1. Marginal analysis is an analytical technique for solving optimization problems that involve changing choice variables by small amounts to determine if the objective function can be further improved. 2. Unconstrained optimization problems allow choice of activity levels from an unrestricted set of values, while constrained problems restrict activity levels. 3. For unconstrained optimization, the optimal activity level is where marginal benefit equals marginal cost, maximizing net benefit.

1. © INTEGRAL
UNIVERSITY
MARGINAL ANALYSIS
FOR OPTIMAL DECISIONS
Mr. Shahab Ud Din
Assistant Professor
DCBM
9580624322

2. CONCEPTS AND TERMINOLOGY
OBJECTIVE FUNCTION
The function the decision maker seeks to maximize or
minimize.
DESCRETE CHOICE VARIABLE
CONTINUOUS CHOICE VARIABLES

3. MARGINAL ANALYSIS
Analytical technique for solving optimization problems that involve
changing values of choice variables by small amounts to see if the
objective function can be further improved.
UNCONSTRAINED OPTIMIZATION
An optimization problem in which the decision maker can choose the
level of activity from an unrestricted set of values.
CONSTRAINED OPTIMIZATION
An optimization problem in which the decision maker can choose the
level of activity from an restricted set of values.

5. OPTIMIZATION
An optimization problem involves the
specification of three things:
– Objective function to be maximized or
minimized
– Activities or choice variables that determine
the value of the objective function
– Any constraints that may restrict the values of
the choice variables

6. UNCONSTRAINED
OPTIMIZATION
Net Benefit (NB)
– Difference between total benefit (TB) and total
cost (TC) for the activity
– NB = TB – TC
Optimal level of the activity (A*) is the level
that maximizes net benefit

7. OPTIMAL LEVEL OF ACTIVITY

8. TOTAL BENEFIT AND TOTAL
COST CURVES

9. Marginal Benefit & Marginal Cost
Marginal benefit (MB)
– Change in total benefit (TB) caused by an
incremental change in the level of the activity
Marginal cost (MC)
– Change in total cost (TC) caused by an
incremental change in the level of the activity

10. TB
MB
A

 

Change in total benefit
Change in activity
TC
MC
A

 

Change in total cost
Change in activity

11. Relating Marginals to Totals
Marginal variables measure rates of
change in corresponding total variables
– Marginal benefit & marginal cost are also
slopes of total benefit & total cost curves,
respectively

13. 1. Consider the slope of TB at point C.
2. The tangent line at point C raises by 640
units/dollars over a hundred unit run.
3. TOTAL BENEFIT= 640/100= $ 6.40 .
4. It means adding the 200th unit of activity(
going from 199 to 200 units) causes total
benefit to rise by $ 6.4.

14. Using Marginal Analysis to Find
Optimal Activity Levels
If marginal benefit > marginal cost
– Activity should be increased to reach highest net
benefit
If marginal cost > marginal benefit
– Activity should be decreased to reach highest net
benefit
Optimal level of activity
– When no further increases in net benefit are possible
– Occurs when MB = MC

15. USING MARGINAL ANALYSIS TO
FIND A*.

16. OPTIMIZATION WITH A
DISCRETE CHOICE VARIABLE

17. Constrained Optimization
The ratio MB/P represents the additional
benefit per additional dollar spent on the
activity
Ratios of marginal benefits to prices of various
activities are used to allocate a fixed number of
dollars among activities

21. Irrelevance of Sunk, Fixed, &
Average Costs
Sunk costs
– Previously paid & cannot be recovered
Fixed costs
– Constant & must be paid no matter the level of activity
Average (or unit) costs
– Computed by dividing total cost by the number of
units of the activity
These costs do not affect marginal cost & are
irrelevant for optimal decisions

23. THANK YOU