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!