Question

Now, you probably noticed something very interesting while playing with the graph. Revenues are maximized when the price is $50—exactly halfway down the demand curve. And, at that price, the elasticity of demand is exactly 1!

Revenue-Maximizing Prices and Demand Elasticity

Is this a coincidence? What’s magical about the price at which elasticity equals 1? Think about why this would be the revenue-maximizing price.

What is the intuition for why elasticity is 1 at the revenue-maximizing price?

Answer 1

At the price elasticiy of 1, the gain made from increasing the price is compensated by decrease in quantity, so to speakwe arrived at optimization point on the curve.

lets say elasticity is 2, at this point increasing , if P increases by 1%, Qd will decrease by 2 %.. Similarly, if P decreases by 1%, Qd will increase by 2%. And If the firm decrease price, then the loss from price effect is smaller than the gain from quantity effect, so this change increase firm's profit.

if the price elasticity of demand is -0.2, that means, if P increases by 1%, Qd will decrease by 0.2%.. Similarly, if P decreases by 1%, Qd will increase by 0.3%. So If the firm increase price, then the gain from price effect is larger than the loss from quantity effect, so this change increase firm's profit.