If there is a price increase then the decrease in quantity is bigger than the increase in price, the revenue decrease. If there is a price decrease then the increase in quantity is bigger than the decrease in price, the revenue increase.
If there is a price increase then the decrease in quantity is smaller than the increase in price, the revenue increase. If there is a price decrease then the increase in quantity is smaller than decrease in price, the revenue decrease.
P(1-1/e), this expression is a numerical relationship between marginal revenue and elasticity which can be used in place of MR in the marginal analysis rule MR > MC, and MR < MC.
The expression interpretation is that the left side of the expression shows the current margin of price over marginal cost, (P-MC)/P, and the right side is desired margin, 1/e (inverse of elasticity). If the current margin is greater than desired margin means that the MR>MC so reduce price, if the current margin is less than the desired margin then increase price since MR<MC.
Shows how many units you can lose before an increase in price becomes unprofitable. It is a function of the magnitude or size of price increases and the contribution margin: Percentage change in quantity = percentage change in Price / (percentage change in Price + margin), margin = (P-MC)/P.
If there is an increase in price and the expected decrease in quantity demanded is smaller than the stay even quantity, the price increase is profitable. The stay-even shows what changes in quantity demanded support a given change in price. The elasticity estimates on the other hand shows what quantity changes will be.
Cost based pricing: Many companies use cost-based price which is cost plus desired fixed margin for each unit of product equal price per unit. The marginal analysis specifically optimal price which is MR = MC or (P-MC)/P = 1/e do consider both cost structure and consumer demand.