be just as useful. If you need more precision, keep the same method and add digits to the inputs rather than adjusting the method itself.
Do I have to fill in every field?
Only the fields a particular result depends on. If you leave one blank, the results that need it simply show a note instead of a number, and everything else still works.