Chapter 3 discusses marginal analysis as a crucial tool for managers to make optimal decisions regarding business activities by analyzing benefits and costs. It emphasizes that sunk costs, fixed costs, and average costs are irrelevant for decision-making, with a focus on maximizing net benefits through optimal activity levels. The chapter outlines key concepts, including maximization and minimization problems, and provides frameworks for employing marginal analysis in both unconstrained and constrained optimization scenarios.

1. Marginal Analysis for Optimal Decisions
Chapter 3

2. Objectives:
3.1 Define several key concepts and terminology.
3.2 Use marginal analysis to find optimal activity levels in unconstrained
maximization problems and explain why sunk costs, fixed costs, and average
costs are irrelevant for decision making.
3.3 Employ marginal analysis to find the optimal levels of two or more activities in
constrained maximization and minimization problems.

3. Marginal Analysis for Optimal Decisions
• Making optimal decisions about the levels of various business activities
is an essential skill for all managers, one that requires managers to
analyze benefits and costs to make the best possible decision under a
given set of circumstances.
• A manager’s decision is optimal if it leads to the best outcome under a
given set of circumstances.
• Marginal analysis supplies the fundamental logic for making optimal
decisions. Managers benefit from understanding marginal analysis
because it enables them to make better decisions avoiding some rather
common errors in business decision making.

4. Marginal Analysis for Optimal Decisions
– Marginal analysis builds the essential foundation for
making everyday business decisions, such as choosing the
number of workers to hire, the amount of output to
produce, the amount to spend on advertising, and so on.
EXAMPLE:
If a company has room in its budget for another employee and is
considering hiring another person to work in a factory, a marginal
analysis indicates that hiring that person provides a net marginal
benefit. In other words, the ability to produce more products outweighs
the increase in labor costs.

5. 3.1 CONCEPTS AND TERMS

6. Concepts and Terminology
• Objective function
- The function the decision
maker seeks to maximize
or minimize.
• Maximization problem
- An optimization problem
that involves maximizing
the objective function.
• Minimization problem
- An optimization problem that
involves minimizing the objective
function.
• Activities or choice variables
- Variables that determine
the value of the objective
function.

7. Concepts and Terminology
• Discrete choice variables
- A choice variable that can take
only specific integer values.
• Continuous choice variables
- A choice variable that can take
any value between two end
points.
• Unconstrained optimization
- An optimization problem in
which the decision maker can
choose the level of activity from
an unrestricted set of values.

8. Concepts and Terminology
• Constrained optimization
- An optimization problem in
which the decision maker
chooses values for the choice
variables from a restricted set
of values.
• Marginal analysis
- Analytical technique for solving
optimization problems that
involves changing values of choice
variables by small amounts to see
if the objective function can be
further improved.

9. 3.2 Use marginal analysis to find optimal
activity levels in unconstrained
maximization problems and explain why
sunk costs, fixed costs, and average
costs are irrelevant for decision making.

10. UNCONSTRAINED MAXIMIZATION
• Net benefit
• The
objective
function to
be
maximized:
NB =TB - TC.
Decision makers will want to choose the level of activity to obtain
the maximum possible net benefit from the activity, where the net
benefit (NB) associated with a specific amount of activity (A) is
the difference between total benefit (TB) and total cost (TC)
for the activity
NB= TB- TC
Net benefit, then, serves as the objective function to be
maximized, and the amount of activity, A, represents the choice
variable. Furthermore, decision makers can choose any level of
activity they wish, from zero to infinity, in either discrete or
continuous units. Thus, we are studying unconstrained
maximization in this section.

11. The Optimal Level of Activity

12. Optimal level of activity- The level of activity that maximizes net benefit (A*).

13. MARGINAL BENEFIT AND MARGINAL COST
Marginal benefit (MB)
The change in total benefit
caused by an
in_x0002_cremental change in
the level of an activity.
Marginal cost (MC)- The
change in total cost caused by
an incremental change in the
level of an activity

14. Panel A — Measuring slopes along TB and TC

15. Panel B — Marginals give slopes of totals

16. Using Marginal Analysis to Find A*

17. Principle of marginal analysis:
• The optimal quantity of an activity is the quantity at which
marginal benefit is equal to marginal cost. Rational people
will always choose a quantity of an activity where marginal
benefit equals marginal cost!

18. Why is marginal analysis important?
• Marginal analysis is important because it helps business strategists to
determine where they should allocate their resources. If net benefits are
positive, it is in the best interest of the business to invest an that
additional output. If negative, it would be a poor investment choice.
• To determine the quantity of any activity that will maximize its net
benefit, we apply the marginal decision rule: If the marginal benefit of an
additional unit of an activity exceeds the marginal cost, the quantity of
the activity should be increased. If the marginal benefit is less than the
marginal cost, the quantity should be reduced. Net benefit is maximized
at the point at which marginal benefit equals marginal cost. The marginal
decision rule is at the heart of the economic way of thinking. The rule
basically says this: If the additional benefit of one more unit exceeds the
extra cost, do it; if not, do not.

19. SUNK COSTS AND FIXED COSTS
• Sunk costs are those costs that happened and there is not one thing we can do
about it. These costs are never relevant in our decision making process because
they already happened. These costs are never a differential cost, meaning, they
are always irrelevant.
• If you own a business, your ultimate goal is to continuously make a profit.
Meantime, while you might experience revenue and profit, you're also bound to
incur unavoidable expenses or costs.
• Sunk cost examples:
– Marketing example
– Research and development example
– Training example
– Hiring example

20. • There is a marginal cost when there are changes in the total cost
of production. Since fixed costs are constant, they do not
contribute to a change in total production costs. Therefore,
marginal costs exist when variable costs exist.
• Examples of fixed costs:
– Rent and lease costs
– Salaries
– Utility bills
– Insurance, and
– Loan repayments