according to the theory (if p-p1=q-q1), the total revenue remains the same because the demand decreases by the same percentage price does. If this is the elasticity of a product, the company increasing prices will lead to a decrease in demand but the total revenue will remain the same but the amount spent on producing these products decrease when the demand decreases corresponding to the increase in price.. so since the company is now spending less in the production, isn't it more profitable to increase the price than not change the price?
The theory says that total revenue remains the same. That is not the same as claiming total profit is same.
Total revenue is by definition given as a price times quantity: $R=PQ$.
Total profit on the other hand is given as total revenue minus total costs: $\Pi= PQ -TC$.
Total revenue won’t change when demand is unit elastic (for small changes from current point), but total profit can change.