Chapter 19, Problem 19.1LO

To determine

The relationship between the price elasticity of demand and total revenue

Concept Introduction:

Price Elasticity of Demand – If for a one unit change in the price, the demand increases more than proportionately the demand is said to be elastic. If however, the responsive change in demand is less than proportionate the demand is said to be inelastic while it is said to be unit elasticity if the percentage change in demand is equal to the percentage change in price. If elasticity is ‘e’ then it is defined as:

$e=\frac{\%\Delta Q}{\%\Delta P}$

If e > 1, the demand is elastic

e < 1, the demand is inelastic

e = 1, the demand is unit elastic

e → ∞, the demand is perfectly elastic

e = 0, the demand is perfectly inelastic

Total Revenue- It is the total earnings of the producer/seller by selling Q units of output each at a price of P. Functionally, it is written as:

$TR=QXP$

Explanation of Solution

➢ If the Price Elasticity of Demand is greater than one, an increase in the price causes the TR to fall while a reduction in the prices causes the TR to increase.

➢ If the Price Elasticity of Demand is less than one, an increase or decrease in the prices does not affect the TR much.

➢ If the Price Elasticity is infinite, a minimal change in the price causes the TR to change infinitely.

➢ If the Price Elasticity of Demand is zero, the TR changes significantly.

If the Price is increased by 1 Percent;

$e=\frac{\%\Delta Q<1}{1\%\Delta P}<1$, then TR would rise.

$e=\frac{\%\Delta Q>1}{1\%\Delta P}>1$, then TR would fall

$e=\frac{\%\Delta Q=0}{1\%\Delta P}=0$, then TR would rise significantly

$e=\frac{\%\Delta Q\to \infty }{1\%\Delta P}\to \infty$, then TR would fall infinitely→0

If the Price is decreased by 1 Percent;

$e=\frac{\%\Delta Q<1}{1\%\Delta P}<1$, then TR would rise.

$e=\frac{\%\Delta Q>1}{1\%\Delta P}>1$, then TR would fall

$e=\frac{\%\Delta Q=0}{1\%\Delta P}=0$, then TR would rise significantly

$e=\frac{\%\Delta Q\to \infty }{1\%\Delta P}\to \infty$, then TR would fall infinitely→0