Question

The following is annual financial information for a cell phone repair company that has hired you to conduct some pricing analysis for them. Take this information to answer the following questions. Total Number of repairs................ 3,500 Average price for repairs................ $200 Variable cost for repairs.................. $50 Fixed cost............................... $300,000

1. Assume number of repairs increased to 4,550 at the 20% markup price calculated above. Calculate price elasticity of demand. (5 points)

2. If the company wants to raise the original price by 20%, what would the new price be? (6 points)

Answer 1

Given:

Number of repairs = 3,500

Average Price for repairs = $ 200

Variable cost for repairs = $ 50

Fixed cost = $ 300,000

Solution 1:

Assuming number of repairs increased to 4,550 at the 20% markup price,  price elasticity of demand = ?

Price elasticity of demand measures the change in the demand with respect to the changes in the Price and is given by:

Where, % change in demand quantity is given by:

[(Old Demand- New Demand) / (Old Demand)] * 100

In this case, Old Demand = 3,500

New Demand = 4,550

Hence, % change in demand quantity = [(4550-3500)/3500]*100 = [1050 / 3500] * 100 = 30%

Percentage Change in Price is given by:

[(Old Price- New Price) / (Old Price)] * 100

Old Price = $ 200

New Price = 20% Markup price

Hence,

Here, Cost per Unit can be calculated as follows:

Cost per unit = Variable cost per unit + Fixed cost per unit

Cost per unit = Variable cost per unit + (Total Fixed cost / number of units)

Cost per unit = 50 + (300000/4550)

Cost per unit = 115.93

Hence, Selling Price = 20% * 115.93 + 115.93

Selling Price (New) = 139.12

Hence, Percentage change in Selling Price is given by:

[(Old Price- New Price) / (Old Price)] * 100

=[(139.12 - 200) / 200]* 100

= -30.44%

Hence, Price elasticity of Demand = 30% / (-30.44%) = -1.105

Solution 2:

It the company wants to raise the original price by 20%, New Price = ?

New Price = Old Price + 20% * Old Price

New Price = 200 + 20% * 200

New Price = 200 + 40

New Price = $ 240