Question

# 3. For each of the following cases, what is the expected impact on the total revenue...

3. For each of the following cases, what is the expected impact on the total revenue of the firm? Besides showing numerical values, please explain your reasoning.

a. Price elasticity of demand is known to be -0.5, and the firm raises price by 10 percent.

Price elasticity of demand = % change in quantity demanded / % change in price

Given elasticity=-0.5 and % change in price=10%. Thus % change in quantity demanded=-0.5*10=-5% or the quantity demanded will fall by 5%.

Total Revenue TR=Price*Quantity=p*q

In percentage terms the above relation can be written as : % change in TR= % change in p + % change in q

So % change in price is 10 % and % change in quantity is -5% and hence the % change in TR=10+(-5)=5% or Total revenue increases by 5%.

This happens because demand elasticity is less than 1 in absolute value and so for any percentage change in price, the percentage change in quantity demanded will always be less. So when price increases by 10%, the quantity demanded falls by 5%. But the positive impact of price rise on total revenue outweighs the negative impact of fall in quantity and as a result total revenue rises.

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