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Q = 12S1/2P-2. Q is number of newspapers sold and S is number of inches of news printed. The cost of reporting S units is $10S. The cost of printing one copy of the newspaper is $0.08, so the total cost of Q = $10S + .08Q.
What is the price elasticity of demand?

User Yngccc
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1 Answer

7 votes

Okay, here are the steps to solve this:

1) Identify the variables:

Q = number of newspapers sold

S = number of inches of news printed

Cost of reporting S units = $10S

Cost of printing 1 copy = $0.08

Total cost = $10S + 0.08Q

2) Write the demand function:

Q = 12S1/2P-2 (given)

3) Find the price elasticity of demand (PED):

PED = % change in quantity demanded / % change in price

= (∆Q/Q) / (∆P/P)

4) We need to calculate ∆Q and ∆P in terms of S:

∆Q = 12∆S1/2 (take derivative of demand function)

∆P = 10∆S + 0.08∆Q (take derivative of total cost)

5) Substitute into PED formula:

PED = (12S1/2 ∆S1/2) / (10S ∆S + 0.08(12S1/2 ∆S1/2))

= -2

Therefore, the price elasticity of demand is -2.

Does this make sense? Let me know if you have any other questions!

User RubenDG
by
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