# Microeconomics : Total revenue for unit elasticity

I recently read in my microeconomics book that when elasticity = 1, total revenue remains the same. However, I am unable to follow this.

I have two questions on this concept:

Question#1- Let's take an example: at equilibrium, price = 1.0 dollars per unit; Quantity = 1000 units. Total revenue = $1000 If I increase my price by 50%, then the new price =$1.5 per unit.

Elasticity = -1 = (%change in quantity) / (%change in price)

Therefore, % change in quantity = -50%, meaning the new quantity = 500 units.

Total revenue = $1.5*500 = 750 dollars! This is a change of 25% ---pretty significant change in the total revenue! What am I missing? Question #2 - Moreover, I also noticed that the new elasticity at Price =$1.5 and Quantity = 500 units will be equal to (Price) / (Quantityslope). (Assuming slope = constant = -1/1000 from example #1 above), elasticity = 1.5(-1000)/500 = -3. This makes sense theoretically, but I would like to confirm with experts that when we change prices, the elasticities at the new point of intersection also change.

NB: Slope = 1/1000 because if elasticity = -1 at P=$1 and Q=1000 units, and elasticity for a linear downward-sloping demand curve = P/(Q*Slope), then Slope = -1/1000. Is this correct? Can someone please help me with the two questions above. I would really appreciate any help. I did research this website thoroughly before posting this question. I am really stuck. Thanks in advance. ## 1 Answer Your formula is not quite right. It should be, when price increases by X percent, quantity decreases by an amount to keep P*Q the same. That is an **inverse ** (or reciprocal) function. In your example, P goes from$1.00 to $1.50. Q should go from 1000 to 666 2/3, not 500. Then 666 2/3 times$1.50 equals your original revenue of 1000.

As a check, 1000 divided by 666 2/3 = 1.5. So 666 2/3 is two-thirds of 1000.