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If a monopolist produces q units, she can charge 400 – 4 q dollars per unit. The variable cost is $60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b , use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.

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Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659

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Chapter
Section
BuyFindarrow_forward

Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659
Chapter 7, Problem 49P
Textbook Problem
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If a monopolist produces q units, she can charge 400 – 4q dollars per unit. The variable cost is $60 per unit.

  1. a. How can the monopolist maximize her profit?
  2. b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)?
  3. c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.

a)

Summary Introduction

To determine: The way the profit can be maximized.

Non-linear programming (NLP):

Non-linear programming (NLP) is used in complex optimization problems where the objectives or constraints or sometimes both are non-linear functions of the decision variables. A model can be termed as non-linear for more than one reason.

Explanation of Solution

Model:

Formula:

b)

Summary Introduction

To determine: If the monopolist will increase or decrease the production.

c)

Summary Introduction

To use: The solver table to study how the change of sales tax affects the optimal solution.

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Chapter 7 Solutions

Practical Management Science
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