Explanation Given Information: The provided expression is the demand function for a fixed period of time is given by p + q = 1000 and the supply function before taxation is p = q 2 30 + 2.5 q + 920 . 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. If a quadratic equation is of the form a x 2 + b x + c = 0 , then, x = − b ± b 2 − 4 a c 2 a Calculation: The provided expression is p = q 2 30 + 2.5 q + 920 , After the taxation, the supply function is equal to p = q 2 30 + 2.5 q + 920 + t . The demand function will meet the new supply function is: Put the new supply(after taxation) equal to the demand. q 2 30 + 2.5 q + 920 + t = 1000 − q Solve to equation further to get the value of t, Add − 1000 + q on both the sides, q 2 30 + 2.5 q + 920 + t + ( − 1000 + q ) = 1000 − q + ( − 1000 + q ) q 2 30 + 2.5 q + 920 + t + ( − 1000 + q ) = 0 Deduct t from both the sides, q 2 30 + 2.5 q + 920 + t + ( − 1000 + q ) − t = 0 − t Multiply by -1 on both the sides, 80 − 3.5 q − q 2 30 = t Then, compute the total tax by the formula T = t q , T = q ( 80 − 3.5 q − q 2 30 ) = ( 80 q − 3.5 q 2 − q 3 30 ) Tax is maximized as follows: The first derivative of T = ( 80 q − 3.5 q 2 − q 3 30 ) is as follows: T ′ ( q ) = d d q ( 80 q − 3.5 q 2 − q 3 30 ) = d d q ( 80 q ) − d d q ( 3

MATHMATICAL APPLICATIONS FOR THE MANAGEM

11th Edition

ISBN: 9781305758063

Author: HARSHBARGER

Publisher: CENGAGE C

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Chapter 11.5, Problem 22E

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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+q=1000 and the supply function before taxation is p=q230+2.5q+920.

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Chapter 11.5, Problem 21E

Chapter 11.5, Problem 23E

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Chapter 11 Solutions

MATHMATICAL APPLICATIONS FOR THE MANAGEM

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 + q = 1000 and the supply function before taxation is p = q 2 30 + 2.5 q + 920 .

Solution Summary: The author calculates 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+q=1000 and the supply function before taxation is

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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+q=1000 and the supply function before taxation is p=q230+2.5q+920.

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Chapter 11 Solutions