Explanation Given Information: The provided expression is the demand function for a fixed period of time is given by p = 5000 − 20 q − 0.7 q 2 and the supply function before taxation is p = ( 0.3 ) q 2 1 + 10 q + 500 . If the supply function is f ( q ) , then after taxation, the new supply function is equal to f ( q ) + t . 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. 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 = ( 0.3 ) q 2 1 + 10 q + 500 , After the taxation, the supply function is equal to p = ( 0.3 ) q 2 1 + 10 q + 500 + t . The demand function will meet the new supply function is: Put the new supply(after taxation) equal to the demand. ( 0.3 ) q 2 1 + 10 q + 500 + t = 5000 − 20 q − 0.7 q 2 Solve to equation further to get the value of t, Add − ( 5000 − 20 q − 0.7 q 2 ) on both the sides, ( 0.3 ) q 2 1 + 10 q + 500 + t − ( 5000 − 20 q − 0.7 q 2 ) = 5000 − 20 q − 0.7 q 2 − ( 5000 − 20 q − 0.7 q 2 ) ( 0.3 ) q 2 1 + 10 q + 500 + t − ( 5000 − 20 q − 0.7 q 2 ) = 0 Deduct t from both the sides, ( 0.3 ) q 2 1 + 10 q + 500 + t − ( 5000 − 20 q − 0

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ISBN: 9780357294383

Author: HARSHBARGER

Publisher: CENGAGE L

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Chapter 11.5, Problem 24E

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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=5000−20q−0.7q2 and the supply function before taxation is p=(0.3)q21+10q+500.

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Chapter 11.5, Problem 23E

Chapter 11, Problem 1RE

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Chapter 11 Solutions

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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 = 5000 − 20 q − 0.7 q 2 and the supply function before taxation is p = ( 0.3 ) q 2 1 + 10 q + 500 .

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=5000-20q-0.7q2 and the supply function

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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=5000−20q−0.7q2 and the supply function before taxation is p=(0.3)q21+10q+500.

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