# How to maximize revenue by changing price?

I run a SaaS and I have the following data from it: Number of trials (A), number of subscribers (B), subscribe cost (C) and total revenue (D) for every type of service my SaaS provide. If I increase (C) it can reduce (B) and in result I can get less (D). So, is there a way to find balanced (C) to maximize (D)? Also I think there is some dependency between (A) and (B) that shows subscribers solvency.

Your question does not provide enough information for me to walk you through the process step-by-step using your information, but hopefully I can point you in the right direction.

You question about Price Elasticity of Demand (usually just called Elasticity of Demand). Elasticity of Demand is used to show how responsive demand is to a change in price. For example, if a $1\%$ increase in price leads to a massive drop in the quantity demanded, say 75%, then we would say that the demand is relatively elastic. If an increase in price does not really cause a drop in the quantity demanded then demand is relatively inelastic. The concept of elasticity of demand translates to your question because $price\ multiplied\ by\ quantity\ equals\ revenue$.

You mention that if you increase $(C)$, you reduce $(B)$. Yes, this is (usually) correct because the relationship between price and quantity is negative-- the higher the price, the fewer items sold. As for reducing $(D)$, this depends on the elasticity of demand. For example,

Assume the price for each subscription is $\$2$. Assume that at a price of$\$2$, you sell $1,000$ subscriptions. This gives you a revenue of $\$2,000$: $$\2( 1,000)=2,000$$ Elasticity demand can be calculated a few ways, I'm going to use: $$Elascitity\ of\ Demand = {\frac {{\mathrm {Percent\ Change\ in\ }}Q}{{\mathrm {Percent\ Change\ in\ }}P}}$$ Where$Q$is quantity demanded and$P$is price. Lets consider the following two examples: Scenario 1: Assume that you increase the subscription price from$\$2$ to $\$3$. Now assume that an increase in price from$\$2$ to $\$3$decreases the total number of subscriptions sold from$1,000$to$960$. Notice that the number of subscriptions decreased, but revenue increased from$\$2,000$ to $\$2,880$: $$\3(960)=2,880$$ This happened because the demand for subscriptions is considered inelastic. Price by 50% [$(3-2)/2$], and your quantity decreased by 4% [$(960-1000)/1000$]. Since the percent of the price increase increased by more than the quantity demanded decreased, you increased your revenue. Your elasticity of demand in this scenario is, $$\frac {\mathrm -0.04}{\mathrm 0.50}=-0.08$$ Scenario 2: Assume that you apply the same price increase from$\$2$ to $\$3$per subscription, but this time the quantity sold drops from$1,000$to$400$. Your revenue is now,$\$1,200$ $$\3(400)=1,200$$ In this case an increase in price caused your revenue to decrease. What happened? In this case subscriptions are considered elastic. The price increased by 50% [$(3-2)/2$], and your subscriptions demanded decreased by 60% [$(960-1000)/1000$].Your elasticity of demand in this scenario is, $$\frac {\mathrm -0.6}{\mathrm 0.50}=-1.5$$

To answer your question, you are looking for the place on your demand curve where the % change in price is the same as the percent change in quantity demanded. This is point is called Unit Elastic. In order to calculate this for yourself, you will need to know the relationship between the price of subscriptions and the quantity demanded.

Consider reading more about elasticity of demand as there are a couple of ways to calculate it. When you do the calculations you will get an elasticity of demand number that ranges from $0$ to $-∞$. (Some people will convert these numbers to absolute value... $0$ to $∞$, means the same thing.) The number you get from calculating your elasticity of demand will tell you what to do with your price. For example, if you get an elasticity of demand number that is greater than $-1$ (or less than $1$ if you use absolute value), then increase your price because revenue should increase. If you get back an elasticity of demand number less than $-1$ (or greater than $1$ if you use absolute value) then decrease your price and your revenue should increase. You want to adjust your price until your elasticity of demand number is $-1$ (or $1$ if you use absolute value). $-1$ is the point of unit elastic.

In Microsoft Excel there is a function named Solver that can give you a very accurate measurement of how to maximize profit with a change in price given the products/service price, number of consumers. You would have to input the these constraints in a changeable column and input the constraints of what you want to maximize, minimize in the solver constraints that are located inside the Solver Parameters option.