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

Mathematical Applications for the Management, Life, and Social Sciences

11th Edition

ISBN: 9781305108042

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

Videos

Question

Chapter 11.5, Problem 24E

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.5, Problem 23E

Chapter 11, Problem 1RE

Students have asked these similar questions

solving problem 1

Class, the class silues, and the class notes, whether the series does alternate and the absolute values of the terms decrease), and if the test does apply, determine whether the series converges or diverges. For the ith series, if the test does not apply the let Mi = 2, while if the test determines divergence then M¿ = 4, and if it determines convergence then M¿ = 8. 1: 2: 3 : 4: 5 : ∞ n=1 ∞ (−1)n+1. Σ(-1) +1 n=1 ∞ п 3m² +2 Σ(-1)+1 sin(2n). n=1 ∞ 2n² + 2n +3 4n2 +6 1 e-n + n² 3n23n+1 9n² +3 In(n + 1) 2n+1 Σ(-1) +1 n=1 ∞ Σ(-1)". n=1 Then the value of cos(M₁) + cos(2M2) + cos(3M3) + sin(2M4) + sin(M5) is 1.715 0.902 0.930 -1.647 -0.057 ● 2.013 1.141 4.274

3. FCX14) = x²+3xx-y3 +.

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...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

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

Concept explainers

Videos

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.

Want to see the full answer?

Chapter 11 Solutions