# Aspire incorporated is into education consultancy. In 2011, ABC charges consultancy fee of $1000 per service rendered to each customer. A total of ten (10) institutions registered with Aspire in...

Aspire incorporated is into education consultancy. In 2011, ABC charges consultancy fee of $1000 per service rendered to each customer. A total of ten (10) institutions registered with Aspire in 2011. An economic research firm has estimated that the price elasticity for the company's services as at January 2012 is -2.5. As the chief marketing of Aspire, You are required to a. Use the arc elasticity of demand formulae to determine the price the company should charge if it wants to increase the customer base to 20 institutions b. Calculate the change in total revenue if the new price is implemented.

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Arc elasticity of demand is given as:

n = {(Q1-Q0)/[(1/2)(Q1+Q0)]}/{(P1-P0)/[(1/2)(P1+P0)]}

where, n is arc elasticity of demand = -2.5 (given)

Q1 is new quantity = 20

Q0 is the older quantity = 10

P1 is the new price charged

P0: original price charged = $ 1000

Substituting everything into the above equation, we get:

-2.5 = {(20-10)/[(1/2)(20+10)]}/{(P1-1000)/[(1/2)(P1+1000)]}

solving which, we get: P1 = **$765** (rounded to nearest dollar)

Total revenue earlier = 10 x $1000 = $10,000

New revenue = 20 x $ 765 = $ 15,300

Thus, change in revenue = $ 15,300- $ 10,000 = **$ 5,300**.

Hope this helps.