Price elasticity why is it possible for a business to increase total revenue by reducing price?

Question

Using the concept of price elasticity of demand explain why is it possible for a business to increase total revenue by reducing prices at high prices, but increase total revenue by raising prices at low prices

Answer 1

Price elasticity is measued as E=  (ChD/D)/ /ChP/P) where E stands for elasticity, Ch stands change in D stand for Demand and P for Price.

Now assume that the absolute value of  E is  >1.

Now, Consider Revenue R eqals Price* Demand,

If you  know differential Calculus, then

Change in Revenue/ Change in price

=price *( Change in Demand/ Change in Price)

+  Demand * (Change in price/ Change in price)

or, ChR/ChP = P*(ChD/ChP) + D * (1)

= D [ (ChD/ChP)*(P/D) +1}

= D [E  +1 ]  But value of E is negative, but its absolute value is >1.  So, [E+1] > 0 i.e,  negative . Therefore, D [E  +1 ] <0.

Therefore, Change in Revenue/ Change in Price is a negative number. Which means if the price is reduced, Revenue will increase ( movement in oppositive direction).

You can undestand this very intuitively. When the elasticity is high ie. E<0 but its absolute value is >1, a reduction is price, will lead to proportionately higher increase in demand. This means the effect of a lower price on reduction of  revenue will be more than offset by the increase in revenue resulting more than proportionate increase in demand. When the price is high, a small reduction in price will lead to a higher increase in demand and thus increase revenue. At low level of price, a price increase of the large magnitude would be required to increase revenue to compensate for the fall in demand due to price rise.

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