Question

Suppose seller decreas price by 10% then hiw total revene will affect when ed =1.5 or ed=0.5 or ed=1

Answer 1

$ed = \frac{\% change \space in\space quantity \space demanded}{\% change \space in\space price}$

Here ed is the price elasticity of demand

Since the initial price and quantity are not given let us assume that the price initially was 10 and the quantity was 100.

Thus the initial revenue would be = Price × Quantity demanded

initial revenue $= 10 × 100 = 1000$

When ed = 1.5

% change in price = 10%

$ed = \frac{\% change \space in\space quantity \space demanded}{\% change \space in\space price}$

% change in quantity demanded =  ed × % change in the price

% change in quantity demanded $= 1.5 × 10 = 15$

New revenue = New price × New quantity demanded

New price $= 10−10\%\space of\space 10 = 10−1 = 9$

New quantity demanded $= 100+15\%\space of\space 100 = 100+15 = 115$

New revenue $9 × 115 = 1035,$

% Change in total revenue$=\frac{new \space revenue-initial \space revenue}{initial \space revenue}$

$=\frac{1035-1000}{1000}\times100=\frac{35}{100}\times 100=3.5\%$

Thus we can say that when ed = 1.5 with the decrease in the price level by 10% the total revenue increased by 3.5%. 

When ed = 0.5

% change in price = 10%

$ed = \frac{\% change \space in\space quantity \space demanded}{\% change \space in\space price}$

% change in quantity demanded =  ed × % change in the price

% change in quantity demanded $= 0.5 × 10 = 5$

New revenue = New price × New quantity demanded

New price $= 10−10\%\space of\space 10 = 10−1 = 9$

New quantity demanded $= 100+5\%\space of\space 100 = 100+5 = 105$

New revenue $9 × 105 = 945$

% Change in total revenue$=\frac{new \space revenue-initial \space revenue}{initial \space revenue}$

$=\frac{94-1000}{1000}\times100=\frac{-55}{100}\times 100=-5.5\%$

Thus we can say that when ed = 0.5 with the decrease in the price level by 10% the total revenue decreased by 5.5%. 

When ed = 1

% change in price = 10%

$ed = \frac{\% change \space in\space quantity \space demanded}{\% change \space in\space price}$

% change in quantity demanded =  ed × % change in the price

% change in quantity demanded $= 1 × 10 = 10$

New revenue = New price × New quantity demanded

New price $= 10−10\%\space of\space 10 = 10−1 = 9$

New quantity demanded $= 100+10\%\space of\space 100 = 100+10 = 110$

New revenue $9 × 110 = 990$

% Change in total revenue$=\frac{new \space revenue-initial \space revenue}{initial \space revenue}$

$=\frac{990-1000}{1000}\times100=\frac{-10}{100}\times 100=-1\%$

Thus we can say that when ed = 1 with the decrease in the price level by 10% the total revenue decreased by 1%.