Explanation Given Information: The provided expression is the demand function for a fixed period of time is given by p = 30 − q and the supply function before taxation is p = 6 + 2 q . Formula Used: The following procedure are used to maximizing total tax revenue, Step-1 Write the supply function after taxation, Step-2 Equate the demand function and new supply function to get number of units and tax. Step-3 Calculate the total revue function T that will be product of number of units and tax. Step-4 Calculate the derivative of revenue function and set equal to zero and solve. Step-5 Calculate second derivative test to verify the result. Calculation: The provided expression is p = 6 + 2 q , After the taxation, the supply function is equal to p = 6 + 2 q + t . The demand function will meet the new supply function is: Put the new supply (after taxation) equal to the demand. 6 + 2 q + t = 30 − q Solve to equation further to get the value of t, Add − 30 + q on both the sides, 6 + 2 q + t + ( − 30 + q ) = 30 − q + ( − 30 + q ) 6 + 2 q + t + ( − 30 + q ) = 0 Deduct t from both the sides, 6 + 2 q + t + ( − 30 + q ) − t = 0 − t Multiply by -1 on both the sides, 24 − 3 q = t Then, compute the total tax by the formula T = t q , T = q ( 24 − 3 q ) = ( 24 q − 3 q 2 ) Tax is maximized as follows: The first derivative of T is as follows:

Mathematical Applications for the Management, Life, and Social Sciences

12th Edition

ISBN: 9781337625340

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Chapter 11.5, Problem 15E

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To calculate: The tax per item that will maximize the total tax revenue if the demand function for a fixed period of time is given by p=30−q and the supply function before taxation is p=6+2q.

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Chapter 11.5, Problem 12E

Chapter 11.5, Problem 16E

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Chapter 11 Solutions

Mathematical Applications for the Management, Life, and Social Sciences

Ch. 11.1 - 1. Ch. 11.1 - 2. If Ch. 11.1 - Prob. 3CP Ch. 11.1 - 4. Find . Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Find the derivatives of the functions in Problems...

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The tax per item that will maximize the total tax revenue if the demand function for a fixed period of time is given by p = 30 − q and the supply function before taxation is p = 6 + 2 q .

Solution Summary: The author calculates the tax per item that maximized the total tax revenue if the demand function for a fixed period of time is given by p=30-q and the supply function before taxation

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To calculate: The tax per item that will maximize the total tax revenue if the demand function for a fixed period of time is given by p=30−q and the supply function before taxation is p=6+2q.

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Chapter 11 Solutions