1. marginal revenue at that quantity must be positive.
2. marginal revenue at that quantity must be negative.
3. marginal revenue at that quantity can be either positive or negative.
Choose the option that yields the correct answer.
The correct answer is option 1. Suppose we increase the quantity sold by one unit. If the elasticity of demand is greater than unity in absolute value, the percentage fall of the price will be less than the percentage increase in the quantity. The percentage increase in total revenue due to the increase in quantity must therefore be greater than the percentage reduction in total revenue due to the decline in price. So total revenue will increase along with the increase in quantity. The change in the total revenue divided by the change in the quantity---that is the marginal revenue---will therefore be positive.
From the definition of elasticity,
Φ = ( ΔQ / Q ) / ( ΔP / P ).
This implies that
( ΔP / P = ( ΔQ / Q ) / Φ
which means that if Φ < -1 then ΔP / P must be less than ΔQ / Q in absolute value. To an approximation, the relative change in total revenue can be expressed
ΔTR / TR = ΔP / P + ΔQ / Q
Since ΔP / P is negative but smaller in absolute value than the positive ΔQ / Q , total revenue must increase as quantity increases and marginal revenue must therefore be positive.