economics

1. TOPIC # 2 ECONOMIC OPTIMIZATION
Contents
1) Economic Optimization Process
2) Concept of Marginal Change
3) Marginal change analysis
4) From Marginal to derivatives
5) How to take a derivative
6) 1st, 2nd, 3rd …….. Derivative of an equation
7) Using marginal and derivatives in managerial decision making
8) Practice question
9) From marginal change to incremental change
Dr. Ayesha Serfraz Managerial Economics IAS

2. ECONOMIC OPTIMIZATION PROCESS
• Effective managerial decision making is the process of arriving at the best solution to a problem. “If
only one solution is possible, then no decision problem exists.”
When alternative courses of action are available, the best decision is the one that produces a
result most consistent with managerial objectives. The process of arriving at the best managerial
decision is the goal of economic optimization and the focus of managerial economics.
Optimal Decisions
• When alternative courses of action are available, the decision that produces a result
most consistent with managerial objectives is the optimal decision.
• A challenge that must be met in the decision-making process is characterizing the
desirability of decision alternatives in terms of the objectives of the organization.
Decision makers must recognize all available choices and portray them in terms of
appropriate costs and benefits.
• “Optimization techniques are helpful because they offer a realistic means for
dealing with the complexities of goal-oriented managerial activities.”
Dr. Ayesha Serfraz Managerial Economics IAS

3. CONCEPT OF MARGINAL CHANGE
• Marginal Change means a change in dependent variable (y) caused by 1-unit
change in independent variable (x).
• For Example if y=f(x)
then Δ (change) → ΔY/ΔX= ΔY/ΔX = Y2 – Y1/X2 – X1
The value did not jump from 1 to 3 or 4 so on, Marginal change is measured using
“ONE UNIT” change. Some more examples are as follows
Dr. Ayesha Serfraz Managerial Economics IAS

4. MARGINAL CHANGE ANALYSIS
• Marginal analysis is an examination of the additional benefits of an activity
compared to the additional costs incurred by that same activity. Companies
use marginal analysis as a decision-making tool to help them maximize their
potential profits. Marginal refers to the focus on the cost or benefit of the next
unit or individual.
• Marginal analysis is an examination of the additional benefits of an activity
compared to the additional costs incurred by that same activity. Marginal
refers to the focus on the cost or benefit of the next unit or individual, for
example, the cost to produce one more widget or the profit earned by
adding one more worker.
• Companies use marginal analysis as a decision-making tool to help them
maximize their potential profits.
• When a manufacturer wishes to expand its operations, either by adding new
product lines or increasing the volume of goods produced from the current
product line, a marginal analysis of the costs and benefits is necessary.
Dr. Ayesha Serfraz Managerial Economics IAS

5. FROM MARGINAL TO DERIVATIVES
• The marginal change shows the additional change caused by one-unit
change in independent variable.
• Sometimes the change is too small that it cannot be measure in units and it is
assumed that change in independent variable is almost equal to zero. In such
situations, when manager is not sure of the effect of such small changes on
cost, profit, revenue etc., then the concept of derivative is used which is
derived from marginal change and written as
“ A derivative is a precise specification
of a marginal relation”
In this case Δ changes into d where
D represents derivative
Dr. Ayesha Serfraz Managerial Economics IAS

6. HOW TO TAKE A DERIVATIVE
• If Y = Xn then derivative of Y (change in
y due to change in X which is almost
equal to 0)
dY/dX = nXn-1
This is the general formula of derivative.
Take the exponent (representing time)
down, multiply with independent variable
power to time period minus the change
(which is too small)
Dr. Ayesha Serfraz Managerial Economics IAS

7. 1ST, 2ND, 3RD …….. DERIVATIVE OF AN
EQUATION
Dr. Ayesha Serfraz Managerial Economics IAS
Some rules: derivative of a constant is zero.
power comes down and is multiplied the co-efficient, these steps
are continued until we get a constant showing the exact change. This is
explained the following example.
f(x) is the function
f’(x) is the first derivative
f’’ (x) is the second derivative
f’’’ (x) is the third derivative, after that no
derivation is possible.

8. USING MARGINAL AND DERIVATIVES IN MANAGERIAL
DECISION MAKING
• Profit maximization
• Activity level that generates the highest profit,
• MR = MC and Mπ = 0
• Breakeven point
• Output level at which total profit is zero
• Example
• P = $7,500 – $3.75Q (Demand)
• TR = $7,500Q – $3.75Q2 (Total revenue)
• MR = ΔTR/ΔQ = $7,500 – $7.5Q (Marginal revenue)
• where P is price and Q is output.
• In addition, Storrs’ accounting department has estimated monthly total cost and
marginal
• cost relations of
• TC = $1,012,500 + $1,500Q + $1.25Q2 (Total cost)
• MC = ΔTC/ΔQ = $1,500 + $2.5Q (Marginal cost)
Dr. Ayesha Serfraz Managerial Economics IAS

9. EXAMPLE (CONT)
• These relations can be used to determine the optimal activity level for the firm. Profit will be maximized where MR = MC. This suggests an
activity level of 600 MR = MC
• $7,500 – $7.5Q = $1,500 + $2.5Q
• $10Q = $6,000
• Q = 600 units
• At this optimal activity level, price, total revenue, and the maximum total profit can be calculated
• as
• P = $7,500 – $3.75Q
• = $7,500 – $3.75(600)
• = $5,250 per unit
• TR = $7,500Q – $3.75Q2
• = $7,500(600) – $3.75(6002)
• = $3,150,000
• π = TR – TC
• = $7,500Q – $3.75Q2 – $1,012,500 – $1,500Q – $1.25Q2
• = –$5Q2 + $6,000Q – $1,012,500
• = –$5(6002) + $6,000(600) – $1,012,500
• = $787,500
• To maximize short-run profits, Storrs should expand from its current level of 400 units to 600 units per month. Any deviation from an output of
600 units and price of $5,250 per unit would lower Storrs’short-run profits.
Dr. Ayesha Serfraz Managerial Economics IAS

10. PRACTICE QUESTION
• Profit Versus Revenue Maximization. Presto Products, Inc., manufactures
small electrical
• appliances and has recently introduced an innovative new dessert maker
for frozen yogurt
• and tofu that has the clear potential to offset the weak pricing and sluggish
volume growth
• experienced during recent periods.
• Monthly demand and cost relations for Presto’s frozen dessert maker are as
follows:
• P = $60 – $0.005Q TC = $100,000 + $5Q + $0.0005Q2
• MR = ΔTR/ΔQ = $60 – $0.01Q MC = ΔTC/ΔQ = $5 + $0.001Q
(i) Determine these profit-maximizing and revenue-maximizing price/output
combinations
(ii) Compare the profit-maximizing and revenue-maximizing price/output
combinations
Dr. Ayesha Serfraz Managerial Economics IAS

11. FROM MARGINAL CHANGE TO INCREMENTAL
CHANGE
• The marginal concept is a key component of the economic decision-making
process. It is important to recognize, however, that marginal relations
measure only the effect associated with unitary changes in output or some
other important decision variable.
• Many managerial decisions involve a consideration of changes that are
broader in scope. For example, a manager might be interested in analyzing
the potential effects on revenues, costs, and profits of a 25 percent increase
in the firm’s production level.
• The incremental concept is the economist’s generalization of the marginal
concept. Incremental analysis involves examining the impact of alternative
managerial decisions or courses of action on revenues, costs, and profit. It
focuses on changes or differences between the available alternatives.
• “The incremental change is the change resulting from a given managerial
decision. For example, the incremental revenue of a new item in a firm’s
product line is measured as the difference between the firm’s total revenue
before and after the new product is introduced.”
Dr. Ayesha Serfraz Managerial Economics IAS

12. POTENTIAL PRESENTATION TOPICS
• Use of economic optimization process for arriving at optimal solution taking a
hypothetical/running/in-mind idea od business.
• When Total Profits are Maximum, Marginal Profits are 0, Explain with the help
of example.
• Practical examples of using marginal change, incremental change and
derivatives in management.
• Comparison of marginal, incremental and derivatives
Dr. Ayesha Serfraz Managerial Economics IAS