# What is the relationship between the price elasticity of demand and total revenues?

Price elasticity of demand and total revenue :
-Elasticity of demand is important because it predicts what may happen to total revenue received when a company
changes the price of a product.

-When the price elasticity of demand for a good is inelastic (|Ed| < 1), the percentage change in quantity is smaller than that in price. Hence, when the price is raised, the total revenue of producers rises, and vice versa.

-When the price elasticity of demand for a good is elastic (|Ed| > 1), the percentage change in quantity is greater than that in price. Hence, when the price is raised, the total revenue of producers falls, and vice versa.

-When the price elasticity of demand for a good is unit elastic (or unitary elastic) (|Ed| = 1), the percentage change in quantity is equal to that in price. Hence, when the price is raised, the total revenue remains unchanged. The demand curve is a rectangular hyperbola.

-When the price elasticity of demand for a good is perfectly elastic (Ed is undefined), any increase in the price, no matter how small, will cause demand for the good to drop to zero. Hence, when the price is raised, the total revenue of producers falls to zero. The demand curve is a horizontal straight line. A ten-dollar banknote is an example of a perfectly elastic good; nobody would pay \$10.01, yet everyone will pay \$9.99 for it.

-When the price elasticity of demand for a good is perfectly inelastic (Ed = 0), changes in the price do not affect the quantity demanded for the good. The demand curve is a vertical straight line; this violates the law of demand. An example of a perfectly inelastic good is a human heart for someone who needs a transplant; neither increases nor decreases in price effect the quantity demanded (no matter what the price, a person will pay for one heart but only one; nobody would buy more than the exact amount of hearts demanded, no matter how low the price is).
If Price Elasticity is > 1 then total revenues falls with increase in price (elastic - people stop buying with higher prices)

If Price Elasticity is = 1 then total revenues stay the same (unitary elastic, the change in demand is exactly the same quantity change in the opposite direction as the change in price)

If Price Elasticity is < 1 then total revenues rises with increase in price (inelastic - people still buy with higher prices)
Epd/TR= (d x/dp) x (p/q) / (Total income - Total Costs)
An axiom on costs is necessary.
Case Epd>1 Demand rises when prices rise. This case refers to some particular Giffen goods. Revenues rise.
Case Epd=1 Demand increases at the rate price does. Revenues fall down. Costs cannot be reduced quickly .
Case Epd<1 Demand falls when prices rise. Revenues fall
down in the short run.

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