Cost Theory

Cost Theory in Economics A central economic concept is that getting something requires giving up something else. For example, earning more money may require working more hours, which costs more leisure time. Economists use cost theory to provide a framework for understanding how individuals and firms allocate resources in such a way that keeps costs low and benefits high. 1. Function * Economists view costs as what an individual or firm must give up to get something else. Opening a manufacturing plant to produce goods requires an outlay of money.Once a plant owner spends money to manufacture goods, that money is no longer available for something else. Production facilities, machinery used in the production process and plant workers are all examples of costs. Cost theory offers an approach to understanding the costs of production that allows firms to determine the level of output that reaps the greatest level of profit at the least cost. 2. Features * Cost theory contains various meas ures of costs. These include a firm's fixed costs and variable costs. The former do not vary with the quantity of goods produced.Rent on a facility is an example of a fixed cost. Variable costs change with the quantity produced. If increased production requires more workers, for example, those workers' wages are variable costs. The sum of fixed and variable costs is a firm's total costs. * Additional Measures * Cost theory derives two additional cost measures. Average total cost is the total cost divided by the number of goods produced. Marginal cost is the increase in total cost that results from increasing production by one unit of output.Marginals–including marginal costs and marginal revenue–are key concepts in mainstream economic thought. Falling and Rising Costs * Economists often use graphs, similar to supply-and-demand charts, to illustrate cost theory and firms' decisions about production. An average total cost curve is a U-shaped curve on an economic diagram. This shape illustrates how average total costs decline as output rises and then rise as marginal costs increase. Average total costs decline at first because as production rises, average costs are distributed over a larger number of units of output.Eventually, marginal costs of increasing output rise, which increases average total costs. Maximizing Profits * Economic theory holds that the goal of a firm is to maximize profit, which equals total revenue minus total cost. Determining a level of production that generates the greatest level of profit is an important consideration, one that means paying attention to marginal costs, as well as marginal revenue (the increase in revenue arising from an increase in output). Under cost theory, as long as marginal revenue exceeds marginal cost, increasing production will raise profit.Types of Cost Economics Economists factor costs in many different ways. Though you may read the cost of a soup can at $1 as it’s listed on the grocery sto re shelf, economists view the cost of the soup can in very different ways. For example, an economist asks what you are giving up to buy that can of soup over another item. They measure the firm’s cost of producing that soup can as it relates to their output and factors of production. Thus, the different types of economic costs are varied. 1. Sunk Cost * A sunk cost is an expense that cannot be recouped.Mark Hirschy, author of the book, â€Å"Fundamentals of Managerial Economics,† explains that sunk costs should not factor into a decision when deciding between alternatives. For example, say a person spent $50,000 on a degree in education and earns $60,000 as a teacher. She is later offered a job in marketing that pays her $80,000. Though she may be tempted to factor in her education degree as reason to stay in her current teaching job, her $50,000 degree is regarded as a sunk cost. She already spent this money, and it cannot be recouped.In this case, she should only com pare the respective salaries of the positions. If all else is held equal, she should pursue the marketing job. Opportunity Cost * An opportunity cost is the value of an alternative choice. Though the word â€Å"cost† usually equates to a numerical value, like a dollar figure, this is not always the case. William Baumol and Alan Blinder, authors of the book, â€Å"Economics: Principles and Policy,† state that an opportunity cost calculates intangible things like time, location and job satisfaction.They explain opportunity costs are what you give up to follow one course of action. For example, a college graduate is deciding between a job as a tech consultant in Seattle or an investment broker in New York City. If the grad pursues the investment broker position, the opportunity costs of foregoing the job in Seattle could be a slower pace of life, $10,000 higher salary and lower costs of living like rent and food. * Marginal Cost * A marginal cost is the amount it takes to produce one more item.Under this view of costs, they vary along the production line and in most cases the cost to produce a good reduces over time. Intuitively, this makes sense: the more proficient you become at producing a good, the faster you can do it and less waste is produced. The savings in labor and material as you achieve â€Å"economies of scale† means the cost of production usually decreases. The way economists find the marginal cost is by taking the derivative of the total costs as it relates to the total output. How to Find Marginal Cost in EconomicsDeciding whether to produce more units is often based on marginal cost. The economic concept of marginal cost is the cost associated with producing one additional unit. This information is important to businesses because it allows the company to decide if the additional unit is worth producing from a financial standpoint. When a company produces a small amount of product, the cost of additional units often decrease. However, marginal costs increase when additional units are added once the production level reaches a minimum. This is based on the law of diminishing marginal returns.Instructions 1. * 1 Calculate the change in total variable cost. This is the amount that the costs increased by after additional units are produced. For example, if you'd like to produce more T-shirts and the increase in output would change the costs by $100, then the total variable cost is $100. * 2 Find the change in quantity produced. This represents how many additional units you would like to produce in the given scenario. For example, the change in quantity would be 50 if you'd like to produce 300 T-shirts instead of 250. * 3 Divide the change in total variable costs from Step 1 by the change in quantity from Step 2. This will give you the marginal cost (marginal cost = the change in total variable cost/the change in quantity). For this example, $100 (the change in total variable cost) / 50 (the change in quantity ) = $2 in marginal costs, which is the cost of producing each additional T-shirt. What Is the Relationship Between Production ; Cost? Production costs are linked to the cost of materials and labor.The relationship between production and cost in any manufacturing process varies based on volume produced and whether any part of the manufacturing process is outsourced or performed by subcontractors. Additionally, production and cost ratios vary based on the amount of automation involved in production and the amount of human oversight and involvement required. 1. Factors of Production * The main factors of production are labor, capital and supply costs. Capital is defined as equipment, cash reserves, and physical location or production facility.Labor is defined as the amount of and cost of manpower required to bring a product to market. This includes not only the physical labor and oversight related to product production, but also the associated costs of salaries of positions such as man agers, delivery drivers, warehouse supervisors, marketing directors and even administrative assistance. Supply costs are any fee associated with securing necessary materials for production. Subcontractor or outsourced work is considered a supply cost as well, as the manufacturer is essentially purchasing a product or service for use in the production process.In this example, work such as offsite creation of product packaging or assembly of minor components of a finished product are considered supply costs in the same way the purchase of raw materials are considered supply costs. Volume of Production * Volume of production figures signify the amount of products being produced. Typically, the greater the volume the lower the cost per unit as raw material suppliers often offer discounts on mass or bulk orders. Volume of production is based on a company’s anticipated product needs, past sales records and placed orders. *Volume of Business * The relationship between production and cost is frequently determined by the volume of business a company is doing. An example that illustrates this point is a multinational vitamin supplement company that produces vitamins in bulk compared to a small health food chain that produces its own vitamin line in small quantities. The cost of the product produced by the small company will typically be greater than the cost of the product offered by the bulk manufacturer because the smaller company produces its product in smaller volumes. Price Points The more it costs a company to produce a product, the greater price the company will have to charge consumers. A company’s production costs include the price of materials, the cost of manpower, the production and packaging process, advertising, and distribution. Mass producers may be able to offer more competitive pricing to end users because they have the luxury of working on a thin margin due to the large volume of production. In microeconomics, the long run is the concept ual time period in which there are no fixed factors of production as to changing the output level by changing the capital stock or by entering or leaving an industry.The long run contrasts with the short run, in which some factors are variable and others are fixed, constraining entry or exit from an industry. In macroeconomics, the long run is the period when the general price level, contractual wage rates, and expectations adjust fully to the state of the economy, in contrast to the short run when these variables may not fully adjust. [1] In the long run, firms change production levels in response to (expected) economic profits or losses, and the land, labor, capital goods and entrepreneurship vary to reach associated long-run average cost.In the simplified case of plant capacity as the only fixed factor, a generic firm can make these changes in the long run: * enter an industry in response to (expected) profits * leave an industry in response to losses * increase its plant in resp onse to profits * decrease its plant in response to losses. Long-run average-cost curve with economies of scale to Q2 and diseconomies of scale thereafter. The long run is associated with the long-run average cost (LRAC) curve in microeconomic models along which a firm would minimize its average cost (cost per unit) for each respective long-run quantity of output.Long-run marginal cost (LRMC) is the added cost of providing an additional unit of service or commodity from changing capacity level to reach the lowest cost associated with that extra output. LRMC equalling price is efficient as to resource allocation in the long run. The concept of long-run cost is also used in determining whether the long-run expected to induce the firm to remain in the industry or shut down production there. In long-run equilibrium of an industry in which perfect competition prevails, the LRMC = Long run average LRAC at the minimum LRAC and associated output.The shape of the long-run marginal and averag e costs curves is determined by economies of scale. The long run is a planning and implementation stage. [2][3] Here a firm may decide that it needs to produce on a larger scale by building a new plant or adding a production line. The firm may decide that new technology should be incorporated into its production process. The firm thus considers all its long-run production options and selects the optimal combination of inputs and technology for its long-run urposes. [4] The optimal combination of inputs is the least-cost combination of inputs for desired level of output when all inputs are variable. [3] Once the decisions are made and implemented and production begins, the firm is operating in the short run with fixed and variable inputs. [3][5] Short run All production in real time occurs in the short run. The short run is the conceptual time period in which at least one factor of production is fixed in amount and others are variable in amount.Costs that are fixed, say from existing plant size, have no impact on a firm's short-run decisions, since only variable costs and revenues affect short-run profits. Such fixed costs raise the associated short-run average cost of an output long-run average cost if the amount of the fixed factor is better suited for a different output level. In the short run, a firm can raise output by increasing the amount of the variable factor(s), say labor through overtime. A generic firm already producing in an industry can make three changes in the short run as a response to reach a posited equilibrium: * increase production decrease production * shut down. In the short run, a profit-maximizing firm will: * increase production if marginal cost is less than marginal revenue (added revenue per additional unit of output); * decrease production if marginal cost is greater than marginal revenue; * continue producing if average variable cost is less than price per unit, even if average total cost is greater than price; * shut down if avera ge variable cost is greater than price at each level of output. Transition from short run to long runThe transition from the short run to the long run may be done by considering some short-run equilibrium that is also a long-run equilibrium as to supply and demand, then comparing that state against a new short-run and long-run equilibrium state from a change that disturbs equilibrium, say in the sales-tax rate, tracing out the short-run adjustment first, then the long-run adjustment. Each is an example of comparative statics. Alfred Marshall (1890) pioneered in comparative-static period analysis. [6] He istinguished between the temporary or market period (with output fixed), the short period, and the long period. â€Å"Classic† contemporary graphical and formal treatments include those of Jacob Viner (1931),[7] John Hicks (1939),[8] and Paul Samuelson (1947). [9] The law of diminishing marginal returns The law of diminishing marginal returns to a variable factor applies to th e short run. [10] It posits an effect of decreased added or marginal product of from variable factors, which increases the supply price of added output. [11] The law is related to a positive slope of the short-run marginal-cost curve. 12] Macroeconomic usages The usage of ‘long run' and ‘short run' in macroeconomics differs somewhat from the above microeconomic usage. J. M. Keynes (1936) emphasized fundamental factors of a market economy that might result in prolonged periods away from full-employment. [13] In later macro usage, the long run is the period in which the price level for the economy is completely flexible as to shifts in aggregate demand and aggregate supply. In addition there is full mobility of labor and capital between sectors of the economy and full capital mobility between nations.In the short run none of these conditions need fully hold. The price is sticky or fixed as to changes in aggregate demand or supply, capital is not fully mobile between sector s, and capital is not fully mobile to interest rate differences among countries & fixed exchange rates. [14] A famous critique of neglecting short-run analysis was by John Maynard Keynes, who wrote that â€Å"In the long run, we are all dead,† referring to the long-run proposition of the quantity theory of, for example, a doubling of the money supply doubling the price level. 15] Marginal  Analysis Thinking at the  Margin From Mike Moffatt, former About. com Guide From an economist's perspective, making choices involves making decisions ‘at the margin' – that is, making decisions based on small changes in resources: * How should I spend the next hour? * How should I spend the next dollar? On the surface, this seems like a strange way of considering the choices made by people and firms. It is rare that someone would consciously ask themselves – ‘How will I spend dollar number 24,387? ‘, ‘How will I spend dollar number 24,388? . Treatin g the problem in this matter does have some distinct advantages: * Doing so leads to the optimal decisions being made, subject to preferences, resources and informational constraints. * It makes the problem less messy from an analytic point of view, as we are not trying to analyze a million decisions at once. * While this does not exactly mimic conscious decision making processes, it does provide results similar to the decisions people actually make. That is, people may not think using this method, but the decisions they make are as if they do.Marginal Analysis – An Example Consider the decision on how many hours to work, as given by the following chart: Hour – Hourly Wage – Value of Time Hour 1 – $10 – $2 Hour 2 – $10 – $2 Hour 3 – $10 – $3 Hour 4 – $10 – $3 Hour 5 – $10 – $4 Hour 6 – $10 – $5 Hour 7 – $10 – $6 Hour 8 – $10 – $8 Hour 9 – $15 â €“ $9 Hour 10 – $15 – $12 Hour 11 – $15 – $18 Hour 12 – $15 – $20 The hourly wage represents what I earn for working an extra hour – it is the marginal gain or the marginal benefit. The value of time is essentially an opportunity cost – it is how much I value having that hour off.In this example it represents a marginal cost – what it costs me by working an additional hour. The increase in marginal costs is a common phenomenon; I do not mind working a few hours since there are 24 hours in a day. I still have plenty of time to do other things. However, as I start to work more hours it reduces the number of hours I have for other activities. I have to start giving up more and more valuable opportunities to work those extra hours. It is clear that I should work the first hour, as I gain $10 in marginal benefits and lose only $2 in marginal costs, for a net gain of $8.By the same logic I should work the second and third hours as well. I will want to work until which time the marginal cost exceeds the marginal benefit. I will want to work the 10th hour as I receive a net benefit of #3 (marginal benefit of $15, marginal cost of $12). However, I will not want to work the 11th hour, as the marginal cost ($18) exceeds the marginal benefit ($15) by three dollars. Thus marginal analysis suggests that rational maximizing behavior is to work for 10 hours. Next Lesson: Market Distortions: Altering the Supply and Demand Equilibrium.Marginal Analysis * Marginal Revenue – Glossary – Dictionary Definition of Marginal Revenue * Marginal Significance Value – Glossary – Dictionary Definition of Marginal Si†¦ * Marginal Revenue and Marginal Cost Practice Question Related Articles * Running a Private Practice – Working with Animals * Work Stress – Long Work Hours Are Not the Culprit * Open for Business: Scheduling Your Week – Being a Personal Trainer * Three Union Work Rules That Increase the Cost of Operating Transit * Hold On to Your Sanity – Start Your Own Business AN INTRODUCTION TOCOST BENEFIT ANALYSIS| * Background * Cost-Benefit Analysis (CBA) estimates and totals up the equivalent money value of the benefits and costs to the community of projects to establish whether they are worthwhile. These projects may be dams and highways or can be training programs and health care systems. * The idea of this economic accounting originated with Jules Dupuit, a French engineer whose 1848 article is still worth reading. The British economist, Alfred Marshall, formulated some of the formal concepts that are at the foundation of CBA.But the practical development of CBA came as a result of the impetus provided by the Federal Navigation Act of 1936. This act required that the U. S. Corps of Engineers carry out projects for the improvement of the waterway system when the total benefits of a project to whomsoever they accrue exceed the costs of t hat project. Thus, the Corps of Engineers had created systematic methods for measuring such benefits and costs. The engineers of the Corps did this without much, if any, assistance from the economics profession.It wasn't until about twenty years later in the 1950's that economists tried to provide a rigorous, consistent set of methods for measuring benefits and costs and deciding whether a project is worthwhile. Some technical issues of CBA have not been wholly resolved even now but the fundamental presented in the following are well established. * Principles of Cost Benefit Analysis * One of the problems of CBA is that the computation of many components of benefits and costs is intuitively obvious but that there are others for which intuition fails to suggest methods of measurement. Therefore some basic principles are needed as a guide. There Must Be a Common Unit of Measurement * In order to reach a conclusion as to the desirability of a project all aspects of the project, positiv e and negative, must be expressed in terms of a common unit; i. e. , there must be a â€Å"bottom line. † The most convenient common unit is money. This means that all benefits and costs of a project should be measured in terms of their equivalent money value. A program may provide benefits which are not directly expressed in terms of dollars but there is some amount of money the recipients of the benefits would consider just as good as the project's benefits.For example, a project may provide for the elderly in an area a free monthly visit to a doctor. The value of that benefit to an elderly recipient is the minimum amount of money that that recipient would take instead of the medical care. This could be less than the market value of the medical care provided. It is assumed that more esoteric benefits such as from preserving open space or historic sites have a finite equivalent money value to the public. * Not only do the benefits and costs of a project have to be expressed in terms of equivalent money value, but they have to be expressed in terms of dollars of a particular time.This is not just due to the differences in the value of dollars at different times because of inflation. A dollar available five years from now is not as good as a dollar available now. This is because a dollar available now can be invested and earn interest for five years and would be worth more than a dollar in five years. If the interest rate is r then a dollar invested for t years will grow to be (1+r)t. Therefore the amount of money that would have to be deposited now so that it would grow to be one dollar t years in the future is (1+r)-t.This called the discounted value or present value of a dollar available t years in the future. * When the dollar value of benefits at some time in the future is multiplied by the discounted value of one dollar at that time in the future the result is discounted present value of that benefit of the project. The same thing applies to costs. The net benefit of the projects is just the sum of the present value of the benefits less the present value of the costs. * The choice of the appropriate interest rate to use for the discounting is a separate issue that will be treated later in this paper. CBA Valuations Should Represent Consumers or Producers Valuations As Revealed by Their Actual Behavior * The valuation of benefits and costs should reflect preferences revealed by choices which have been made. For example, improvements in transportation frequently involve saving time. The question is how to measure the money value of that time saved. The value should not be merely what transportation planners think time should be worth or even what people say their time is worth. The value of time should be that which the public reveals their time is worth through choices involving tradeoffs between time and money.If people have a choice of parking close to their destination for a fee of 50 cents or parking farther away and spend ing 5 minutes more walking and they always choose to spend the money and save the time and effort then they have revealed that their time is more valuable to them than 10 cents per minute. If they were indifferent between the two choices they would have revealed that the value of their time to them was exactly 10 cents per minute. * The most challenging part of CBA is finding past choices which reveal the tradeoffs and equivalencies in preferences.For example, the valuation of the benefit of cleaner air could be established by finding how much less people paid for housing in more polluted areas which otherwise was identical in characteristics and location to housing in less polluted areas. Generally the value of cleaner air to people as revealed by the hard market choices seems to be less than their rhetorical valuation of clean air. * Benefits Are Usually Measured by Market Choices * When consumers make purchases at market prices they reveal that the things they buy are at least as beneficial to them as the money they relinquish.Consumers will increase their consumption of any commodity up to the point where the benefit of an additional unit (marginal benefit) is equal to the marginal cost to them of that unit, the market price. Therefore for any consumer buying some of a commodity, the marginal benefit is equal to the market price. The marginal benefit will decline with the amount consumed just as the market price has to decline to get consumers to consume a greater quantity of the commodity. The relationship between the market price and the quantity consumed is called the demand schedule.Thus the demand schedule provides the information about marginal benefit that is needed to place a money value on an increase in consumption. * Gross Benefits of an Increase in Consumption is an Area Under the Demand Curve * The increase in benefits resulting from an increase in consumption is the sum of the marginal benefit times each incremental increase in consumption. A s the incremental increases considered are taken as smaller and smaller the sum goes to the area under the marginal benefit curve. But the marginal benefit curve is the same as the demand curve so the increase in benefits is the area under the demand curve.As shown in Figure 1 the area is over the range from the lower limit of consumption before the increase to consumption after the increase. * Figure 1 * When the increase in consumption is small compared to the total consumption the gross benefit is adequately approximated, as is shown in a welfare analysis, by the market value of the increased consumption; i. e. , market price times the increase in consumption. * Some Measurements of Benefits Require the Valuation of Human Life * It is sometimes necessary in CBA to evaluate the benefit of saving human lives.There is considerable antipathy in the general public to the idea of placing a dollar value on human life. Economists recognize that it is impossible to fund every project whic h promises to save a human life and that some rational basis is needed to select which projects are approved and which are turned down. The controversy is defused when it is recognized that the benefit of such projects is in reducing the risk of death. There are many cases in which people voluntarily accept increased risks in return for higher pay, such as in the oil fields or mining, or for time savings in higher speed in automobile travel.These choices can be used to estimate the personal cost people place on increased risk and thus the value to them of reduced risk. This computation is equivalent to placing an economic value on the expected number of lives saved. * The Analysis of a Project Should Involve a With Versus Without Comparison * The impact of a project is the difference between what the situation in the study area would be with and without the project. This that when a project is being evaluated the analysis must estimate not only what the situation would be with the p roject but also what it would be without the project.For example, in determining the impact of a fixed guideway rapid transit system such as the Bay Area Rapid Transit (BART) in the San Francisco Bay Area the number of rides that would have been taken on an expansion of the bus system should be deducted from the rides provided by BART and likewise the additional costs of such an expanded bus system would be deducted from the costs of BART. In other words, the alternative to the project must be explicitly specified and considered in the evaluation of the project. Note that the with-and-without comparison is not the same as a before-and-after comparison. Another example shows the importance of considering the impacts of a project and a with-and-without comparison. Suppose an irrigation project proposes to increase cotton production in Arizona. If the United States Department of Agriculture limits the cotton production in the U. S. by a system of quotas then expanded cotton production in Arizona might be offset by a reduction in the cotton production quota for Mississippi. Thus the impact of the project on cotton production in the U. S. might be zero rather than being the amount of cotton produced by the project. * Cost Benefit Analysis Involves a Particular Study Area The impacts of a project are defined for a particular study area, be it a city, region, state, nation or the world. In the above example concerning cotton the impact of the project might be zero for the nation but still be a positive amount for Arizona. * The nature of the study area is usually specified by the organization sponsoring the analysis. Many effects of a project may â€Å"net out† over one study area but not over a smaller one. The specification of the study area may be arbitrary but it may significantly affect the conclusions of the analysis. * Double Counting of Benefits or Costs Must be Avoided Sometimes an impact of a project can be measured in two or more ways. For example, when an improved highway reduces travel time and the risk of injury the value of property in areas served by the highway will be enhanced. The increase in property values due to the project is a very good way, at least in principle, to measure the benefits of a project. But if the increased property values are included then it is unnecessary to include the value of the time and lives saved by the improvement in the highway. The property value went up because of the benefits of the time saving and the reduced risks.To include both the increase in property values and the time saving and risk reduction would involve double counting. * Decision Criteria for Projects * If the discounted present value of the benefits exceeds the discounted present value of the costs then the project is worthwhile. This is equivalent to the condition that the net benefit must be positive. Another equivalent condition is that the ratio of the present value of the benefits to the present value of the costs m ust be greater than one. * If there are more than one mutually exclusive project that have positive net present value then there has to be further analysis.From the set of mutually exclusive projects the one that should be selected is the one with the highest net present value. * If the funds required for carrying out all of the projects with positive net present value are less than the funds available this means the discount rate used in computing the present values is too low and does not reflect the true cost of capital. The present values must be recomputed using a higher discount rate. It may take some trial and error to find a discount rate such that the funds required for the projects with a positive net present value is no more than the funds available.Sometimes as an alternative to this procedure people try to select the best projects on the basis of some measure of goodness such as the internal rate of return or the benefit/cost ratio. This is not valid for several reasons . * The magnitude of the ratio of benefits to costs is to a degree arbitrary because some costs such as operating costs may be deducted from benefits and thus not be included in the cost figure. This is called netting out of operating costs. This netting out may be done for some projects and not for others.This manipulation of the benefits and costs will not affect the net benefits but it may change the benefit/cost ratio. However it will not raise the benefit cost ratio which is less than one to above one. For more on this topic see Benefit/ cost Ratio Magnitude. * An Example * To illustrate how CBA might be applied to a project, let us consider a highway improvement such as the extension of Highway 101 into San Jose. The local four-lane highway which carried the freeway and commuter traffic into San Jose did not have a median divider and its inordinate number of fatal head-on collisions led to the name â€Å"Blood Alley. The improvement of the highway would lead to more capacity which produces time saving and lowers the risk. But inevitably there will be more traffic than was carried by the old highway. * The following is a highly abbreviated analysis using hypothetical data. TRIP DATA| No Extension, â€Å"Blood Alley† Only| 101 Extension and â€Å"Blood Alley†| Rush Hours|   |   | Passenger Trips (per hour)| 3,000| 4,000| Trip Time (minutes)| 50| 30| Value of Time ($/minute)| $0. 10| $0. 10| Nonrush Hours|   |   | Passenger Trips (per hour)| 500| 555. 55| Trip Time (minutes)| 35| 25| Value of Time ($/minute)| $0. 08| $0. 08| Traffic Fatalities per year)| 12| 6| * The data indicates that for rush-hour trips the time cost of a trip is $5 without the project and $3 with it. It is assumed that the operating cost for a vehicle is unaffected by the project and is $4. * The project lowers the cost of a trip and the public responds by increasing the number of trips taken. There is an increase in consumer surplus both for the trips which would have been taken without the project and for the trips which are stimulated by the project. * For trips which would have been taken anyway the benefit of the project equals the value of the time saved times the number of trips.For the rush-hour trip the project saves $2 and for the nonrush-hour trip it saves $0. 80. For the trips generated by the project the benefit is equal to one half of the value of the time saved times the increase in the number of trips. * The benefits per hour are: TYPE| Trips Which Would Be Taken Anyway| Trips Generated By the Project| Total| Rush Hour| 6,000. 00| 1,000. 00| 7,000. 00| Nonrush Hour| 400. 00| 22. 22| 422. 22| * To convert the benefits to an annual basis one multiplies the hourly benefits of each type of trip times the number of hours per year for that type of trip.There are 260 week days per year and at six rush hours per weekday there are 1560 rush hours per year. This leaves 7200 nonrush hours per year. With these figures the annual benefits are: TYPE| Trips Which Would Be Taken Anyway| Trips Generated By the Project| Total| Rush Hour| $9,360,000| $1,560,000| $10,020,000| Nonrush Hour| $2,880,000| $160,000| $3,040,000| Total| $12,240,000| $1,720,000| $13,960,000| * The value of the reduced fatalities may be computed in terms of the equivalent economic value people place upon their lives when making choices concerning risk and money.If the labor market has wages for occupations of different risks such that people accept an increase in the risk of death of 1/1,000 per year in return for an increase in income of $400 per year then a project that reduces the risk of death in a year by 1/1000 gives a benefit to each person affected by it of $400 per year. The implicit valuation of a life in this case is $400,000. Thus benefit of the reduced risk project is the expected number of lives saved times the implicit value of a life. For the highway project this is 6x$400,000= $2,400,000 annually. * The annual benefits of the proje ct are thus:TYPE OF BENEFIT| VALUE OF BENEFITS PER YEAR| Time Saving| $13,960,000| Reduced Risk| $2,400,000| * Let us assume that this level of benefits continues at a constant rate over a thirty-year lifetime of the project. * The cost of the highway consists of the costs for its right-of-way, its construction and its maintenance. The cost of the right-of-way is the cost of the land and any structures upon it which must be purchased before the construction of the highway can begin. For purposes of this example the cost of right-of-way is taken to be $100 million and it must be paid before any construction can begin.At least part of the right-of- way cost for a highway can be recovered at the end of the lifetime of the highway if it is not rebuilt. For the example it is assumed that all of the right-of-way cost is recoverable at the end of the thirty-year lifetime of the project. The construction cost is $200 million spread evenly over a four-year period. Maintenance cost is $1 mill ion per year once the highway is completed. * The schedule of benefits and costs for the project are as follows: TIME (year)| BENEFITS ($millions)| RIGHT-OF -WAY ($millions)| CONSTRUCTION COSTS $millions)| MAINTENANCE ($millions)| 0| 0| 100| 0| 0| 1-4| 0| 0| 50| 0| 5-29| 16. 36| 0| 0| 1| 30| 16. 36| -100| 0| 1| * The benefits and costs are in constant value dollars; i. e. , there was no price increase included in the analysis. Therefore the discount rate used must be the real interest rate. If the interest rate on long term bonds is 8 percent and the rate of inflation is 6 percent then the real rate of interest is 2 percent. Present value of the streams of benefits and costs discounted at a 2 percent back to time zero are as follows:   | PRESENT VALUE $ millions)| Benefits| 304. 11| Costs|   | Right-of-Way| 44. 79| Construction| 190. 39| Maintenance| 18. 59| Total Costs| 253. 77| |   | | Net Benefits| 50. 35| | *independent rounding| * The positive net present value of $50. 35 million and benefit/cost ratio of 1. 2 indicate that the project is worthwhile if the cost of capital is 2 percent. When a discount rate of 3 percent is the benefit/cost ratio is slightly under 1. 0. This means that the internal rate of return is just under 3 percent. When the cost of capital is 3 percent the project is not worthwhile. It should be noted that the market value of the right-of-way understates the opportunity cost of having the land devoted to the highway. The land has a value of $100 million because of its income after property taxes. The economy is paying more for its alternate use but some of the payment is diverted for taxes. The discounted presented value of the payments for the alternate use might be more like $150 million instead of $100 million. Another way of making this point is that one of the costs of the highway is that the local governments lose the property tax on the land used. * Summary By reducing the positive and negative impacts of a project to the ir equivalent money value Cost-Benefit Analysis determines whether on balance the project is worthwhile. The equivalent money value are based upon information derived from consumer and producer market choices; i. e. , the demand and supply schedules for the goods and services affected by the project. Care must be taken to properly allow for such things as inflation. When all this has been considered a worthwhile project is one for which the discounted value of the benefits exceeds the discounted value of the costs; i. . , the net benefits are positive. This is equivalent to the benefit/cost ratio being greater than one and the internal rate of return being greater than the cost of capital. * History of Cost-Benefit Analysis * CBA has its origins in the water development projects of the U. S. Army Corps of Engineers. The Corps of Engineers had its origins in the French engineers hired by George Washington in the American Revolution. For years the only school of engineering in the Uni ted States was the Military Academy at West Point, New York. In 1879, Congress created the Mississippi River Commission to â€Å"prevent destructive floods. † The Commission included civilians but the president had to be an Army engineer and the Corps of Engineers always had veto power over any decision by the Commission. * In 1936 Congress passed the Flood Control Act which contained the wording, â€Å"the Federal Government should improve or participate in the improvement of navigable waters or their tributaries, including watersheds thereof, for flood-control purposes if the benefits to whomsoever they may accrue are in excess of the estimated costs. The phrase if the benefits to whomsoever they may accrue are in excess of the estimated costs established cost-benefit analysis. Initially the Corps of Engineers developed ad hoc methods for estimating benefits and costs. It wasn't until the 1950s that academic economists discovered that the Corps had developed a system for t he economic analysis of public investments. Economists have influenced and improved the Corps' methods since then and cost-benefit analysis has been adapted to most areas of public decision-making.