ECONOMIC-OPTIMIZATION-Lec-2.pptx

Economic
Optimization
Lecture 2

Overview
Managers make tough choices that involve benefits and
costs. Before, it was simply impractical to compare relative
pluses and minuses of a large number of managerial decisions
under a wide variety of operating conditions. For many large
and small organizations, economic optimization remained an
elusive goal (Hirschey, 2012).

Overview
The rise of personal computers and invention of
spreadsheets were a pivotal innovation because they put the
tools for insightful demand, cost, and profit analysis at the
finger tips of decision makers. (Hirschey, 2012).

Overview
Electronic computing capability is not the only thing needed
by managers to process information efficiently. It is
imperative for them to have a basic understanding of basic
economic relations.

Economic Optimization Process
The process of arriving at the best managerial
decision is the goal of economic optimization
(Hayden Economics, 2023).

• Should the quality of inputs be enhanced to better meet
low-cost import competition?
• Is a necessary reduction in labor costs efficiently achieved
through an across-the-board decrease in staffing, or is it
better to make targeted cutbacks?
• Following an increase in product demand, is it preferable to
increase managerial staff, line personnel, or both?

Optimal Decision
The answers to the questions in the previous slide depend on
the objective and preferences of management. Optimal
decision is the choice alternatives that produces result most
consistent with managerial objectives.

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 (Hirschey, 2012).

Optimal Decision
The description of decision alternatives is greatly enhanced
through application of the principles of managerial economics.
Managerial economics also provides tools for analyzing and
evaluating decision alternatives. Economic concepts and
methodology are used to select the optimal course of action
in light of available options and objectives (Hirschey, 2012).

Optimal Decision
Principles of economic analysis form the basis for describing
demand, cost, and profit relations. Once basic economic
relations are understood, the tools and techniques of
optimization can be applied to find the best course of action
(Hirschey, 2012).

Optimal Decision
Most important, the theory and process of optimization gives
practical insight concerning the value maximization theory of
the firm. Optimization techniques are helpful because they
offer a realistic means for dealing with the complexities of
goal-oriented managerial activities (Hirschey, 2012).

Maximizing the Value of the Firm
In managerial economics, the primary objective of the management is
assumed to be maximization of the value of the firm. It is expressed in
this equation.
This maximizing equation is a complex task that involves consideration
of future revenues, costs, and discount rates.

Total revenues are directly determined by the quantity sold and the
prices obtained. Factors that affect prices and the quantity sold include
the choice of products made available for sale, marketing strategies,
pricing, distribution policies, competition, and the general state of the
economy.

Cost analysis includes a detailed examination of the prices and
availability of various input factors, alternative production schedules,
production methods, and so on.

The relationship between an appropriate discount rate and the
company’s mix of products and both operating and financial leverage
must be determined. All these factors affect the value of the firm as
seen in the equation above.

To determine the optimal course of action, marketing, production,
and financial decisions must be integrated within a decision analysis
framework. Decisions related to personnel retention and development,
organization structure, and long-term business strategy must be
combined into a single integrated system that shows how managerial
initiatives affect all parts of the firm (Hirschey, 2012).

The value maximization model provides an attractive basis for such
integration. Using the principles of economic analysis, it is also possible
to analyze and compare the higher costs or lower benefits of
alternative suboptimal courses of action (Hirschey, 2012).

Revenue Relations
Price and Total Revenue
Tables are the simplest and most direct form for presenting economic
data. When these data are displayed electronically in the format of an
accounting income statement or balance sheet, the tables are referred
to as spreadsheets.

Revenue Relations
Price and Total Revenue
When the underlying relation between economic data is simple, tables
and spreadsheets may be sufficient for analytical purpose. A simple
graph or visual representation of the data can provide valuable insights.

Revenue Relations
The effectivity of production and pricing decisions depend upon a
careful understanding of revenue relations. Complex economic
relations require more sophisticated methods of expression. An
equation is an expression of the functional relationship or connection
among economic variables.

Revenue Relations
The easiest way to examine basic economic concepts is to consider the
functional relations incorporated in the basic valuation model.
Consider the relation between output, Q and total revenue, TR. The
functional notation is: TR = f(Q). This means that total revenue is a
function of output. TR is the dependent variable while output, Q is the
independent variable.

Revenue Relations
TR = f(Q) does not indicate the specific relation between output and
total revenue. It merely states that some relation exists. This next
equation provides a more precise expression of this functional relation.
TR = P x Q
Where P represents price at which each unit of Q is sold. Total revenue
is equal to price times quantity sold.

Revenue Relations
Example: if price is constant at $3.50, regardless of the quantity sold,
the relation between quantity and total revenue is this:
TR = $3.50 x Q
In agricultural commodity markets, small producers are able to sell as
much output as they can produce at the going price.

Revenue Relations
Going price is based on its market price—what competitors with
similar offerings are selling their products for. If the going price of corn
is $3.50 per bushel (25.40 kg), the total revenue derived by an
individual farmer from corn sales would simply be TR = $3.5Q, where Q
is the number of bushels of corn produced and sold.

Revenue Relations
In most instances, firms face a downward sloping demand curve. This means that prices must be cut to
increase the quantity sold. To better understand this, let us continue with our corn example. The table
shows the revenue and price relations.

Revenue Relations
Suppose that the quantity rises as price is
reduced. Notice that 4 units of output are
sold at a price of $18, and the quantity sold
rises to 7 units per month when price is
reduced to $13.50. This is enough
information to allow the firm to estimate a
linear demand curve for its product.

Revenue Relations
A linear demand curve is written as P = a + bQ; where a represents the
intercept and b is the slope coefficient.
18 = a + b(4)
- 13.5 = a + b(7)
4.5 = -3b
-1.5 = b

Revenue Relations
If b is -1.5, then by substitution we get a.
18 = a + b(4)
18 = a – 1.5(4)
18 = a – 6
24 = a

Revenue Relations
We now know the value of
a and b, therefore we can
write the demand curve.
P = 24 – $1.5Q
The graph shows the
relation between price and
output.

Revenue Relations
Then we show the functional relation between price and output as
shown in the TR equation.
TR = P x Q
TR = ($24 – $1.5Q) (Q)
TR = $24(Q) - $1.5(Q)2

Revenue Relations
To be sure, such relations are only useful approximations within the
range of price-output combinations used to derive them. Example: a
firm could use such demand curve to estimate the quantity demand
during a given period for prices ranging from $24 to $9 per unit. It
should not be used to estimate the umber of units that might be sold at
exceptionally low or high prices.

Marginal Revenue
Precise information about the effect of a change in output on total
revenue is given by the marginal relation between revenue and profit.
Marginal relation is the change in the dependent variable caused by a
1-unit change in the independent variable. Marginal revenue is the
change in total revenue associated with a 1-unit change in output.
MR = ΔTR/ΔQ

Using the example that we have about the corn. You can see here that revenue rises from $72 to
$82.50 when units sold rise from 4 to 5. This means that the marginal revenue is $10.50 over the range
from 4 to 5 units. Marginal revenue is $7.50 over the range from 5 to 6 units. Notice also that marginal
revenue is positive so long as total revenue is increasing, as is true over the range from 1 to 8 units sold.

The total revenue begins to decrease beyond where marginal revenue turns negative.
What you can et from this is this: marginal revenue is positive when total revenue is
increasing, but marginal revenue becomes negative when total revenue is
decreasing.

Marginal Revenue
When a linear relation exists between price and the number of units
sold, a linear relation also exists between marginal revenue and units
sold. In this instance, both price and marginal revenue relations begin
at the same point, but marginal revenue falls twice as fast as price with
respect to output.
MR = $24 – $3Q

Revenue Maximization
This is the activity level that generates the highest revenue, MR = 0.
At every output level, the marginal revenue relation can be used to
precisely identify the change in total revenue that occurs with a 1-unit
change in the number of units sold.

To find the revenue-maximizing output level, set MR = 0, and solve for
Q.
MR = 0
$24 - $3Q = 0
$3Q = $24
Q = 8
:

When Q = 8, total revenue is maximized at $96 because:
TR = $24Q - $1.5Q2
TR = $24 (8) - $1.50 (82)
TR = $96
If fewer than 8 units are sold, total revenue can be increased with an expansion in
output. If more than 8 units are sold, total revenue would decline from $96and
could be increased with a reduction in volume. Only at Q = 8 is total revenue
maximized.

In other instances, savvy firms employ a short-run revenue-maximizing
strategy as part of their long-term profit maximization. Enhanced
awareness among consumers, increased customer loyalty, potential
economies of scale in marketing and promotion, and possible
limitations in competitor entry, and growth are all potential advantages
of short-term revenue maximization (Hirschey, 2012).

To be consistent with long-run profit maximization, such advantages of
short-run revenue maximization must be at least sufficient to
compensate for the corresponding loss in short-run profitability
(Hirschey, 2012).

Cost Relations
Meeting customer demand efficiently depend upon a careful
understanding of cost relations.
The proper use of relevant cost concepts requires an
understanding of various relations between costs and output,
or cost functions.

Cost Relations
There are two basic cost functions that are used in managerial
decision-making: short-run cost functions, used for day-to-day
operating decisions, and long-run cost functions, used for
long-term planning (Hirschey, 2012).

Cost Relations
In economic analysis, the short run is the operating period
during which the availability of at least one input is fixed. In
the long run, the firm has complete flexibility with respect to
input use. (Hirschey, 2012).

Cost Relations
Total Costs are comprised of fixed and variable expenses.
Fixed cost do not vary with output. These costs include
interest expense, rent or leased plant and equipment,
depreciation charges associated with the passage of time,
property taxes, and salaries of employees not laid off during
period of reduced activity (Hirschey, 2012).

Cost Relations
Because all costs are variable in the long run, long-run fixed
costs always equals to zero. In the short run, operating
decisions are typically constrained by prior capital
expenditures. In the long run, no such restrictions exist.

Cost Relations
Example: A management consulting firm operating out of
rented office space might have a short-run period as brief as a
few weeks, the time remaining on the office lease. A firm in
the hazardous waste disposal business has significant long-
lived assets and may face 20-30 year period of operating
constraints.

Cost Relations
Variable costs fluctuate with output. Expenses for raw
materials, depreciation associated with the use of equipment,
the variable portion of utility charges, some labor costs, and
sales commissions are all examples of variable expenses.

Cost Relations
A sharp distinction between fixed and variable costs is neither
always possible nor realistic.
Example: CEO and staff salaries may be largely fixed, but
during severe business downturns, even CEOs take a pay cut.

Cost Relations
The longer the duration of abnormal demand, the greater the
likelihood that some fixed costs will actually vary.
The total cost can be expressed as the sum of fixed and
variable cost.
TC = FC + VC

In this example, let the FC = $8 and VC = $4Q + 0.5Q2. As you can see in the table,
the fixed cost $8 is constant and do not depend on the level of output. While the
variable costs rise with the amount of production.

In this example, variable costs rise faster than output because the variable cost function is quadratic
in nature; it involves output squared Q2, because total cost equals fixed cost plus variable cost, the
total cost function can be expressed as:
TC = $8 + $4Q + 0.5Q2
Total cost rise with the amount produced.

Marginal and Average Cost
Marginal cost is the change in total cost associated with a 1-
unit change in output:
MC = ΔTC/ΔQ

As you can see in the example. Total cost rises from $24.50 to $32.00 when the number of units
produced when the number of units produced rises from 3 to 4 units. This means that marginal cost
is $7.50 when output rises from 3 to 4 units. Marginal cost is $8.50 when the number of units
produced rises from 4 to 5. Notice that marginal cost is positive and increasing over the range from
1 to 10 units produced.

Marginal cost is almost always positive because almost all
goods and services entail at least some labor and/or materials.
It is also common for marginal costs to rise as output expands,
but this is not universally true (Hirschey, 2012).

Average cost is simply the cost divided by the number of units
produced (Hirschey, 2012).
AC = TC/Q

Notice that average cost is falling when
MC < AC. Also notice that average cost
is rising when MC > AC. This is always
true. Whenever the marginal is less
than the average, the average will fall.
Whenever the marginal is greater than
the average, the average will rise.

If the marginal is equal to the average, the average is either a minimum
or a maximum. Distinguishing maximums from minimums is easy with a
simple numerical example. If MC = AC, and average cost falls with an
expansion in output, then AC is at maximum. If MC = AC, and average
cost rises with an expansion in output, then AC is at a minimum
(Hirschey, 2012).

Average Cost Minimization
At every output level, the relationship between marginal cost and
output indicates the change in total cost that will occur with a 1-unit
change in the number of units produced. Similarly, the relationship
between marginal cost and average cost can be studied to determine
the change in average cost that will occur with a 1-unit change in the
number of units produced (Hirschey, 2012).

In the example
TC = $8 + $4Q + $0.5Q2
MC = ΔTC/ ΔQ = $4 +$1Q
AC = TC/Q
AC = $8 + $4Q + $0.5Q2/Q
AC = $8/Q + $4 + $0.5Q

With average cost minimization, the lowest possible average cost is achieved. To
find this MC = AC, and then solve for Q.
$4 +$1Q = $8 + $4Q + $0.5Q2
0.5Q = 8/Q
Q2= 8/0.5
Q = √16
Q = 4

This is the relations between total cost, marginal cost, average cost, and
output.

Notice that when Q = 4, MC = AC = $8. It is obvious that average cost is
rising when Q > 4, so Q = 4 indicates a point of minimum (rather than
maximum) average cost.

From a strategic point of view, the point of minimum average cost is important
because it shows the level of output necessary to achieve maximum productive
efficiency. In some cases, small firms find that in order to be competitive, they
need to “get big, or get out” of a particular market. At the same time, it is
important to recognize that average-cost minimization involves consideration of
cost relations only; no revenue relations are considered in the process of
minimizing average costs. To determine the profit-maximizing activity level, both
revenue and cost relations must be considered (Hirschey, 2012).

Profit Relations
Total profit is the difference between total revenue and total cost.
Profit maximization involves a careful comparison of revenue and cost
relations (Hirschey, 2012).

Total and Marginal Profit
π = TR – TC
We are using pi for price because P is already used to describe
price. This equation is read as total profit = total revenue
minus total cost.

Marginal profit is the change in total profit due to a 1-unit
change in output.
Mπ = Δπ/ΔQ
Equivalently, marginal profit can be thought of as the
difference between marginal revenue and marginal cost.
Mπ =MR -MC

Quantity, Revenue, Cost, and Profit Relations

When Q = 0, total revenue is zero, and fixed cost represent the
money loss for the firm. When Q = 0, π = -$8. Given that Mπ >
0, total profit rises as output expands over the range from Q =
1 to Q = 5. Beyond Q = 5, the increase in total cost associated
with an expansion in output exceeds the increase in total
revenue, and total profit begins to decline.

In general, total profit will rise if Mπ > 0. Total profit will fall
whenever Mπ < 0. Similarly, total profit will rise so long as MR
> MC because that means M π > 0. Total profit will fall if MR <
MC because that means Mπ <0.

The profit maximization rule states that total profit will be
maximized when marginal profit equals zero, provided that profit
declines with a further expansion in output. In functional form,
profit is maximized only if Mπ = 0 and profit falls with a further
increase in output. Because Mπ = MR = MC = 0 at the profit-
maximizing activity level, MR = MC (Hirschey, 2012).

Once again profit maximization requires that profit falls with any further increase in output.

Profit Maximization
The profit is rising over the range from Q = 1 to Q =5 where
marginal profit is positive. Profit is falling over the range from
Q =6 to Q = 10 where marginal profit is negative. Zero profits
are achieved at the lower and upper breakeven points.

Profit Maximization
In equation form, the relevant profit relation can be expressed
as:
π = TR – TC
=$24Q – 1.5Q2 – ($8 + $4Q +0.5Q2)
= -$8 + $20Q -$2Q2

Profit Maximization
Similarly, the relevant marginal profit relation can be
expressed as:
Mπ = MR – MC
= $24Q – 3Q – ($4 + $1Q)
= $20 - $4Q

Profit Maximization
At every output level, the marginal profit relation can be used
to precisely identify the change in total profit that occurs with
a 1-unit change in the number of units sold. To find the profit-
maximizing output level, set Mπ 0, and solve for Q:
Mπ = 0
$20 $4Q = 0
4Q = 20
Q = 5

Profit Maximization
From this marginal profit relation, Mπ 0 when Q 5. Also
observe that MR = MC at this point because MR = $24 - $3(5)
= $9 and MC = $4 + $1(5) = $9 when Q = 5. As shown in the
table when Q = 5, total profit is maximized at $42 because
π = - $8 + $20Q - $2 Q 2
= -$8 + $20(5) - $2(52)
= $42

Profit Maximization
If fewer than 5 units were sold, total profit could be increased
with an expansion in output. If more than 5 units were sold,
total profit would decline from $42 and could be increased
with a reduction in volume. Only at Q = 5 is total profit
maximized.

Relations Between Total Profit, Marginal Profit, and Output

Profit Maximization
At the profit-maximizing activity level, MR = MC and the added
amount of revenue brought in by the last unit produced (marginal
revenue) is just sufficient to offset added cost (marginal cost), and
profit would fall with an expansion in production. Because almost
all goods and services entail the use of at least some labor and raw
materials, MC = 0 in all but the most unusual circumstances
(Hirschey, 2012).

Profit Maximization
This fact has important implications for profit versus revenue
maximization. With a downward-sloping demand curve, both price and
marginal revenue decline following an increase in the number of units
sold, and MR = MC will occur at a lower level of activity than where MR 0.
The amount produced and sold at the profit-maximizing activity level will
be the same as the amount produced and sold at the revenue-maximizing
activity level only in the unlikely event that MR = MC = 0 (Hirschey, 2012).

Profit Maximization
The profit-maximizing activity level will also tend to differ from the
average-cost–minimizing activity level where MC = AC. Recall that
finding the point of lowest average costs involves a consideration
of marginal cost and average cost relations only, no revenue
implications are considered. The point of profit maximization can
be less than, equal to, or greater than the point of average cost
minimization (Hirschey, 2012).

Marginal versus Incremental Concept
It is important to recognize that marginal relations measure
the effect associated with unitary changes in output. Many
managerial decisions involve a consideration of changes that
are broader in scope. (Hirschey, 2012).

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. Alternatively, a
manager might want to analyze the profit impact of
introducing an entirely new product line, or assess the cost
impact of changing an entire production system (Hirschey,
2012).

In all managerial decisions, the study of differences or changes
is the key element in the selection of an optimal course of
action. The marginal concept, although correct for analyzing
unitary changes in output, is too narrow to provide a general
methodology for evaluating all alternative courses of action
(Hirschey, 2012).

The incremental concept is the economist’s generalization of
the marginal concept. Incremental analysis involves examining
the impact of alternative managerial decisions or course of
action on revenues, costs, and profit. It focuses on changes or
differences among available alternatives (Hirschey, 2012).

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 (Hirschey, 2012).

Incremental Profits
It is the profit gain or loss associated with a given managerial
decision. Total profit increases so long as incremental profit is
positive. When incremental profit is negative, total profit
declines (Hirschey, 2012).

Incremental Profits
The incremental concept is so intuitively obvious that it is easy
to overlook both its significance in managerial decision making
and the potential for difficulty in correctly applying it
(Hirschey, 2012).

Incremental Profits
The incremental concept is sometimes violated in practice. Example: A firm may refuse to
sublet excess warehouse space for $5,000 per month because it figures it cost $7,500 per
month—a price paid for a long-term lease on the facility. However, if the warehouse space
represents excess capacity with no current value to the company, its historical cost of
$7,500 per month is irrelevant and should be disregarded. The firm would forego $5,000 in
profits by turning down the offer to sublet the excess warehouse space. Similarly, any firm
that adds a standard allocated charge for fixed costs and overhead to the true incremental
cost of production runs the risk of turning down profitable business. (Hirschey, 2012).

Incremental Profits
Care must be exercised to ensure against incorrectly assigning
overly low incremental costs to a decision. Incremental
decisions involve a time dimension that cannot be ignored.
Not only must all current revenues and cost considered, but
any likely future revenues and costs also must be incorporated
in the analysis.

Incremental Profits
Example: Assume that the excess warehouse space came
about following a downturn in the overall economy. Assume
that the excess warehouse space was sublet for 1 year at a
price of $5,000 per month, or a total of $60,000. An
incremental loss might be experienced if the firm later had to
lease additional, more costly space to accommodate increase
in production.

Incremental Profits
Example: If $75,000 had to be spent to replace the sublet
warehouse facility, the decision to sublet would involve an
incremental loss of $15,000. To be sure, making accurate
projections concerning future pattern of revenues and cost is
risky and subject to error. Nevertheless, expectations about
the future cannot be ignored in incremental analysis.

References:
Economic Optimization Process - Managerial Economics. (2023, July 11). Hayden
Economics. https://www.rhayden.us/managerial-economics/economic-optimization-
process.html
Hirschey, M. (2012). Managerial Economics (12th ed.). Cengage Learning Asia Pte Ltd.

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