FINANCIAL SERVICES AND FINANCIAL INSTITUTIONS:
VALUE CREATION IN THEORY AND PRACTICE
J. Kimball Dietrich
CHAPTER 23
Financial Institution Operating Costs
Introduction
Cost efficiency is an obvious source of value for financial institutions as with any firms.
Financial institution managers must be even more conscious of costs in today's competitive
environment. Some questions good managers must address are:



What characteristics of costs and service production are relevant to value maximizing
strategies?
How can costs be estimated?
What does the reported evidence concerning financial institution costs suggest about cost
efficiency and what issues are unresolved?
This chapter opens with a general discussion of the economics of cost functions as relevant to
financial institutions. We discuss problems in cost measurement unique to financial service
firms. We review standard methods of estimating costs and particular problems experienced in
applying these methods to financial firms. Finally, we review the voluminous research on
financial service firm costs and find that it leaves many critical questions unanswered.
23.1 Costs and Activities
Costs are central to value production in all businesses. Costs determine return on
investment (ROI) as shown in the simple ROI formula introduced in Chapter 2:
Return on Investment =
(Price - Cost)xQuan tity
Investment
Despite the importance of costs to financial service performance, a lack of knowledge and many
disagreements surround financial institution costs. Many financial service firms came relatively
late -- following deregulation and increased competition in the 1970s -- to a sense of urgency
concerning knowing and controlling their costs. The lack of urgency was partly the result of
operating in protected markets with limited competition where profitability was guaranteed.
A basic disagreement among observers of the financial services industry is whether large
firms are more efficient. Efficiency means lower costs. One issue is whether financial
institutions, like commercial banks, have economies of scale. Another issue is whether there are
synergies between various financial services offered by one firm or economies of scope. To
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appreciate these issues, we must review some technical details from microeconomics.
Single Product or Activity Production
With a single product or activity, economies of scale are well defined. Firms experience
economies of scale when increases in their single level of activity does not raise costs
proportionately. For example, if activity triples and total costs double, there are economies of
scale. Diseconomies of scale occur when increases in activity levels increase costs more than
proporationately, as when activity doubles and total costs triple. We show total costs for various
levels of output using four different production methods in Panel A of Table 23-1.
The relation between total costs and output is called a cost function. Cost functions can
be seen as graphs of total costs on one axis and output on the other. We show the four cost
functions from Table 23-1 labelled as production methods (1) to (4) in Figure 23-1, Panel A.
Total costs can be divided into fixed and variable costs. Fixed costs do not change with
activity levels. Variable costs change with changes in output or activity. Fixed costs are defined
with respect to a range of activity levels and over a given period of time. For example, the
leasing cost of a facility like a bank branch or teller machine do not change over the lease period
whether or not the branch is used a little or a lot. Over time fixed costs can change and are not
fixed if new facilities are added to handle higher volumes of activity or if leases on facilities
lapse or facilities are worn out (fully depreciated) or sold. The key defining characteristic of
fixed costs is that up to a point in time and level of production, facilities cost the same no matter
how much activity there is. These costs are considered fixed.
Variable costs change with the level of activity. Economists call variable costs marginal
or incremental costs. Marginal costs are defined:
Marginal Cost = TC = TC(Output X + 1) - TC(Output X)
23-2
where TC(X) is total costs at output X and ΔTC is the change in total cost. Marginal costs for
the four production methods are shown in Panel B of Table 23-1.
Marginal costs increase or decrease with increases in activity levels according to the
underlying technology or process involved in providing the service activity. When variable costs
per unit of service decrease at high activity levels, marginal costs are said to be declining.
Declining marginal costs occur as production reaches efficient levels. When variable costs
increase with activity levels, marginal costs are increasing. Marginal costs might occur as
facilities or personnel are strained and become inefficient. Marginal or variable costs can be
constant if output levels do not affect productivity.
Average costs are total costs divided by the level of output, specifically:
Average Cost =
Total Costs
TC
=
Level of Output
X
23-3
using the above abbreviations. Average costs are shown in Panel C of Table 23-1 for the four
production methods. Plotting average costs for different levels of output produces the average
cost curve. The shape of the average cost curve relative to activity determines whether there are
2
economies or diseconomies of scale.
Economies of scale over a range of activity levels mean that average costs per unit of
activity are falling as output levels increase in that range. When average costs are falling,
marginal costs per unit of activity must be below average costs. Average costs increase at higher
activity levels when there are diseconomies of scale and marginal costs are above average costs.
When costs and activity levels are proportional, average costs and marginal are constant. For
many products and services, there may be both decreasing and increasing average costs over
ranges of activity.
Figure 23-1, Panel B, shows average and marginal cost curves for activities produced
with the four production methods from Panel A. Process (1) has constant marginal cost and
average costs and is not shown in Panel B of Figure 23-1. Methods (2) and (3) display
economies of scale since average costs (2) and (3) are falling. Marginal costs (2) and (3) are
below average costs in line with the above discussion. Process (4) has a so-called U-shaped cost
function where average costs fall over a range of activity and then increase. Marginal costs for
process (4) are below average cost over the range where average costs are falling and is above
average costs when they start to rise.
If fixed costs are a large element in performing an activity and variable costs are not
increasing, average costs will fall with larger outputs. In Figure 23-1, cost function (1) is a
process having no fixed costs and constant variable costs. Method (2) has positive fixed costs
but lower variable costs than process (1). Method (1) has constant average cost ($1 per unit).
Panel B of Figure 23-1 shows method (2) has declining average costs because fixed costs are
averaged over more and more units. Average cost curves for processes (3) and (4) show different
combinations of fixed and variable costs which change with the level of output.
A labor intensive operation with no equipment would be an example of a production
activity with no fixed costs. A computer or machine intensive way of performing the same
activity would have fixed costs. Over some levels of output, the no fixed cost method might
have lower average costs. At higher levels, the method with fixed costs could be cheaper. We
can see this with the average cost curve for cost function (2), which starts out higher than the $1
average for process (1), but which falls below that average costs after approximately 70 units.
All the processes have relatively higher or lower average costs depending on their mixture of
fixed and variable costs and the level of activity.
Some observers believe that large fixed costs relative to other costs cause economies of
scale in many financial services. Branch systems, clearing facilities, securities trading
organizations, and so forth, require extensive data processing equipment and communications
gear representing fixed costs. Personnel operating these systems require expensive training, also
representing large fixed costs needed to provide these and other financial services. These
services may operate at high or low activity levels with little change in costs. Many analysts
assume that economies of scale are widespread in financial services, an important assumption
and one we examine carefully in this chapter.
Multiple Outputs
The discussion of costs to this point considers only one output or activity. Multiple
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products or activities introduce a number of complications into the discussion of costs. Financial
service firms typically provide a number of services representing a number of outputs or
activities. We provide an example of a two-activity cost function in Table 23-2. Panel A of the
table shows the costs of producing two activities A and B separately while Panels B and C shows
total costs of producing the two activities in different fixed ratios, 50:1 and 25:1.
With many outputs, total costs are the same as with one activity but average and marginal
cost concepts require additional definition. With multiple activity levels, you cannot divide one
activity number into total costs to obtain average costs. Discussion of costs for multi-activity
firms must also account also for interrelationships between costs of different activities. A total
cost graph like Figure 23-1 is not adequate to capture costs of performing two activities1.
Figure 23-2 is a three-dimensional drawing showing total costs of producing the two
activities A and B provided in Table 23-2. Figure 23-2 shows total costs as the vertical distance
from the horizontal plane. Levels of two activities are shown on the two axes on the horizontal
plane. If A and B are produced independently, total cost curves are defined as in Figure 23-1 as
the graph above the horizontal A and B axes. If produced jointly, total costs represent the
vertical distance of a point on the cost surface from the horizontal plane. Cost functions with
multiple products become cost surfaces in three-dimensional or higher dimension space. Many
activities conceptually could be drawn in multidimensional space where total costs are associated
with combinations of outputs.
The A and B activities in Table 23-2 shown in Figure 23-2 could be two financial
services, like balance accounting and check clearing. Line X from the origin represents
combinations of B and A in fixed proportions 50 to 1 given in Panel B of Table 23-2, for
example 1000 checks cleared and 20 customer accounts or 2000 checks and 40 accounts, and so
on. Line Y repesents a different proportion, 25 to 1, given in Panel C of Table 23-2, for example
1000 checks and 40 accounts or 1600 checks and 65 accounts. Straight lines from the origin like
X and Y in Figure 23-2 are rays from the origin representing different proportions of two
activities.
While many activities are possible, two activities are sufficient to define terms and
illustrate important cost concepts with multiple outputs in a graph. The total costs of producing
A and B can be looked at from a number of angles, as illustrated in Panels A through E of Figure
23-3. Panels A and B of Figure 23-3 shows the total cost curves for output combinations along
rays X and Y. Each combination of A and B along rays X and Y is an output bundle of A and B
in fixed proportions. A bundle consists of customer accounts and checks processed. In the
figure, bundles on ray X have twice as much B activity as a bundles along ray Y. If we count
each bundle by how many units of A is included (account balances), we can see that total costs
are higher along ray X because of the higher B activity levels in those bundles.
Another angle to look at costs of producing two activities is to hold one activity level
fixed while varying the other activity. One example is to hold account balances fixed while
varying checks processed or vice versa. Total costs in this case are the intersection of the cost
surface in Figure 23-2 with lines representing fixed amounts of one activity. For example, the
1
See Baumol et al, especially Chapters 3 and 4, for a technical discussion of multiple product cost
concepts.
4
middle line in Panel C shows total costs when fixing activity B at 5000 units and varying activity
A from 0 to 200 units, corresponding to the line marked (B=5000) in Figure 23-2. Panels C and
D in Figure 23-3 show total costs of several bundles of producing activities A and B holding B
constant in Panel C and A constant in Panel D.
Another angle to look at the cost surface in Figure 23-2 is to change the proportions of
activities. We can look at total costs from 100 percent concentration in one output to 100 percent
in another and varying proportions in between. For example, the lower cost curve shown in
Panel E of Figure 23-3 provides total costs of moving from 100 percent concentration in activity
A (an (A,B) bundle of (100,0)) to 100 percent concentration in B (an (A,B) bundle of (0,5000)
and intermediate points in between, for example (50,2500). The left end of the lower total curve
represents 100 accounts and no check processing and the right end 5000 checks and no accounts.
The second and higher total cost curve represent doubling the outputs of A and B. Since the
upper curve dips in the middle, it is described as concave with respect to joint production. The
shapes of these curves are very different with the lower scale operations displaying a convex
shape (bulging upward.)
If activities or outputs are in fixed combination, they can be considered a composite good
and average costs computed for them along a ray. Ray average costs represent average costs for
fixed combinations of outputs over a range of output levels. The last column of Panels B and C
of Table 23-2 compute ray average costs for the X and Y combinations of A and B. These
average cost curves are shown in Figure 23-4, Panel A for ray X and Panel B for ray Y. Ray X
shows a U-shaped average cost curve, reaching a minimum at 50 (A,B) bundles (produced at a
ratio of 50:1), whereas ray Y average costs decrease to 190 bundles.
Economies of scale are defined for ray average costs in the same way as average costs are
defined for a single activity except that the level of output is a combination of activities. If
average costs decline for a fixed combination of goods along a ray over some range of output,
producing more of the activity will reduce costs and there are economies of scale. Larger activity
levels can be produced more cheaply, favoring larger size activity levels. Ray Y combinations of
(A,B) show economies of scale over nearly the entire output range shown. If average costs
increase over a range of outputs or activity levels, there are diseconomies of scale over that range
of activity. Ray X shows diseconomies of scale after 50 bundles.
The concept of ray average costs and economies of scale for combinations of activities is
valid for specified combinations of goods. In Figure 23-3, minimum average costs for
combination X and Y are achieved at different levels of the single activities A and B. If X and Y
represent different production methods, for example one capital intensive and one labor
intensive, cost minimization must consider the combination of outputs in determining the low
cost method of production.
When producing multiple outputs, the interrelationship of joint production become
important. When changing the proportions or scope of activities produced, proportions of inputs
and even the technology used for efficient production may change. An important concept in
considering the effect of joint production of two or more activities is termed economies of scope,
in the case of two activities technically defined as:
5
Cost(A,0) + Cost(0, B) - Cost(A, B) > 0
meaning that A and B can be produced jointly at lower total cost than independently. For
example, using data from Table 23-2, producing 100 units of A and 5,000 units of B
independently has a total cost of $415 ($110 and $305 from Panel A of the table) but can be
produced for $390 (Panel B) jointly at a point on ray X. Cost of joint production of activities A
and B show economies of scope.
Economies of scope may not be true everywhere on a total cost surface for multiple
outputs. In our example, producing 10 units of A and 250 units of B on ray Y can be done at
lower cost independently than jointly, that is for $71.78 separately as opposed to $71.65.
Economies of scope cannot be simply taken for granted as characteristic of joint production of
two or more outputs with any combination of activities (along any ray) at any scale of production
(distance from the origin.) Minimizing costs depends on the proportion of outputs and the scale
of operations.
One important aspect of the analysis of total costs not considered to this point is
efficiency. In our discussion, we have assumed that the total costs on each point of the cost
surface for each combination of multiple outputs, A and B in our example, is produced at
minimum total cost or are produced efficiently. Points along the total cost surface represent
different efficient -- cost minimizing -- technologies.
For example, efficient production methods to produce combinations of goods in
proportions represented by rays like X and Y in our example may represent two ways of
producing activities A and B. The cost efficient method used for production combinations along
ray X might use a mainframe computer with low skill clerical employees and the method for
combinations along ray Y might use more highly trained employees using microcomputers.
The above discussion makes it possible to distinguish two kinds of inefficiency. The first
type of inefficiency is using wrong technology for a given output combination, for example a
mainframe and low-cost clerical employees to produce an output combination along ray Y.
Economists refer to this type of inefficiency as allocative inefficiency since inputs into
production are not cost minimizing. The other type of inefficiency is simply not minimizing
costs or producing maximum output with a technology. This type of inefficiency is sometimes
called X-inefficiency, especially when unnecessary costs benefit management at the expense of
investors and customers of the firm. X inefficiencies are presumed to be more prevalent in noncompetitive or regulated markets where price competition does not enforce discipline on
managers. We return to these concepts below.
Since the total cost surface in Figure 23-2 represents the lowest total costs which
management can achieve, relevance to management decision making implies that management is
aware of and knows how to implement the best technological solutions to producing each output
bundle. Implicitly, management must understand the technology and have the incentive to
minimize costs. In practice, there are many reasons why total costs could be more than those
implied by the efficient cost surface for producing multiple outputs. Poor incentives or
uninformed management may not be able to realize theoretically available economies of scale
and scope.
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We emphasize two important attributes of costs with multiple outputs in financial
services using Figures 23-2 to 23-4. First, the low cost technology depends on both the
proportions of outputs needed and the scale of operations. This is true in all financial services
with multiple outputs. Using our customer accounts and check processing example from above,
a low volume of check users in small deposit-taking firms, perhaps serving a special market
niche, may require a different technology from a large scale operation with high activity in
accounts. With multiple outputs, simple discussions of economies of scale are not meaningful.
Managers must consider the composition of output and the scale of output.
Second, an important characteristic of the cost functions shown in the figures is that
economies of scale do not have a simple interpretation and vary along different combinations of
output or rays in the total cost diagrams. Ray average costs can reflect economies of scale in
producing combinations of activities but the relevance of these combinations cannot be
determined independently of customer demand or marketing plans. Economies and
diseconomies of scale do not simply occur with large size when there is more than one activity.
While this discussion is general for any business or economic activity, the analysis of cost
curves for financial services is particularly critical for the managerial and policy issues
confronting this industry in the future because of the pervasiveness of joint production.
Managers wish to create value for investors by producing services at low costs and policy-makers
strive for economic efficiency through laws and regulation. Application of these cost concepts
and implementation of cost measurement to achieve these objectives are difficult in financial
services for many reasons. We deal with conceptual problems first and then analyze problems in
cost measurement in subsequent sections of this chapter.
23.2 Inputs into Production of Financial Services
A conceptual framework to assess the nature of costs in financial services is essential to
understanding cost factors determining profitability. Our discussion of costs in financial services
begins with a brief review of the six activities in the value chain for financial services as
introduced in Chapter 2. This classification of activities is useful in a common-sense
consideration of what inputs go into producing financial services. The goal is developing fresh
insights into cost efficiency and the nature of inputs required to provide financial services.
Pricing/Term Setting: This activity, as analyzed at length in the chapters of Part II, is an
important source of value. When performed effectively, these activities are based on research,
negotiation, or application of advanced analytical techniques. In all cases, labor and human
capital are important inputs. Training, experience, and careful evaluation of complex technical,
market, and customer specific information are required in most financial service pricing
problems.
In retail markets, pricing and other terms are intrinsic to product design. In wholesale
markets, more complicated and specific problems must be analyzed and negotiated. In all
financial services, from new credit vehicles to sophisticated risk management products,
innovation is an important source of short-term excess returns and value. Competitive advantage
requires offering products for which there is little competition at the terms and prices demanded.
7
What are the cost elements in this activity? Product pricing and negotiations are labor
intensive activities requiring skilled, creative, entrepreneurial people. While some computer and
communications experience is required in some cases, costs of labor and human capital appear to
be important if not dominant in pricing and term setting.
Marketing/Information: Developing information about demand and competition for financial
services and telling potential customers about useful services at reasonable terms requires
communication. In most wholesale financial services, communication is between institutional
customers, usually represented by officials, and financial service firms, often represented by
calling officers or other officials. This communication is a labor intensive activity. In order to
communicate effectively about complex financial needs requiring sophisticated products or
services, experienced and educated people are required.
Marketing and information gathering for retail markets also relies on personal customer
contacts. In retail financial services requiring data input or routine communication, modes of
communication which save on labor costs through minimization of labor time, level of worker
training, or substitution of labor by other means, can be used. Labor may be minimized by using
automated response systems or employing telephones and computers to program marketing calls
in telemarketing. Training for workers may be reduced by relying on computerized artificial
intelligence or other analytical devices, like credit scoring. Capital in the form of computers and
communication equipment may substitute for branches with high labor costs to reduce labor
expenses.
Labor, skilled or unskilled, cannot be eliminated from the marketing and information
activities required to produce retail financial services using capital intensive methods. Systems
minimizing or substituting for labor must be designed and tested by skilled professionals.
Systems relying on lower trained and less expensive labor must be managed by motivated
management staff. Labor costs are large in the marketing and information activities in both the
wholesale and retail markets are hence a major cost item for financial services.
Monitoring/Controlling: Keeping track of contract provisions as is required by monitoring can
use computers or labor intensive systems. Control procedures required when contracts are
violated such as special collection efforts or legal actions can be triggered automatically by
computer systems or introduced after careful analysis and judgment of the best strategies in
dealing with unwanted outcomes of financial relationships. In all cases, monitoring and control
activities require managerial review and motivated personnel to be an effective source of value.
Retail and wholesale markets may require different approaches, given differences in the number
and homogeneity of contracts or relationships in that market. Both require substantial labor
inputs.
In keeping track of timeliness of loan or insurance premium payments in retail,
computerized accounting systems can flag late or missing payments and produce exception
reports. Well designed systems assuring a high level of contract performance must be created by
programmers and systems analysts with a complete understanding of the financial products and
their customers. Systems must be updated and changed to respond to changes in the economic
8
environment, the market, and regulation. At some point, the functioning of the system must be
assured by motivated management. Often computerized systems require substantial clerical and
customer contact staff to input results and assure compliance.
While computerized and otherwise automated monitoring and control systems may
reduce labor inputs or replace expensive professional staff time with less skilled labor, design
and management of these systems typically require management of sophisticated system
development and maintenance personnel and management of large clerical staffs. To be cost
effective, systems subtituting capital for lower cost labor do not avoid problems of management
of large and expensive support personnel and managerial talent.
In wholesale markets, contract enforcement through monitoring and control activities is
more likely part of a complex customer relationship. Specific contract language and complex
specific business circumstances determine the most appropriate course of action for management
and officials involved. For example, should a loan for which interest is late and covenants
violated be called and a firm liquidated or should the loan be renegotiated or work-out specialists
brought in? These decisions are as important as the original credit decision and may involve
accountants, attornies, and other professionals. Legal action as part of controls can be extremely
expensive and cause greater losses than non-enforcement of contract terms. Clearly these actions
require use of trained experienced personnel. Monitoring and control of specific institutional
contracts, like credit instruments, insurance policies, underwriting services, and so on, is a labor
intensive business.
Production/Delivery: Activities associated with production and delivery of financial services
include staffing branches, back offices, computer centers, distribution systems, communication
facilities, and all the other required support for officials of financial firms generating credit
instruments, securities exchanges and issues, insurance policies, transaction processing, asset
management services, or information and advice. Modern communications and computing
technology has probably had a greater impact on the production and delivery of financial services
than on any other link in the value chain.
All of the production and delivery systems associated with financial services have been
heavy users of low-skilled clerical and secretarial workers. The back offices of many banks and
securities firms are staffed with part-time workers and students. Many of these production
systems, like loan or check processing or securities delivery, rely on large scale computer
systems. Many of the production and delivery systems for financial services consist of data
entry, document preparation, information retrieval, and report generation, based on large
integrated data bases.
Despite the heavy investment in computers and often other physical assets like branches,
telecommunications equipment, trading floors, trucks and airplanes, labor is an important input
into production and delivery activities. As with monitoring and control systems, talented system
design and management personnel are required to manage the many people involved in operating
and maintaining large scale systems, despite the heavy use of capital-intensive technology.
Nearly all financial institutions report salary and wages as the largest non-financial expense,
followed by equipment, communications, and space expenses.
9
Funding/Investing: Finding the cheapest funds or highest return investments to perform financial
services requires personnel trained and experienced in evaluation and use of financial market
technical, market, and customer specific information. The communications and data processing
revolution has only increased the range of alternatives available to managers responsible for the
financing activities of financial institutions. Management of funding and investing activities is
extremely labor intensive. Salaries and responsibilities of chief financial officers of financial
institutions are evidence of both the importance of this activity and the high labor cost of
efficient operations.
Funds or investments can be made more cheaply in large lots. Some believe that
economies of funding and investing may lower costs from large scale operations. Management
time and transactions costs are definitely reduced for large financial transaction amounts. These
considerations argue for economies of scale for large scale funding or investing operations.
Offsetting these cost-reducing aspects of large scale funding and investing activities are
management control problems involved with large numbers of sophisticated financial personnel
handling large sums of money. Costs from errors in judgment or losses from uncontrolled
activity by officials increase with transaction size as well.
Professional labor costs are important in the costs of funding and investing activities of
treasury and trading areas of financial institutions. Aside from financial costs determined by
market conditions (interest expense and so on,) portfolio management, transactions, and
safekeeping are the large costs. The question is whether economies in these costs extend to very
large amounts of funds associated with larger financial institutions. Given that management of
professional organizations characteristic of the treasury and investment divisions of financial
firms are complex, it is likely that economies of scale are exhausted at a smaller asset size than
the largest banks and other financial institutions, perhaps $500 million2. In competitive financial
markets with active asset management available for small amounts of funds and competition for
trading and safekeeping services, lower labor costs in funding and investing are probably not a
source of economies of scale for financial firms with billions of dollars in assets.
Risk Bearing/Sharing: Risk management activities have become an important aspect of financial
service firm operations. In managing financial market risks, new markets (like the swap market)
and risk management instruments (like options and futures) have increased the necessary training
and experience of personnel assigned to supervise and implement financial risk strategies. Most
of the above discussion of labor costs with funding and investing activities applies to the
management of financial risk.
Financial risks are large but not the only risks confronting financial institution managers
as discussed in Part IV of this book. For example, liquidity and operating risks may not be
shifted or shared but may not be reduced through large size. These risks may or may not be
reduced from diversification or redundancy with large scale operations if those operations are
highly focused in providing services to narrowly defined markets, for example on mortgage
lending. In other cases, as discussed in elsewhere in this book, benefits of diversification can be
2
See McAllister and McManus (1993) for economies of scale discussion focussing on bank portfolio
(total assets) size.
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achieved without large size, for example by diversifying credit risk with loan sales and
participations. The benefits from diversification can be enjoyed by effective use of new risk
management instruments. In any case, all risk management activities require trained and
experienced personnel who must be motivated, managed, and monitored.
Summary of Costs in Activities in Value Chain for Financial Firms
The above discussion is intended to highlight the inputs into performance of the activities
in the value chain for financial services. Aside from financial costs like interest or market losses,
inputs into these activities tend to be dominated by labor expenses. The labor is either
professional labor or management and low-skilled labor. Computers and modern technology in
communications have not reduced labor expenses so much as increased the services possible to
financial service firm customers. We noted in Chapter 1 that employment in financial services is
increasing.
Managing production of services in labor intensive operations limits the possibility of
economies of scale. Identifying talent, motivating people, and monitoring performance are not
economic functions which increase in efficiency with size of operations. Large financial
corporations must be broken down in specialized divisions and functional areas. Coordination
and communication between parts of the organization become more difficult. Flexibility to
exploit opportunities or avoid problems is limited if layers of corporate structure must be
penetrated to gain approval for decisions. On the other hand, rogue or dissident management
groups can often underperform or create problems undetected in large bureaucratic organizations
dealing in complex transactions and information. The importance of primarily variable labor
costs in financial institutions offsets the likely importance of the fixed costs of facilities which
some argue are the source of economies of scale.
23.3 Financial Service Firm Outputs
Output measurement in any industry is difficult. For example, auto manufacturers
produce sedans, sports cars, and light trucks, and other vehicles. Output can be measured simply
as the number of vehicles produced but such a simple output measure misses wide differences in
the attributes of individual units. Quality of output is another dimension difficult to measure
aspect of production. Recalls or future repair records are not reflected in a unit count of
production although they reflect the quality of units produced. Crude as they are, though,
manufacturing output measurements are precise relative to financial service output measurement.
Despite the dominance of service industry output in advanced economies and the growth
in service sectors discussed in Chapter 1, controversy surrounds measurement of service sector
output3. Estimates of productivity growth prepared by government agencies, like the Commerce
3
This discussion draws heavily on Griliches, "Introduction," and financial service chapters in Griliches
(1992). This discussion is recommended for an advanced level summary and review of the issues in
financial service firm output measurement.
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and Labor Departments in the United States, produce opposite results. For example, between
1979 and 1989, the Bureau of Economic Analysis (Commerce Department) finds no change in
productivity in banking in the United States, while the Bureau of Labor Statistics (Labor
Department) in contrast finds an important annual 2.3 percent increase.
Cost functions like those discussed above relate total costs to output. In the case of
multiple outputs, a cost surface relates the cost of efficient input combinations to levels of
activity or outputs. Measurement of costs requires a clear definition of output. Definition of
output for financial services, as with many service industries, is not only not well defined, as
discussed above, but whatever measures are used are determined by data availability rather than
carefully designed output measurement proxies.
Most analysis of financial institution costs have been directed at commercial banking.
Much of this literature is relevant to other financial service firms as well. Berger and Humphrey
(1992) distinguish three general approaches to output measurement in banking: (1) the asset
approach; (2) the user cost approach; and (3) the value added approach. We discuss each of these
in the following, noting that all are inadequate but that some are better proxies of true output than
others.
The asset approach in the context of banking argues that banks produce bank assets,
primarily loans, using as inputs labor and capital, causing operating costs, and financial inputs
providing funds, like deposits and borrowed money, which cause interest costs. Many studies
use loans as a measure of outputs and include deposits as well as other physical inputs as inputs4.
The limitations of measuring output in terms of asset amounts, or even number of assets (like
loans) are obvious. Financial services can be provided to a greater or lesser degree with different
assets and of course financial services are provided with liabilities, like transaction accounts.
A more flexible approach is the user cost approach which does not prespecify whether
assets or liabilities are inputs or outputs but rather determines whether they make a net
contribution or reduction to revenues or returns5. User costs for a given period are defined as:
ux i =  - hx i
23-5
where user cost, u, for an asset or liability xi is the firm's opportunity cost, ρ minus the holding
cost, h, for that asset or liability6. The holding cost includes interest and gains received minus
loan losses. If user costs are negative, products, like loans, are outputs since negative costs are
positive returns. If user costs are positive, the products, like deposits, are inputs. Assignment of
inputs and outputs is determined by whether user costs are positive or negative and are
determined by the factors shown in the formula. Categorizations of inputs and outputs is
determined by the data but can change through time. While the user cost approach is flexible, it
emphasizes financial quantities like balance sheet items and interest costs and does not focus on
financial institution operations.
4
For example, Kolari and Zardkoohi (1987) and references.
5
See Hancock (1985), a seminal contribution to this approach.
6
See Fixler and Zieschang (1992) for a detailed discussion.
12
The value added approach considers all financial activities to have the potential of
providing outputs in terms of services and concentrates on operating costs of financial
institutions. For example, using Federal Reserve bank cost statistics discussed below, capital and
labor costs are allocated to financial data. According to one study, demand deposits in 1988
accounted for 36 percent of bank value added and commercial and industrial loans for 14
percent. These value added figures are identified with output of services7.
While all three approaches to output measurement have been widely used, they are all
problematic from the managerial decision point of view emphasized in this book. The question
of relevance to management is, "What are we good at?" which can mean "What can we produce
at low cost relative to competitors?" Answers to these questions are used to organize activities in
the value chain to create the most value in financial services.
In most financial service firms, operating costs incurred by financial service firms are due
to hiring resources necessary to produce activities, like negotiating or monitoring, which are the
source of competitive advantage. Many of these activities do have measurable outputs. For
example, successful negotiations produce a deal: the number of loan deals could be counted as
output. But the negotiated terms in a deal can also be a source of value, as we discussed in Part
II. Counting pages of loan contracts or number of covenants does not seem adequate to capture
this value creation. Moreover, credit arrangements take place over time: monitoring, controlling,
and other activities affecting value creation occur during this time. Some of these activities can
also be counted, such as number of inventory counts or loan file reviews. All financial service
activities could be scrutinized for measurable activities, but item counts seem inadequate output
measure for many of these activities8.
For some financial service activities, such as transaction processing, item counts may
serve effectively as an output measure: checks cleared seems like a reasonable measure of output
from a check clearing system. But narrow output definitions do not do justice to complex
financial services. A transaction account, to continue the example, includes many other services,
such as check cashing, balance maintenance, balance inquiries, non-check transfers, automatic
payment, and so on.
Strategic Importance of Operating Costs for Financial Services
Enumeration of activities to relate outputs to costs of providing financial services is
conceptually feasible. Given the inadequacy of some of enumerations as output measures and the
expenses of making enumerations, the focus on output measurement may not always be justified
by the refinement of costs estimates they provide. Despite the importance of cost control as a
source of value, a pragmatic approach may be all that management can take to the problem of
identifying efficient production of financial services.
7
See Berger and Humphrey (1992.) This classification draws on their discussion.
8
See Bresnahan et al (1992), Fixler et al (1992), and Mester (1992) for innovative attempts to measure
financial service output in terms of the information value and monitoring services produced in securities
trading and banking segments.
13
The critical issue for management is whether a firm has a competitive advantage in some
activities required for financial service production. If the firm does not have a cost advantage as
determined from estimates of cost functions, market competition, or common sense, management
must decide whether other suppliers perform the activity and jointly provide the service with
contractors or to drop the service from the financial institution's marketing strategy. These
questions may not have clear answers, but intelligent managers must be aware of the relevance of
the questions, the implications of crude measures of costs, and alert to confirming or denying
evidence in any form which suggests answers, such as inability to match competitors' terms.
Two issues related to costs have dominated much of the strategy question for financial
service firms: economies of scale and economies of scope. If there are economies of scale, large
size provides a competitive advantage. If there are economies of scope, cost minimizing output
combinations can define a profitable strategy. In the next section we review approaches to
estimating cost functions for financial institutions. Estimates of these function have been used to
evaluate scale and scope economies in financial institutions. We warn readers that the answers
are not clear and the evidence is clouded by the problems of input and output definition and
measurement we have discussed.
23.4 Estimating Costs
Three approaches are used to estimate the costs of business activity and have been applied
to financial service firms. These approaches are (1) cost accounting; (2) statistical cost analysis;
and (3) process analysis. None of these approaches has satisfactorily answered the strategic
questions raised in the previous section. Creative managers will want to improve on the standard
approaches in future cost analyses. Most of the published work using these approaches has
analyzed costs of commercial banking. We discuss each cost estimation approach using banking
as examples in the following discussion, but emphasize that these approaches are equally
relevant to non-banking financial services.
Cost Accounting:
Cost accounting uses information generated by firms' accounting systems.
The objective of cost accounting is to measure costs associated with some business unit,
product, or project, called a cost object9. Costs incurred during the accounting period are
allocated to the cost object. Incurred costs are either direct costs which can be associated with
the cost unit or indirect costs which can be allocated to the unit on some pro rata basis.
The best widely available example of cost accounting for financial service firms is the
Functional Cost Analysis (FCA) study of the Federal Reserve Bank. The FCA is a voluntary
effort where participating banks complete surveys of their activities, financial data, and cost
allocations to fifteen cost objects grouped into three overall functions: (1) fund-providing
functions, composed of demand deposit, time deposit, and non-deposit funds; (2) fund-using
functions, composed of investments, and real estate, installment, credit card, commercial,
agricultural, and construction loans; and (3) non-fund using functions, including international,
safe deposit, trust, data services for banking and non-banking and customer use.
Table 23-3 provides selected tables from the "National Average Report: Commercial
9
See Horngren and Foster (1991) for an extended treatment.
14
Banks" for 1989 from the FCA banks for demand deposits and installment loans as an illustration
of cost accounting. The tables illustrate several requirements for cost accounting of narrowly
defined functions. For example, officer and employee salary costs are allocated to functions
according to time allocations of personnel collected or made by accountants in participating
banks10. Indirect costs like publicity and "other operating expenses" are assigned to each
function based on sharing rules (based on historical data.) Finally, in order to compute item
costs, compound output measures are calculated. For demand deposits, a "weight unit" of
transactions (on-us debits, deposits, transit checks and account maintenance) is used to compute
average costs. For installment loans, costs are assigned to acquisition and maintenance of loans.
The FCA is valuable to participating banks. Each bank receives an individual report and
is compared to similar banks in that report. For comparison purposes, the report is useful to
management in comparing average costs. Similar cost analysis is possible for all financial
institutions. Total allocated expenses to functions can be compared and estimated average costs
for some outputs, like loan acquisitions, can be calculated.
Cost accounting like the FCA has several shortcomings as a basis for strategic decision
making where costs are a important factor. First, the costs are historical accounting costs, not
current economic costs. Second, costs are average costs and not marginal costs useful in making
incremental pricing or product design decisions. Third, average costs like those calculated in the
FCA are based on arbitrary weighted output measures and overhead allocations based on
comparables or experience not relevant to new initiatives. Finally, in reflecting reported
accounting performance of financial firms, costs derived from cost accounting may not reflect
efficient production or costs associated with a changed market environment or mix in outputs.
Statistical Cost Estimation
Statistical cost estimation estimates the relation between total costs and output using
econometric techniques. For example, in many studies least squares regression analysis is used
to estimate the best functional relationship between total costs and output. Multivariate
regression analysis allows incorporating many variables into the relations to adjust for output mix
and input amounts and prices.
Ad hoc Cost Functions: In statistical cost estimation, the choice of the functional form is very
important. In some practical applications, functions relating costs to output are simply chosen
for convenience. For example, a simple linear regression estimates an intercept, a, and slope
term, b, for costs as a function of output:
23-6
TC = a + bX
where TC is total costs, X is output, and a and b are estimated. A linear cost function has a
constant marginal costs (the slope or b). A linear cost function implies decreasing average costs
over all output ranges whenever the intercept term (fixed costs captured in the intercept a) is
positive.
10
This discussion is based on the Instruction Manual (1988) for the FCA from the Federal Reserve.
15
Other cost functions can be used. Common cost functions are the quadratic and cubic,
written as follows:
TC = a + bX + cX2
TC = a + bX + cX2 + dX 3
23-7
23-8
A quadratic cost function can be concave or convex, implying falling or increasing average costs
and economies or diseconomies of scale. At some output range, quadratics become dominated
by the square term and can become negative if c is negative or very large if c is positive in
equation 23-(5). Cubic cost functions can be U-shaped over some range, demonstrating both
economies and diseconomies of scale, but at some output will also be dominated by the highest
power term. These functions are not satisfactory for many purposes because of they may have
extreme values when evaluated outside the estimation sample. They are also atheoretical in
relating costs to outputs.
Production Functions and Cost Functions: Often cost functions are derived from production
functions linking output to inputs. An example of a common production function is the CobbDouglas production function, which relates output to inputs as follows:
Y = AL K
23-9
where L and K are inputs (labor and capital are often used) and α and β are parameters. If α + β
= 1, output is characterized by the constant returns to scale. If α + β > 1, there are economies of
scale in that output increases more than proportionally to inputs, and the opposite is the case if
the parameters sum to less than one.
Cost functions can be derived from production functions if the firm is assumed to
maximize efficiency. Since total costs in the two input case can be written:
23-10
TC = wL + rK
where w and r are the costs associated with using different levels of L and K. By optimizing the
production function with respect to inputs and substituting optimal input combinations into the
cost function, a cost function can be derived. In the case of Cobb-Douglas, the logarithmic form
of the cost function becomes11:
lnTC = a + blnY + clnw + dlnr
23-11
In this form, output and factor prices are used to explain costs of different firms or the same firm
at different points in time if the firm is economically efficient. This function can be statistically
estimated from data on input prices, output, and total costs. Statistical tests can be constructed to
test whether α + β > 1, that is, whether there are economy of scale.
Translog Production and Cost Functions: Cobb-Douglas production functions are limited
11
See Kolari and Zardkoohi (1987), Chapter 2, or Pindyck and Rubeinfeld (1989), Chapter 7 and
Appendix, for derivations.
16
because they imply diseconomies or economies of scale at all output levels. Cobb-Douglas
functions can also only have one output. Many cost studies use other forms for the cost function.
More general production functions and cost functions which allow multiple outputs and Ushaped costs curves have wider application. The most common function in studies of banking
and other financial institution costs is the "transcendental logarithmic" or translog function12.
This cost function in a two output case, where Y1 and Y2 are the outputs, can be written:
lnTC = a + b Y1 + c ln Y2 + d ln w + e ln r +
f ln Y12 + g ln Y22 + h ln w 2 + i ln r 2 + j ln w ln Y1 +
23-12
+ k ln w ln Y2 + l ln r ln Y1 + m ln r ln Y2 +
n ln Y1 ln Y2 + o ln w ln r
In the simple two output, two input case shown in equation 23-(12), the parameters a,b,c, and so
forth, fifteen in all, must be estimated in regression analysis. Such an estimation uses logarithms
of output measures, input prices, their squares and all possible cross products. A fairly large
sample must be available to estimate this many parameters.
More complex translog cost equations can and have been used to estimate cost surfaces
with more than two outputs and with more than two inputs, but they obviously get much more
complicated in terms of number of parameters (a, b, c, etc.) to be estimated. All versions of the
translog cost function includes levels, squares, and cross products of the output and input price
variables. The advantage of the translog cost function is that is is U-shaped. This more general
shape allows ray economies and diseconomies of scale over different output ranges. It is also
used by many analysts to calculate of economies of scope for financial service firms when total
cost comparisons include positive level of all outputs13.
The translog cost function has been criticized by McAllister and McManus (1993)
because it imposes a U-shape on total costs. When the cost function is estimated for banks of
different size classifications, the low point of the U is reached at different levels. These authors
argue that U-shape total cost functions estimated in studies using smaller banks, such as those
participating in the FCA study having less the $1 billion in assets, cannot be compared to those
studies using banks having larger than $1 billion in assets. Different samples with different low
points in U-shaped cost functions yield contradictory evidence on the relevance of economies of
scale in banking.
12
The translog cannot be derived directly from a production function except as an approximation. See
Kolari and Zardkoohi (1987), p.45.
13
Specialized firm costs cannot be used in the translog cost function because it is multiplicative in outputs
(see Berger et al (1993), p. 225.
17
Process Analysis
Process analysis consists of careful measurement and analysis of narrowly defined
processes necessary to perform an activity, such as demand deposit processing. Process analysis
focuses on the physical inputs like capital and labor required to produce carefully specified
activities. Time and motion studies, which analyze the amount of labor and the time taken to
accomplish tasks, is an input into process analysis. This approach is closer to industrial
engineering than accounting and takes a much more microeconomic look at the costs of
particular functions.
Process analysis has the advantage of not being distorted by overhead allocations,
required for cost accounting, or assumptions about error terms or efficiency, required for
statistical cost analysis. Managers benefit from the close analysis of production technology and
cost estimates can be varied over a wide variety of operating environments to assess costs and
resource needs. The importance of resource availability to production capacity is highlighted by
process analysis.
Process analysis can also be used to evaluate shadow costs, defined as the costs of
resource limitations in terms of lost profits. If values can be attached to outputs, given the
relation of output to inputs provided by process analysis, the change on the value of output by
incremental relaxation of input restrictions can be calculated. Incremental profits are identified
as the opportunity costs of resource limitations. By comparing input costs to shadow costs of
resource limitations, managers may be able to identify costly bottlenecks in service production.
Process analysis is limited to narrow applications of well-defined production of outputs.
Usually, the production technology is linear, meaning the outputs are proportional to variable
inputs. The relation between inputs and outputs may be difficult and expensive to establish
clearly. These relations, as we shall see, are critical to the accuracy of cost estimates derived
from process analysis.
Osborne (1982) provides an example of process analysis applied to demand deposit
processing. The process analysis he uses is readily applicable to other routine transaction
processing financial services, like claims processing or securities clearing. More complex
financial activities like price and term negotiations or monitoring activities could be analyzed in
a similar form but since labor costs in these activities vary so much and there are many variables
determining measures of output, such as how many covenants in a loan agreement, the best use
of process analysis would seem to be in routine operating activities.
In Osborne's analysis, demand deposit processing occurs within five cost areas: (1) the
depositor; (2) the teller; (3) the check processing contractor; (4) the back room; and (5)
everything else -- here the clearing system. There are two transaction items: teller items and
nonteller items. Costs are analysed are estimated for contractor's services, teller handling, backroom handling, statement mailing, and shipping. Outputs (cost objects) are account balance
services and account activity (teller and nonteller items.)
Process analysis requires minimum labor, capital and space requirements for each
activity. For example, Osborne assumes teller handling requires tT minutes of teller employee
costing eT cents per minute for each teller transaction. In addition, a teller window capital cost is
computed as the rental value of the space and capital improvements required for a teller to
18
perform teller transactions, kKT. Tellers can perform a maximum number of transactions per
time period, M, at a teller window. The total teller items requiring handling per month is HT.
Osborne's example assumes tellers take 2.2 minutes per transaction, labor time at
prevailing teller wage rates costing $.15. Teller windows have a maximum capacity of 5000
items per month. A teller window occupies space worth $400, estimated as the value of safedeposit boxes which could occupy the same space as a teller's window. In this analysis, the cost
of teller items is:
C = .15 HT + 400T u( HT )
5000
23-13
where u is the minimum number of windows required to handle teller item volume. For
example, volume of 5,000 items has teller costs of $1,150 per month, while 8,000 items $2,000,
requiring two teller windows.
The total cost in Osborne's process analysis of demand deposit processing is the sum of
the five separate cost areas.
Because of capacity restrictions, such as teller maximum or machine maximums in other
processes, the average cost function for each activity in terms of output will have spikes where
additional resources, like teller windows, are needed to handle higher volumes. The total cost
function will include spikes coming from restrictions in all activities analysed. For example, a
spike at 5001, 10001, 15001, and so on, teller items will occur because a new teller window is
needed over each of those levels of teller item handling.
Since outputs are typically a proportional to inputs in process analysis except for capacity
constraints producing spikes in cost functions, economies of scale will be determined by the
relation of costs of expanding capacity, like leasing a new teller window, and variable costs, like
teller time. Economies of scope will only exist if facilities can be shared to produce more than
one output. Process analysis may be instructive for management in understanding determinants
of costs in precisely defined areas, but the assumed cost, time, and capacity numbers will
determine the importance of scale and scope economies.
Cost Analysis in Practice
In many real applications, some or all of the three approaches to estimating costs are used
together. For example, many statistical cost estimations have been based on the FCA data which
is derived from accounting data. The FCA data, as we have discussed, depends on time
allocations similar to those required for process analysis. For managers, the importance of
knowing costs requires that creative use of all potential sources of information be exploited to
assess marginal and average costs of providing financial services.
6. Empirical Estimation of Costs and Implications
The research on financial institutions is voluminous and is reviewed several places14. We
14
See Kolari and Zardkoohi (1987) for banks and more recently the Journal of Banking and Finance,
19
review and critique briefly the published literature estimating financial institution cost functions
in this section. The summary conclusion is that managers of financial service firms have a lot to
learn about the costs of providing financial services. Not only are marginal costs estimated
crudely, but the question of existence or non-existence of economies of scale and scope is open.
Because of the labor intensivity of financial services, presumptions of scale economies must be
tested rigorously. Managers assuming the existence of scope economies must be careful to
incorporate the influence of output mix, as discussed with our example cost functions.
All cost studies use cost and output data for many financial institutions, usually several
banks. Most studies assume that banks are efficient by using the cost functions derived explicitly
from production functions, as in the Cobb-Douglas case above, or implicitly, as in the translog
case. In estimating regression equations, an error term is added to the equations. A least squares
estimation program minimizes the sum of the least squares. Other estimation techniques
optimize estimation by alternative criteria, such as maximizing the likelihood function or
probability of the parameters correctly producing the sample. Most regression techniques fit cost
curves with roughly equal positive (higher cost) and negative (lower cost) departures from the
line. Several authors reviewed in Berger et al (1993) have pointed out a shortcoming of this
approach when financial institutions are inefficient.
Inefficiency means financial institutions do not combine inputs to minimize cost for given
output levels. Since efficiency means minimum costs, departures from the minimum costs
should all be positive. Several analysts have dealt with this problem using regression analysis
not assuming symmetric error terms or using non-parametric techniques, for example assuming
that the lowest cost firms are efficient and comparing their costs and activities with others.
Berger et al (1993) review these studies. They find that this research has produced
estimates of bank efficiency in the range of 68 percent (Grabowski (1993)) to 88 percent (Pi and
Timme (1993)), meaning that efficient firms' costs are somewhere between two-thirds and 88
percent less costly than average banks. The most efficient credit unions are about 20 percent less
costly than average inefficient credit unions. Efficient life insurance firms appear on average to
be half as costly as average insurance firms. These results are controversial but suggest
widespread inefficiency in the financial services industry.
Results on scale and scope economies are also controversial. Most financial institution
cost research until recently has concentrated on banking. In banking, recent work has extensively
employed the translog cost function discussed above. Economies of scale disappear at fairly low
size for studies using smaller banks, typically relying on FCA data. For example, Berger et al
(1993) report that average costs are minimized for banks with assets in the range of $ 75 to $300
million in assets, very small by international standards. When analyzing banks over $1 billion in
assets, McAllister and McManus (1993) find constant average costs after $10 billion in assets,
again small in terms of multinational banks. Berger et al (1993) find limited evidence for
economies of scale in other financial services. Finally, other studies of insurance industry and
securities industry costs suggest little evidence of economies of scale or scope15.
"Special Issue on the Efficiency of Financial Institutions," edited by Berger et al (1993,) for all financial
institutions, including banks.
15
For example, Geehan (1977) for insurance, Goldberg et al (1991) for securities industry.
20
Additional evidence on the relation of size and cost efficiency can be obtained from
analysis of mergers. Again, most of the published research deals with banks. For example,
Cornett and Tehranian (1992) and Berger and Humphrey (1992) both examine post merger
performance of commercial banks. Both studies report that based on many operating
characteristics, such as cash flow or operating ratios like return on assets, only modest (if any)
improvements in bank performance are detected after mergers using large samples of bank
combinations. The implication of this is that larger size is not a source of cost efficiency and
may be considered further evidence supporting the absence of economies of scale in banking.
Finally, market performance of financial service firms belies the hypothesis that large
firms are more efficient as investments than smaller firms. Analysis of financial firms in the
Fortune Service 500 through 1993 reveals that the three largest U.S. bank holding companies -Citicorp, Bank America, and Chemical -- ranked 80, 73 and 75 respectively out of 100 based on
their ten year total return to investors (dividends plus gains.) Smaller banks, like Fifth Third
(fifty-fifth in size) and State Street (fortieth) ranked first and second based on ten year total
returns. These top performing banks had assets between $10 and $16 billion while the largest
banks had assets between $140 to $214 billion. The best total returns of the seven largest thrifts
reporting ten year total returns was Washington Federal which had total assets of $2.7 billion
compared to the largest thrift, H. F. Ahmanson, which ranked sixth out seven and had total assets
of $48 billion. The top ranked firm ranked on the basis of total return from the largest diversified
financial firms in the Fortune 500 was Old Republic of Chicago with assets of $4 billion. The
three largest diversified financials aside from Federal National Mortgage Association, a quasiprivate firm, ranked 29, 32, 26 out of 35.
Financial services are labor intensive organizations as stressed above. Large scale
organizations are not necessary more efficient. Motivating and controlling people in large
organizations is difficult. The probability of rogue operations or shirking is increased as the
depth and breadth of a firm's operations increase. There may be economies of scale and scope in
financial services, but managers building strategies on the assumption of cost efficiences from
large size coming either from growth or acquisition should analyze the evidence carefully.
Summary
Improved knowledge of operating costs is critical for financial institution managers.
Management's objective is to understand a firm's cost curve or cost surface to exploit economies
of scale and scope. Managers can approach cost estimation using several techniques, including
cost accounting, statistical cost estimation, and process analysis. Reported research results leave
many cost-related questions open to managers of financial institutions. The evidence suggests
that many firms are inefficient and that economies of scale and scope are minor or at least elusive
sources of value. The reported evidence on financial institution costs is not persuasive for many
reasons. Financial firm managers must be creative in estimating and assessing their costs in the
future.
21
References
Baumol, William J., John C. Panzer and Robert D. Willig. 1982. Contestable Markets
and the Theory of Industry Structure. Harcourt Brace Jovanovich, Inc. New
York.
Bresnahan, Timothy F., Paul Milgrom, and Jonathan Paul. 1992. "The Real Output of the
Stock Exchange," Chapter 5 in Griliches (1992), pp. 195-216.
Berger, Allen N. and David B. Humphrey. 1992. "Measurement and Efficiency Issues in
Commercial Banking," Chapter 7 in Griliches (1992), pp. 245-300.
Berger, A. N., W. C. Hunter and S. G. Timme. 1993. "The efficiency of financial
institutions: A review and preview of research past, present, and future," Journal
of Banking and Finance 17, No. 2-3 (April), pp. 219-220.
Federal Reserve Bank. 1988. Instruction Manual for Uniform Preparation of Schedules
and Assempbly of Required Data: Functional Cost Analysis (not further
identified)
Fixler, Dennis J. and Kimberly D. Zieschang. 1992. "User Costs, Shadow Prices, and the
Real Output of Banks," Chapter 6 in Griliches (1992), pp. 219-243.
Geehan, Randall. 1977. "Returns to scale in the life insurance industry," Bell Journal of
Economics 8. pp. 497-514.
Goldberg, Lawrence G., Terald A. Hanweck, Michael Keenan, and Allan Young. 1991.
"Economies of Scale and Scope in the Securities Industry," Journal of Banking
and Finance 13, pp. 91-107.
Griliches, Zvi (editor). 1992. Output Measurement in the Service Sectors. The University
of Chicago Press. Chicago, Illionois.
Hancock, Diana. 1985. "The Financial Firm: Production with Monetary and
Nonmonetary Goods," Journal of Political Economy 93, No. 5, pp. 859-880.
Horngren, Charles T. and George Foster. 1991. Cost Accounting (7th Edition).
Prentice-Hall. Englewood Cliffs, New Jersey.
Kolari, James and Asghar Zardkoohi. 1987. Bank Costs, Structure, and Performance.
Lexington Books. Lexington, Massachusetts.
McAllister, Patrick H. and Douglas McManus. 1993. "Resolving the scale efficiency
22
puzzle in banking," Journal of Banking and Finance 17, Nos. 2-3. pp. 389-405.
Mester, Loretta J. 1992. "Traditional and nontraditional banking: An informationtheoretic approach," Journal of Banking and Finance 16, pp. 545-566.
Osborne, Dale K. 1982. "The Cost of Servicing Demand Deposits," Journal of Money,
Credit, and Banking, Vol 14, No. 4 (November, Part I), pp. 479-493.
Pindyck, Robert S. and Daniel L. Rubinfeld. 1989. Microeconomics. Macmillan. New
York.
23
DISCUSSION QUESTIONS AND EXERCISES
1. Compute total costs for the following cost functions for output X at levels of 10, 20,
30, and so forth to 100:
(1) TC1 = 150 + .75*X
(2) TC2 = 50 + .10*X + .05*X2
(3) TC3 = 200 + .5*X - .01*X2
What kind of cost functions are these? Which function is low cost over what
range of output? How do these cost functions perform at higher levels of output,
like 200 or 1000?
2. Calculate the marginal costs from these the three cost functions in question 1.
Characterize these as constant, declining, or increasing cost functions.
3. Calculate average costs for the three cost functions in question 1. Do the marginal
costs in question 2 conform to the average cost curves as discussed in the text?
Do any of the cost functions display economies or diseconomies of scale? Over
what range of outputs?
4. Economies of scope are sometimes refered to as cost synergies. Discuss two (or more)
financial services offered by a single financial firm like a bank, broker, or
insurance company in terms of the cost determinants of these services and the
likelihood of cost synergies in providing these services.
5. If two financial service firms of equal size with different output mixes of two services
C and D (output bundles of 10:1 (C:D) and 20:1 merge, what can you say output
the merged firm output mix (assuming no change in their business from the
merger)? Assuming each firm produced 10,000 C, draw their pre- and postmerger outputs on a diagram in terms of rays.
6. How could the cost surface over the rays in question 5 explain how the merged firm
had reduced or increased costs? Show the implications for the cost surface of
economies of scope.
7. If main frame computers in one method of producing a financial service are a fixed
cost of $100,000 per year and need operators costs $25,000 year for each 100
units of output, and another method uses personal computers costing $2,000 per
year and uses professionals costing $75,000 per year for each 100 units of output,
at what output levels is one method better than another? Can you cite examples
where these two methods might capture difference financial services?
24
8. Assume a process analysis reveals that a facility costing $300 per month (30 days) can
handle 500 transactions priced at $1 per transaction a day with operators who can
process 200 transactions in an eight-hour day and make $10 per hour. Draw the
total cost function for production levels up to 2000 transactions assuming
operators can use more than one machine and can work part time. What is the
marginal cost at 100, 500, 800, and 1000 transactions? If you have only one
facility, what revenues are lost if demand over 500 transactions must be turned
away? How does the analysis change if operators can only use one machine
during a day or cannot work part time?
9. The user cost of loans is - 10 percent and deposits + 5 percent. Which is an input and
which an output? Explain what this concept of inputs and outputs means. Could
it be possible for a low-cost provider of deposits to have a user cost of - 2 percent?
What would be the outputs of this firm?
10. Why might not cost efficiencies be reflect in stock market performance? What other
sources of value can offset cost inefficiencies? Can you use these arguments to
explain mergers in financial institutions or the performance of the largest financial
firms discussed in the text?
25
Table 23-1
Costs of Providing Financial Activity
Panel A: Total Costs for Four Methods
Activity
Method
Level
(1)
(2)
(3)
(4)
0
0
30
10
10
10
10
34
11
20.45
20
20
38
14
29.8
30
30
42
19
38.05
40
40
46
26
45.2
50
50
50
35
51.25
60
60
54
46
56.2
70
70
58
59
60.05
80
80
62
74
62.8
90
90
66
91
64.45
100
100
70
110
65
Panel B: Marginal Costs for Four Methods
10
1
0.4
0.1
1.05
20
1
0.4
0.3
0.94
30
1
0.4
0.5
0.83
40
1
0.4
0.7
0.72
50
1
0.4
0.9
0.61
60
1
0.4
1.1
Panel C: Average Costs for Four Methods 0.5
70
1
0.4
1.3
0.38
80
1
0.4
1.5
0.28
90
1
0.4
1.7
0.17
100
1
0.4
1.9
0.05
Panel C: Average Costs for Four Methods
10
20
30
40
50
60
70
80
90
100
1
1
1
1
1
1
1
1
1
1
3.4
1.9
1.4
1.15
1
0.9
0.83
0.78
0.73
0.7
26
1.1
0.7
0.63
0.65
0.7
0.77
0.84
0.93
1.01
1.1
2.05
1.49
1.27
1.13
1.03
0.94
0.86
0.79
0.72
0.65
Table 23-2
Costs of Providing Two Financial Activities
Panel A: Activity A and B Produced Independently
Activity A
Activity B
Activity Total
Activity Total
Level Cost
Level
Cost
--------------------------------------------0
10.00
0.00
50.00
1
11.10
50.00
50.08
2
12.20 100.00
50.20
3
13.29 150.00
50.38
4
14.38 200.00
50.60
5
15.48 250.00
50.88
6
16.56 300.00
51.20
7
17.65 350.00
51.58
8
18.74 400.00
52.00
9
19.82 450.00
52.48
10
20.90 500.00
53.00
20
31.60 1000.00
61.00
30
42.10 1500.00
74.00
40
52.40 2000.00
92.00
50
62.50 2500.00 115.00
60
72.40 3000.00 143.00
70
82.10 3500.00 176.00
80
91.60 4000.00 214.00
90 100.90 4500.00 257.00
100 110.00 5000.00 305.00
110 118.90 5500.00 358.00
120 127.60 6000.00 416.00
130 136.10 6500.00 479.00
140 144.40 7000.00 547.00
150 152.50 7500.00 620.00
160 160.40 8000.00 698.00
170 168.10 8500.00 781.00
180 175.60 9000.00 869.00
190 182.90 9500.00 962.00
200 190.00 10000.00 1060.00
27
Table 23-2 (Continued)
Costs of Providing Two Financial Activities
Panel B: B and A Produced in Proportion 50 to 1 (Ray X)
Level of Activity
A
B
0
0
1
50
2
100
3
150
4
200
5
250
6
300
7
350
8
400
9
450
10
500
20
1000
30
1500
40
2000
50
2500
60
3000
70
3500
80
4000
90
4500
100
5000
110
5500
120
6000
130
6500
140
7000
150
7500
160
8000
170
8500
180
9000
190
9500
200
10000
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
Total Ray Average
Cost
Cost
60.00
61.17 $ 61.17
62.39 $ 31.19
63.64 $ 21.21
64.94 $ 16.24
66.29 $ 13.26
67.67 $ 11.28
69.10 $ 9.87
70.58 $ 8.82
72.09 $ 8.01
73.65 $ 7.37
91.60 $ 4.58
113.85 $ 3.80
140.40 $ 3.51
171.25 $ 3.43
206.40 $ 3.44
245.85 $ 3.51
289.60 $ 3.62
337.65 $ 3.75
390.00 $ 3.90
446.65 $ 4.06
507.60 $ 4.23
572.85 $ 4.41
642.40 $ 4.59
716.25 $ 4.78
794.40 $ 4.97
876.85 $ 5.16
963.60 $ 5.35
1,054.65 $ 5.55
1,150.00 $ 5.75
28
Table 23-2 (Continued)
Costs of Providing Two Financial Activities
Panel C: B and A Produced in Proportion 25 to 1 (Ray Y)
Level of Activity
A
B
0
0
1
25
2
50
3
75
4
100
5
125
6
150
7
175
8
200
9
225
10
250
20
500
30
750
40
1000
50
1250
60
1500
70
1750
80
2000
90
2250
100
2500
110
2750
120
3000
130
3250
140
3500
150
3750
160
4000
170
4250
180
4500
190
4750
200
5000
Total Ray Average
Cost
Cost
60
61.13
61.13
62.27
31.13
63.41
21.14
64.56
16.14
65.73
13.15
66.89
11.15
68.07
9.72
69.26
8.66
70.45
7.83
71.65
7.17
84.1
4.21
97.35
3.25
111.4
2.79
126.25
2.53
141.9
2.37
158.35
2.26
175.6
2.2
193.65
2.15
212.5
2.13
232.15
2.11
252.6
2.11
273.85
2.11
295.9
2.11
318.75
2.13
342.4
2.14
366.85
2.16
392.1
2.18
418.15
2.2
445
2.23
29
Figure 23-1
Cost Functions and Average and Marginal Costs
Panel A - Cost Functions
30
Figure 23-1 (Continued)
Cost Functions and Average and Marginal Costs
Panel B - Average and Marginal Costs
31
Figure 23-2
Multiple Activity Cost Functions and Cost Surface
32
Figure 23-3
Multiple Activity Cost Functions
Panel A - Ray X (B:A = 50:1) Total Costs
33
Figure 23-3 (continued)
Panel B - Ray Y (B:A = 25:1) Total Costs
34
Figure 23-3 (continued)
Panel C - Varying Activity A with B at Three Activity Levels
35
Figure 23-3 (continued)
Panel D - Varying Activity B with A at Three Activity Levels
36
Figure 23-3 (continued)
Panel E - Varying Proportions of Activities A and B
37
Figure 23-4
Ray Average Costs
Panel A - (B,A) at 50:1
38
Figure 23-4 (continued)
Ray Average Costs
Panel B - (B,A) at 25:1
39