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Demand Elasticity :sample question on ATM fees

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The non-customer demand for an ATM transactions is Q = 19,000 - 6,000P. Right now the company handles 10,000 non-customer ATM transactions per day at a fee of $1.50.

a. What is the own price elasticity for ATM fees charged to non-customers? At the current ATM fee, should you raise or lower your ATM fees? Why?

b. What should your new ATM fee be if your marginal cost of servicing an ATM transaction is $0 (zero) and you are only considering maximizing profits derived from ATM fees?

Please show your work.

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Solution Summary

The solution calculates own price elasticity and the price for maximizing profits.

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Please see the attached file.
a. What is the own price elasticity for ATM fees charged to non-customers? At the current ATM fee, should you raise or lower your ATM fees? Why?

Point price elasticity = (- delta Q / Q ) / ( delta P /P) = ( -delta Q / delta P ) * ( P/Q)

Q = 19,000 - 6,000P --- (Given)
differentiating Q with respect ...

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