Question

If demand is elastic, a reduction in price causes total revenue to rise because:

A)the percentage decrease in price exceeds the percentage increase in quantity demanded.

B) demand is unresponsive to changes in price.

C)the percentage increase in quantity demanded exceeds the percentage decrease in price.

D)the percentage changes in quantity demanded and price are the same.

Answer 1

Answer: C) the percentage increase in quantity demanded exceeds the percentage decrease in price.

If demand is elastic, a reduction in price causes total revenue to rise because the percentage increase in quantity demanded exceeds the percentage decrease in price.

The quantity demanded of a good is the function of its price, i.e. Q = f(P) .....(1)

The price elasticity of demand($\varepsilon$_d) for a good is the responsiveness of the change in quantity demanded of a good for the change in its price.

$\therefore$$\varepsilon$_d = - (dQ / Q) / (dP / P)

Or, $\varepsilon$_d = -(dQ / dP) * (P/Q)

The total revenue(R) is the product of price(P) of the good and quantity sold(Q) of the good.

$\therefore$ R = P * Q

Or, R = P * f(P) , from equation (1)

Now, dR / dP = P * f^'(p) + f(P)

Or, dR / dP = P * f^'(p) + Q , as Q = f(P)

Or, dR / dP = [Q{P/Q * f^'(p)} + 1] ....(2)

Now, from equation (1) , f(P) = Q

$\therefore$ f^'(P) = dQ / dP

So, we can write equation(2) as,

dR / dP = [Q{P/Q * dQ / dP} + 1]

Now, $\varepsilon$_d = - (dQ / dP) * (P/Q)

$\therefore$ dR / dP = Q( - $\varepsilon$_d + 1)

Or, dR / dP = Q(1 - $\varepsilon$_d)

When the price elasticity of demand for a good is elastic, then the percentage change in quantity demanded is more than the percentage change in price.

$\therefore$$\varepsilon$_d$>$1 , when price elasticity of demand for a good is elastic.

$\therefore$ Q(1 - $\varepsilon$_d) $<$0

Or, dR / dP $<$0 , when  $\varepsilon$_d$>$1

So, when demand is elastic, the change in revenue and change in price move in opposite direction, i.e. a reduction in price causes total revenue to rise.

_________________________________________________________