Explanation Given Information: The provided expression is the demand function for a fixed period of time is given by p = 800 − 2 q and the supply function before taxation is p = 100 + 0.5 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 = 100 + 0.5 q , After the taxation, the supply function is equal to p = 100 + 0.5 q + t . The demand function will meet the new supply function is: Put the new supply(after taxation) equal to the demand. 100 + 0.5 q + t = 800 − 2 q Solve to equation further to get the value of t, Add 2q-800 on both the sides, 100 + 0.5 q + t + ( 2 q − 800 ) = 800 − 2 q + ( 2 q − 800 ) t + ( 2.5 q − 700 ) = 0 Deduct t from both the sides, t + ( 2.5 q − 700 ) − t = 0 − t Multiply by -1 on both the sides, − ( 2.5 q − 700 ) = t Then, compute the total tax by the formula T = t q , T = − q ( 2.5 q − 700 ) = ( − 2.5 q 2 + 700 q ) Tax is maximized as follows: The first derivative of T = ( − 2

WebAssign Printed Access Card for Harshbarger/Reynolds' Mathematical Applications for the Management, Life, and Social Sciences, 12th Edition, Multi-Term

12th Edition

ISBN: 9781337630542

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 17E

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=800−2q and the supply function before taxation is p=100+0.5q.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.5, Problem 16E

Chapter 11.5, Problem 18E

Students have asked these similar questions

43-46. Directions of change Consider the following functions f and points P. Sketch the xy-plane showing P and the level curve through P. Indicate (as in Figure 15.52) the directions of maximum increase, maximum decrease, and no change for f. T 45. f(x, y) = x² + xy + y² + 7; P(−3, 3)

In Problems 1 and 2 find the eigenfunctions and the equation that defines the eigenvalues for the given boundary-value problem. Use a CAS to approximate the first four eigenvalues A1, A2, A3, and A4. Give the eigenfunctions corresponding to these approximations. 1. y" + Ay = 0, y'(0) = 0, y(1) + y'(1) = 0

A normal distribution has a mean of 50 and a standard deviation of 4. Solve the following three parts? 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the answer of the second part.) 2. Compute the probability of a value greater than 55.0. Use the same formula, x=55 and subtract the answer from 1. 3. Compute the probability of a value between 52.0 and 55.0. (The question requires finding probability value between 52 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 52, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…

Chapter 11 Solutions

WebAssign Printed Access Card for Harshbarger/Reynolds' Mathematical Applications for the Management, Life, and Social Sciences, 12th Edition, Multi-Term

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 = 800 − 2 q and the supply function before taxation is p = 100 + 0.5 q .

Solution Summary: The author explains how 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=800-2q and the supply function before taxation is

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=800−2q and the supply function before taxation is p=100+0.5q.

Want to see the full answer?

Chapter 11 Solutions