University of Southern California



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:

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1

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 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:

[pic] 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:

[pic] 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 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 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 activities[1].

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 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:

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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 non-competitive 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.

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.

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 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.

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 million[2]. 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 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 output[3]. Estimates of productivity growth prepared by government agencies, like the Commerce 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 inputs[4]. 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 returns[5]. User costs for a given period are defined as:

[pic] 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 liability[6]. 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.

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 services[7].

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 activities[8].

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.

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 object[9]. 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 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 banks[10]. 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:

[pic] 23-6

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.

Other cost functions can be used. Common cost functions are the quadratic and cubic, written as follows:

[pic] 23-7

[pic] 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 Cobb-Douglas production function, which relates output to inputs as follows:

[pic] 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:

[pic] 23-10

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 becomes[11]:

[pic] 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 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 U-shaped costs curves have wider application. The most common function in studies of banking and other financial institution costs is the "transcendental logarithmic" or translog function[12]. This cost function in a two output case, where Y1 and Y2 are the outputs, can be written:

[pic] 23-12

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 outputs[13].

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.

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, back-room 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 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 safe-deposit boxes which could occupy the same space as a teller's window. In this analysis, the cost of teller items is:

[pic] 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 places[14]. We 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 scope[15].

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 quasi-private 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.

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 puzzle in banking," Journal of Banking and Finance 17, Nos. 2-3. pp. 389-405.

Mester, Loretta J. 1992. "Traditional and nontraditional banking: An information-theoretic 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.

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 post-merger 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?

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?

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 |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

Panel C: Average Costs for Four Methods

|10 |1 |3.4 |1.1 |2.05 |

|20 |1 |1.9 |0.7 |1.49 |

|30 |1 |1.4 |0.63 |1.27 |

|40 |1 |1.15 |0.65 |1.13 |

|50 |1 |1 |0.7 |1.03 |

|60 |1 |0.9 |0.77 |0.94 |

|70 |1 |0.83 |0.84 |0.86 |

|80 |1 |0.78 |0.93 |0.79 |

|90 |1 |0.73 |1.01 |0.72 |

|100 |1 |0.7 |1.1 |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 |

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 Total Ray Average

A B Cost Cost

|0 |0 | $ 60.00 |- |

|1 |50 | $ 61.17 | $ 61.17 |

|2 |100 | $ 62.39 | $ 31.19 |

|3 |150 | $ 63.64 | $ 21.21 |

|4 |200 | $ 64.94 | $ 16.24 |

|5 |250 | $ 66.29 | $ 13.26 |

|6 |300 | $ 67.67 | $ 11.28 |

|7 |350 | $ 69.10 | $ 9.87 |

|8 |400 | $ 70.58 | $ 8.82 |

|9 |450 | $ 72.09 | $ 8.01 |

|10 |500 | $ 73.65 | $ 7.37 |

|20 |1000 | $ 91.60 | $ 4.58 |

|30 |1500 | $ 113.85 | $ 3.80 |

|40 |2000 | $ 140.40 | $ 3.51 |

|50 |2500 | $ 171.25 | $ 3.43 |

|60 |3000 | $ 206.40 | $ 3.44 |

|70 |3500 | $ 245.85 | $ 3.51 |

|80 |4000 | $ 289.60 | $ 3.62 |

|90 |4500 | $ 337.65 | $ 3.75 |

|100 |5000 | $ 390.00 | $ 3.90 |

|110 |5500 | $ 446.65 | $ 4.06 |

|120 |6000 | $ 507.60 | $ 4.23 |

|130 |6500 | $ 572.85 | $ 4.41 |

|140 |7000 | $ 642.40 | $ 4.59 |

|150 |7500 | $ 716.25 | $ 4.78 |

|160 |8000 | $ 794.40 | $ 4.97 |

|170 |8500 | $ 876.85 | $ 5.16 |

|180 |9000 | $ 963.60 | $ 5.35 |

|190 |9500 | $ 1,054.65 | $ 5.55 |

|200 |10000 | $ 1,150.00 | $ 5.75 |

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 Total Ray Average

A B Cost Cost

|0 |0 | 60 | - |

|1 |25 |61.13 |61.13 |

|2 |50 |62.27 |31.13 |

|3 |75 |63.41 |21.14 |

|4 |100 |64.56 |16.14 |

|5 |125 |65.73 |13.15 |

|6 |150 |66.89 |11.15 |

|7 |175 |68.07 |9.72 |

|8 |200 |69.26 |8.66 |

|9 |225 |70.45 |7.83 |

|10 |250 |71.65 |7.17 |

|20 |500 |84.1 |4.21 |

|30 |750 |97.35 |3.25 |

|40 |1000 |111.4 |2.79 |

|50 |1250 |126.25 |2.53 |

|60 |1500 |141.9 |2.37 |

|70 |1750 |158.35 |2.26 |

|80 |2000 |175.6 |2.2 |

|90 |2250 |193.65 |2.15 |

|100 |2500 |212.5 |2.13 |

|110 |2750 |232.15 |2.11 |

|120 |3000 |252.6 |2.11 |

|130 |3250 |273.85 |2.11 |

|140 |3500 |295.9 |2.11 |

|150 |3750 |318.75 |2.13 |

|160 |4000 |342.4 |2.14 |

|170 |4250 |366.85 |2.16 |

|180 |4500 |392.1 |2.18 |

|190 |4750 |418.15 |2.2 |

|200 |5000 |445 |2.23 |

Figure 23-1

Cost Functions and Average and Marginal Costs

Panel A - Cost Functions

Figure 23-1 (Continued)

Cost Functions and Average and Marginal Costs

Panel B - Average and Marginal Costs

[pic]

1

Figure 23-2

Multiple Activity Cost Functions and Cost Surface

[pic]

2

Figure 23-3

Multiple Activity Cost Functions

Panel A - Ray X (B:A = 50:1) Total Costs

[pic]

3

Figure 23-3 (continued)

Panel B - Ray Y (B:A = 25:1) Total Costs

[pic]

4

Figure 23-3 (continued)

Panel C - Varying Activity A with B at Three Activity Levels

[pic]

5

Figure 23-3 (continued)

Panel D - Varying Activity B with A at Three Activity Levels

[pic]

6

Figure 23-3 (continued)

Panel E - Varying Proportions of Activities A and B

[pic]

7

Figure 23-4

Ray Average Costs

Panel A - (B,A) at 50:1

[pic]

8

Figure 23-4 (continued)

Ray Average Costs

Panel B - (B,A) at 25:1

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9

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    [1] See Baumol et al, especially Chapters 3 and 4, for a technical discussion of multiple product cost concepts.

    [2] See McAllister and McManus (1993) for economies of scale discussion focussing on bank portfolio (total assets) size.

    [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.

    [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.

    [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.

    [9] See Horngren and Foster (1991) for an extended treatment.

    [10] This discussion is based on the Instruction Manual (1988) for the FCA from the Federal Reserve.

    [11] See Kolari and Zardkoohi (1987), Chapter 2, or Pindyck and Rubeinfeld (1989), Chapter 7 and Appendix, for derivations.

    [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.

    [14] See Kolari and Zardkoohi (1987) for banks and more recently the Journal of Banking and Finance, "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.

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