Question

At $80 , a firm can sell 4,715 stereo earphones (3.5 mm for android). At this price, elasticity is estimated at 2.2. What is the change in total revenue (+ or -) if the firm drops price by 12%? Round your answer to the nearest dollar.

At $171, a firm can sell 19,195 stereo earphones (3.5 mm for android). These are premium earphones, guaranteed for 5 years. At this price, elasticity is estimated at 0.4. What is the change in total revenue (+ or -) if the firm drops price by 10%?

Answer 1

Solution:

Situation 1:

Here the Elasticity is 2.2

Old quantity is 4,715 stereo at $80

Price drops by 12%

Step 1: Computation of Change in quantity

Elasticity = % change in quantity/% change in price

2.2 = % change in quantity / 12

So, % change in quantity is 26.4%

So, the change in quantity is 4,715*26.4% = 1,244.76 stereo

Step 2: New Quantity computation

New quantity = old quantity + change in quantity (as the elasticity is positive)

= 4,715 + 1,244.76

= 5959.76 stereos

Step 3: New Price Computation

New Price = Old price - Change in price

= $ 80 - ($80*12%)

= $80 - $9.6

  = $70.4

Step 4: Old revenue Computation

Old revenue = Old Quantity * Old Price

= 4,715 * $ 80

= $377,200

Step 5: New Revenue Computation

New revenue = New Quantity * New Price

= 5959.76 * $70.4

= $419,567.104

Step 6: Computation of total change in revenue

Change in Total Revenue = New Revenue - Old revenue

= $ 419,567.104 - $377,200

= $ 42,367.104 or $ 42,367

So, the change in total revenue when there is a price drop by 12% is $ 42,367. That is an increase in revenue.

Situation 2:

Here the Elasticity is 0.4

Old quantity is 19,195 stereo at $171

Price drops by 10%

Step 1: Computation of Change in quantity

Elasticity = % change in quantity/% change in price

0.4 = % change in quantity / 10

So, % change in quantity is 4%

So, the change in quantity is 19195*4% = 767.8 stereo

Step 2: New Quantity computation

New quantity = old quantity + change in quantity

= 19195+767.8

= 19962.8 stereos

Step 3: New Price Computation

New Price = Old price - Change in price

= $ 171 - ($171*10%)

= $171 - $17.1

  = $153.9

Step 4: Old revenue Computation

Old revenue = Old Quantity * Old Price

= 19,195 * $ 171

= $3,282,345

Step 5: New Revenue Computation

New revenue = New Quantity * New Price

= 19962.8 * $153.9

= $3,072,274.92

Step 6: Computation of total change in revenue

Change in Total Revenue = New Revenue - Old revenue

= $ 3,072,274.92 - $3,282,345

= -$210,070.08 or -$210,070

So, the change in total revenue when there is a price drop by 10% is -$210,070. That is a decrease in revenue.