Explanation Given Information: The provided expression is the demand function for a fixed period of time is given by p = 2800 − 8 q − q 2 3 and the supply function before taxation is p = 400 + 2 q . Where t is the tax per unit. The total tax T is equal to T = t q , where t is the tax per unit and q is the number of units. The tax revenue is maximized by finding the value of the variable at first derivative is equal to 0. Also checking by verifying that T ″ ( q ) ≤ 0 or not. If the supply function is f ( q ) , then after taxation, the new supply function is equal to f ( q ) + t . 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 = 400 + 2 q , After the taxation, the supply function is equal to p = 400 + 2 q + t . The demand function will meet the new supply function is: Put the new supply (after taxation) equal to the demand. 400 + 2 q + t = 2800 − 8 q − q 2 3 Solve to equation further to get the value of t, Add − ( 2800 − 8 q − q 2 3 ) on both the sides, 400 + 2 q + t − ( 2800 − 8 q − q 2 3 ) = 2800 − 8 q − q 2 3 − ( 2800 − 8 q − q 2 3 ) t − 2400 + 10 q − q 2 3 = 0 Deduct t from both the sides, t − 2400 + 10 q − q 2 3 − t = 0 − t Multiply by -1 on both the sides, t = 2400 − 10 q + q 2 3 Then, compute the total tax by the formula T = t q , T = q ( 2400 − 10 q + q 2 3 ) = ( 2400 q − 10 q 2 +

Mathematical Applications for the Management, Life, and Social Sciences

11th Edition

ISBN: 9781305108042

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Chapter 11, Problem 36RE

To determine

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=2800−8q−q23 and the supply function before taxation is p=400+2q.

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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 = 2800 − 8 q − q 2 3 and the supply function before taxation is p = 400 + 2 q .

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=2800-8q-q23

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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=2800−8q−q23 and the supply function before taxation is p=400+2q.

Chapter 11 Solutions