Personnel Economics by William S. Neilson PDF

© Copyright 2007, 2015 by William S. Neilson All rights reserved This book was previously published by: Pearson Education, Inc. Now available for free via download at: http://web.utk.edu/~wneilson/Personnel.pdf  PERSONNEL ECONOMICS...

© Copyright 2007, 2015 by William S. Neilson All rights reserved This book was previously published by: Pearson Education, Inc. Now available for free via download at: http://web.utk.edu/~wneilson/Personnel.pdf  PERSONNEL ECONOMICS INCENTIVES AND INFORMATION IN THE EMPLOYMENT RELATIONSHIP WILLIAM S. NEILSON DEPARTMENT OF ECONOMICS UNIVERSITY OF TENNESSEE, KNOXVILLE TABLE OF CONTENTS Preface 1. INTRODUCTION The Economics of the Employment Relationship The Economics of Incentives and Information 2. OPTIMIZATION “How Much” Decisions and Marginal Analysis Global Optimization General Lessons A Classic Example: The Short-Run Competitive Firm 3. TRADITIONAL LABOR MARKET ANALYSIS The Firm’s Problem The Worker’s Problem Labor Markets Labor Market Analysis and Personnel Economics 4. COMPENSATION AND MOTIVATION Worker Effort and Efficiency Compensation Schemes and Effort Choices Piece rates. Straight salary. Box: Do workers on salary work less than those who are paid for performance? Quotas. Commission. Box: Do workers really work harder when commission rates go up? General Lessons 5. PIECE RATES Piece Rates at Safelite Glass Optimal Piece Rates General Lessons A Closer Look at the Salary Component Optimal Sales Commissions Motivating the Wrong Behavior 6. PROBLEMS WITH PIECE RATES Should Teachers be Paid for Performance? Box: Do incentives lead to “teaching to the test?” Multiple Tasks Imperfectly-Observed Effort General Lessons The Equal Compensation Principle. The Incentive Intensity Principle. 7. MOTIVATING MULTIPLE TYPES The Full-Information Case Moral Hazard The Optimal Contract for the Hidden-Information Setting General Lessons PERSONNEL ECONOMICS W. NEILSON 8. GAME THEORY What is a Game? The Concept of Equilibrium Simultaneous Games Application: Assigning duties in a team. Lessons about simultaneous games. Simultaneous Games with Infinitely Many Possible Strategies Application: Output in a duopoly. Sequential Games Lessons about sequential games. 9. TOURNAMENTS Some Examples A Model of a Tournament Optimal Effort for an Individual Worker Competition Between Workers Box: Do larger prizes really induce more effort? A numerical example. Implications for Motivating Workers Pay for performance? Pay structures in hierarchies. Box: The prize structure in golf tournaments. The Peter Principle. Promotions from within vs. hiring from outside. Tournaments when One Worker has an Advantage Ability differences. Favoritism. Influence Activities Sucking up. Backstabbing. Misrepresenting Information. 10. EFFICIENCY WAGES A Model of Efficiency Wages Repetition. Harsh punishment. Repetition and harsh punishment together. General Lessons Restrictions on the Firm’s Behavior Restrictions on wage reductions. Restrictions on firing. Unemployment insurance. 11. TEAM INCENTIVES Why Teams? Complementarities. Identification of contributions. Knowledge transfer. Fairness. Three Approaches to Analyzing Teams A game-theoretic approach. A public goods approach. A mathematical approach. Box: Splitting the bill in a restaurant. General lessons. When Can Team Compensation Work? Profit-Sharing and Gain-Sharing 12. COMPARISON OF INCENTIVE SCHEMES Getting Workers to Work When Can the Different Schemes be Used? Who Gets the Surplus? A Comparison of Problems Choosing the Right Incentive Scheme Technical support operators. College football coaching staffs. Dental hygienists. 13. EXECUTIVE COMPENSATION A Few Examples Aligning the CEO’s and the Owners’ Interests TABLE OF CONTENTS 2 PERSONNEL ECONOMICS W. NEILSON Stock vs. Stock Options Insulating CEOs from Broad Market Swings Box: Do CEOs benefit from laying off workers? Why are CEOs Paid So Much? 14. PERFORMANCE EVALUATION A Tale of Two Firms The Supervisor’s Problem Box: How many rating categories should there be? The Worker’s Problem Forced Rating Distributions General Lessons 15. ADVERSE SELECTION Trying to Hire the Best Workers Box: Adverse selection an hiring airport security screeners. When Does Adverse Selection Occur? Box: Can baseball teams identify high-productivity players? Solving the Adverse Selection Problem Piece rates. Probationary contracts. Adverse Selection in Other Areas of Economics Used cars. Car repairs. Health insurance. 16. SIGNALING Getting an Education Discounting the future. General lessons about getting an education. Some real world numbers. Education as a Signal of Quality Signaling and Equilibrium Is Education Really Just a Signal? Other Examples of Signaling Dressing for success. Licensing. Celebrity endorsements of charities. Deductibles in insurance. Warranties. Signals in nature. 17. SEARCH Benefits and Costs of Search Costs. Benefits. Optimal Search Important features of the optimal search rule. Box: Do people use the optimal search strategy? Determinants of the Amount of Search Job Search Searching for a first job. Searching for a job when already employed. Searching for a job while collecting unemployment benefits. 18. BARGAINING The Goal of Bargaining Sequential Bargaining The simplest possible bargaining game. A two-round bargaining game. A three-round bargaining game. Impatience, Uncertainty, and Risk Aversion Impatience. Uncertainty. Risk Aversion. The Nash Approach to Bargaining What can we learn from the Nash bargaining solution? General Lessons TABLE OF CONTENTS 3 PERSONNEL ECONOMICS W. NEILSON 19. TRAINING Training in Professional Sports Training and Human Capital Bargaining and the Value of Training Bargaining. Conditions for training to occur. Making Training Worthwhile for the Firm Reducing the portability of skills. Training and the Incentives to Remain with a Firm 20. BENEFITS The Issue of Child Care Preferences over Benefits and Pay The most-preferred package vs. the one offered by the firm. Cost Advantages for the Firm The sources of cost advantages. Box: Pharmacies at Caesars casinos. The Problems Faced by Small Firms Glossary TABLE OF CONTENTS 4  PERSONNEL ECONOMICS INCENTIVES AND INFORMATION IN THE WORKPLACE PREFACE Personnel Economics is, at its core, a book about the economics of incentives and information, but with all of its motivation, examples, and applications taken from the employment relationship. In the language prevalent in the economics research literature it covers such topics as principal-agent theory, moral hazard in terms of both imperfectly observed actions and privately-known types, adverse selection and signaling, and repeated games. In the more compelling (to students) language of the employment relationship, these topics translate respectively into using compensation schemes to motivate employees, motivating workers when their actions are only imperfectly monitored by supervisors, motivating workers when different workers have different productivity levels that are unknown to the supervisor, trying to hire high-productivity workers while avoiding low-productivity ones, and using efficiency wages as a motivational tool. The language of the employment relationship is an appropriate channel for introducing students to these important topics from economics, primarily because undergraduate students find the employment relationship both relevant and inherently interesting. After all, most of them will be entering the work force in the near future, and many of them have worked somewhere and will be able to relate to the material in the course. The topics covered are of interest from both the employer’s and the employee’s side of the market. More specifically, students will learn how their employers attempt to motivate them and also about many issues related to the job search, including models of optimal search and bargaining. The book is written so that all problems are motivated by the employment relationship, not the theoretical topic to be discussed. The topics in this course either do not appear or receive only limited coverage elsewhere in the undergraduate curriculum. In particular, labor economics texts typically have only one chapter on how compensation affects productivity, while half of this book is devoted to covering that topic in depth. OUTLINE OF THE BOOK The book is loosely organized around the two major topics of paying and hiring employees. The compensation section can be subdivided into a section on piece rate pay and a section on other, more strategic methods of compensation. The hiring section can be subdivided into one on adverse selection and one on finding a job and negotiating a PERSONNEL ECONOMICS W. NEILSON contract, and one on other, less information-based topics. The text contains two tools chapters, one on optimization, but without calculus, and one on game theory. The text begins with a chapter reviewing optimization without calculus (Chapter 2). This will be a review chapter for every student who has ever taken an economics course, but I have found it best to reacquaint them with the concepts of marginal analysis and cost-benefit analysis since these are the primary tools used in the analysis of incentive schemes. A chapter on traditional labor market analysis follows. It shows how time and output are treated as being the same thing in the traditional supply and demand model, and it therefore serves as a point of departure for a discussion of how workers must be paid to work, and otherwise they will not produce anything. The next chapter takes a simple setting and shows that if the worker is paid on the basis of time he will produce as little as possible, but that there are a number of ways to base pay on output that can get the worker to produce the Pareto efficient level of output. The text then moves on to specific compensation schemes, beginning with piece rate schemes in Chapter 5. These are the familiar linear incentive contracts from principal-agent theory, and all of the major results from principal-agent theory make their way into the book, but of course with the firm taking the role of the principal and the worker taking the role of the agent. The terms “principal” and “agent” do not appear in the book. Chapter 5 establishes the importance of aligning incentives with the worker’s effort costs if the firm is to obtain the efficient level of output, Chapter 6 shows that compensation must be equated across tasks and that incentives should be reduced in the presence of imperfect monitoring, and Chapter 7 shows that when linear incentive schemes are used with high- and low-effort-cost agents incentives are reduced for the high-cost agents and the low-cost agents earn information rents. Chapter 8 is a game theory chapter, covering the basics of simultaneous and sequential games that are needed for later chapters. The chapter is not intended to be comprehensive, or even remotely so; instead it is designed to provide students with only the game theory tools they will need for the remainder of the book. Game theory is used in the analysis of tournaments, efficiency wages, team incentives, and bargaining. The tournament chapter is constructed using a model that is roughly analogous to the Cournot duopoly model. Specifically, the workers’ marginal conditions are used to derive best-response functions which can then be used to identify the equilibrium. It is shown how workers respond to increases in their opponent’s effort level and how an increase in the size of the prize leads contestants to exert more effort. Efficiency wages are also presented as a way to motivate employees, and this analysis is based on Benoit- Krishna-style finitely-repeated games. An efficiency wage scheme is defined as the event in which the firm pays an above-market wage and the worker exerts extraordinary effort. The focus is on the aspects of the game needed to obtain an efficiency wage scheme. Chapter 10 discusses team incentives using the approaches of game theory, marginal analysis, and the idea of team effort as a public good. Chapter 12 reviews and compares the four basic compensation methods (piece rates, tournaments, efficiency wages, and team incentives). Chapter 13 uses knowledge PREFACE ii PERSONNEL ECONOMICS W. NEILSON of these methods to discuss executive compensation, and Chapter 14 concludes the compensation portion of the book with a discussion of performance evaluation. The focus turns to the hiring of workers in Chapter 15, which concerns adverse selection. It introduces basic problem of a firm trying to hire workers who have private information about their own productivity levels, and two solutions to the adverse selection problem are proposed. A third solution, signaling, is introduced in Chapter 16. Chapter 17 uses marginal analysis to examine the search process and Chapter 18 moves on to the issue of bargaining, covering both alternating-offers bargaining and the Nash bargaining solution. Many firms offer their workers benefit packages, and Chapter 19 discusses benefits. The final chapter explores employee training and its effect on the bargaining position of the worker. Each chapter contains numerous motivating examples, a thorough economic analysis of the problem, and a summary of the general lessons to be learned. There are also homework problems at the end of each chapter (except the introductory one). LEVEL AND PREREQUISITES The book is written for students who have already completed a course in intermediate microeconomics. Two of the chapters (Chapter 3 on traditional labor markets and Chapter 19 on benefits) use indifference curve-budget line analysis. Many of the chapters use game theory, but since some intermediate micro courses cover game theory in more depth than others, the text includes a chapter on the game theoretic techniques that are actually used to study personnel economics. The text is intended for an upper-division undergraduate economics class, but may be suitable for master’s students in economics or an analytical course in an MBA program. PREFACE iii  CHAPTER 1 INTRODUCTION Taking a job in exchange for pay is, for most people, the single largest transaction they make in their lives. And while people buy things almost every day, the labor market is one of the few markets in which people are the sellers. The supply side of the market is fundamentally different from the demand side, especially when the sellers have private information about the product they are selling that they can conceal from the buyers. Personnel economics is the study of the employment relationship, and it pays particular attention to the information problems inherent in any employment relationship. It also covers topics from all aspects of a worker’s career. The employer must pay the worker enough to attract him to the job, and also in a way that gets him to actually produce something and not just collect a paycheck. Bad workers might pretend that they are good workers so that they can get a job, but once they are hired good workers might pretend that they are bad workers so that less is expected of them and they do not have to work as hard for their money. Employers have to search for employees, workers have to search for a job, and once a match is made the employer and employee must negotiate a contract. These new workers must be trained. Finally, compensation includes not only pay but also benefits. All of these issues lend themselves to economic analysis. This book concerns all of these aspects of the employment relationship. As such, it is really a book about personnel issues. It is more than that, though. It is also a book about incentives since the employer must give workers an incentive to actually produce something. Economists have studied incentives in a number of different settings, not just the employment relationship. Accordingly, this book can also be thought of as one about the economics of incentives, but with all of the motivation and examples taken from the employment relationship. Incentives are not the only issue, though. Workers often know things about themselves that firms do not. For example, a worker knows more about his abilities than the firm does before the worker is hired, and a worker knows more about how hard he is PERSONNEL ECONOMICS W. NEILSON working than the firm does. If the firm is not careful, workers can take advantage of this information. Economists have long been concerned with how agents deal with situations in which one party has information that another party does not. The third way to think about this book is as being about the economics of information, but with all of the motivation and examples taken from the employment relationship. 1. THE ECONOMICS OF THE EMPLOYMENT RELATIONSHIP The employment relationship has two basic components: the hiring process and the compensation process. The hiring process begins when the firm decides what qualifications to require of its applicants. Why do some jobs require a bachelor’s degree, even in an unrelated field, while other jobs do not? After posting their requirements, the firm searches for a worker, but how does a firm know when to hire a particular worker and when to hold out for someone better? On the other side of the market, when does a worker accept a job and when does he wait for a better offer? After the firm decides on a worker with whom to proceed, the two parties must negotiate a contract, and the bargaining process is of interest to economists. The hiring process does not end with a successful agreement, though. Some firms train their workers, and some firms start their workers off with probationary periods during which they get low pay and can get fired immediately if their performance is unacceptable. The rationale for these decisions is of interest. Compensation must achieve two goals. First, it must be sufficiently high to attract workers to the job and keep them there. Second, it must provide workers with an incentive to produce output, because workers who do not produce do not generate any revenue (or profit) for the firm. Firms use many methods to motivate workers. Some methods pay the worker directly for output, such as when a salesperson is paid on commission. Other methods are less direct, such as when a firm awards periodic bonuses to top performers, or promotes top performers to higher-paying positions. Some firms even pay workers for other people’s hard work, such as when workers are paid as part of a team or when the firm uses a profit sharing plan. Finally, some firms motivate workers by threatening to fire them if the do not perform. Workers decide how hard to work in response to the compensation plan offered by the firm. Firms must design compensation plans that induce workers to put forth a level of effort that maximizes the firms’ profit. Some compensation plans work better in some situations than in others. All of them are complicated by the fact that the worker’s supervisor cannot always observe perfectly how hard the worker works. The tools of economics, especially marginal analysis and game theory, allow us to analyze when and how well these compensation schemes work. Before too long most of you will be entering the labor force. Some of you will have employees to hire and supervise. The material in this course will provide you with CH. 1: INTRODUCTION 2 PERSONNEL ECONOMICS W. NEILSON information that will allow you to do a better job in these tasks. Whether or not you become supervisors, all of you will go through the hiring process and be compensated. The material in this course will help you understand how the firm goes about hiring and illuminate some of the practices that employers follow. 2. THE ECONOMICS OF INCENTIVES AND INFORMATION One of the central tenets of economics is that people and firms respond to incentives. In fact, most people share this belief. For example, it is widely assumed that if the police begin enforcing speed limits more strenuously, drivers will slow down. The incentive for driving slower is being able to avoid paying a fine (and higher insurance premiums), and drivers respond to this incentive. A child whose parents pay him a fixed amount for every book read will read more books. The incentive is the payment, and the child responds to the incentive. When the market price of a good rises, firms produce more of that product. The incentive for increasing production is the increased revenue from each unit sold. A lack of incentives is also important. If speed limits are not enforced, drivers will not obey them. If it is difficult for people to vote, they will not do so. If people are unwilling to pay for a product, no firm will produce it. The economic analysis of incentives is concerned with the design of systems that provide the incentives for an agent to achieve a desired outcome. In the language of the employment relationship, if the firm wants the worker to produce a certain amount of output, it must design a compensation scheme which induces the worker to produce exactly that amount of output. This problem is complicated by the fact that the firm cares about how hard the worker works, but cannot compensate the worker for effort. Instead, it must compensate the worker for something tangible, like output or time spent at the job. Sometimes, though, the worker exerts a lot of effort but has no output to show for it, such as when a salesman works every day but does not manage to close any deals in a month. The firm must find a way to deal with the fact that pay is not perfectly correlated with effort. This same problem occurs in the classroom. Some students work really hard but do poorly on exams, while other students do not study at all and still perform well. The instructor may even know which students are working and which ones are not, but must still assign grades based on tangible outcomes, in this case test scores. In many cases professors make grades depend on more than just test scores so that those students who work hard but test poorly can get better grades. The construction of course requirements is the design of a compensation policy. Someday many of you will hire someone to build a house for you. You would like the builder to do a good job and do it on time, but many things are outside of the builder’s control, such as the weather and the availability of subcontractors. How do you CH. 1: INTRODUCTION 3 PERSONNEL ECONOMICS W. NEILSON design a contract that gets the builder to make the right tradeoff between speed and quality? This is a problem in the economics of incentives. Information causes problems for the design of incentive schemes in two ways. First, as already discussed, the firm cannot reward the worker based on effort, but must reward the worker based on something tangible, such as output or time spent working. Second, the worker sometimes possesses information that would be valuable to the firm, but it is not in his best interest to reveal it. For example, the firm may want to pay highly-skilled workers differently from less-skilled workers, but it cannot tell which workers are which. The workers know which group they belong in, but they might find it worthwhile to behave as if they are in the other group. The firm must design an incentive scheme that gets workers to reveal this information. This problem obviously arises in the hiring process. A firm might want to hire a highly-skilled worker but not a less-skilled one. Put differently, it might want to pay a highly-skilled worker but not a less-skilled one. Often, though, the two types of workers look the same on paper, so the firm has no basis for determining which workers are in which group. The firm must design a compensation scheme that allows it to hire only highly-skilled workers and not less-skilled ones. The economics of incentives and information is a major research topic among academic economists. This course provides you with an introduction to the topic. CH. 1: INTRODUCTION 4  CHAPTER 2 OPTIMIZATION The primary fundamental principle used throughout this book is optimization. Workers take actions that are in their own best interest and make themselves as well off as possible. Firms take actions that are in their own best interest and maximize profits. None of this should come as a surprise to economists, and the techniques discussed in this chapter are also discussed in introductory classes. Why, then, discuss optimization here? There are three good reasons. First, it refreshes your memory. Second, it gets you to think about optimization in the way that it will be used in the book. Third, in principles classes optimization is almost hidden inside of the sections on consumer and producer behavior. Here optimization is treated as a general principle, hopefully reinforcing and extending what you learned in your introductory class. 1. “HOW MUCH” DECISIONS AND MARGINAL ANALYSIS Many of the important questions in economics involve “how much” decisions. How much of a product does a consumer buy? How much should a firm produce? How much labor should a firm employ? How many hours should a worker work? All of these questions involve choosing the amount of an activity. The answer to all of these questions involves marginal analysis. Marginal benefit is the additional benefit from engaging in one more (small) unit of the activity. Marginal cost is the additional cost involved in engaging in one more unit of the activity. If marginal benefit is greater than marginal cost, the individual should engage in more of the activity, and if marginal cost is greater than marginal benefit, the individual should decrease the activity. Marginal benefit typically either decreases or is constant as more of the activity is undertaken. For example, when consuming pizza, the first slice provides more benefit than the second, which provides more benefit than the third, and so on. The marginal PERSONNEL ECONOMICS W. NEILSON benefit of a slice of pizza decreases as the number of pieces consumed rises. An example of constant marginal benefit comes from a firm in a perfectly competitive industry. The benefit a competitive firm receives from selling an additional unit of output is the price of that output, and when the firm is competitive, that price is constant no matter how much the firm sells (for a review of perfect competition, see Section 4 of this chapter). The line labeled MB in Figure 2.1 shows a declining marginal benefit curve. FIGURE 2.1 Marginal benefit curves MB, MC typically slope downward, MC and marginal cost curves typically slope upward. At activity level a1 the marginal benefit of the activity exceeds the marginal cost, so the individual should increase the activity. At level a2, MB < MC, so the individual should MB decrease the activity. At a*, activity a1 a* a2 MB and MC are equal, and the individual should neither increase nor decrease the activity. Marginal costs typically either increase or are constant as more of the activity is undertaken. For example, the cost of removing the first 10% of pollutants from automobile exhaust costs a lot less than removing the last 10% of pollutants. For an example with constant marginal cost, the price a person must pay for a gallon of milk at the grocery store is the same no matter how many gallons he buys. The line labeled MC in Figure 2.1 shows an increasing marginal cost curve. When the activity level is a1 in Figure 2.1, the marginal benefit curve is higher than the marginal cost curve. This means that the extra benefits generated by a small increase in the level of the activity outweigh the extra costs, and so the level of the activity should increase. More specifically, increasing the activity by one unit increases benefit by MB and increases cost by MC, and so net benefit, defined as benefit minus CH. 2: OPTIMIZATION 6 PERSONNEL ECONOMICS W. NEILSON cost, increases by MB − MC which is greater than zero. This is true for every activity level where the marginal benefit curve lies above the marginal cost curve. When the activity level is a2, the marginal cost curve is higher than the marginal benefit curve. This time a decrease in the level of the activity leads to a cost saving that outweighs the loss in benefits. By decreasing the activity by one unit, costs fall by MC and benefits fall by MB. Since MC > MB, decreasing the activity by one unit leads to an increase in net benefit of MC − MB, which is greater than zero. This is true for every activity level where the marginal cost curve lies above the marginal benefit curve. When marginal benefit and marginal cost are equal there is no reason to either increase or decrease the activity by a small amount. In the figure, this is activity level a*, where the marginal benefit and marginal cost curves intersect. This is a local optimum, with the term “local” meaning that there is no nearby activity level that generates higher net benefit. So, at a local optimum, neither a small increase nor a small decrease in the activity level leads to an increase in net benefit. 2. GLOBAL OPTIMIZATION Marginal analysis is an important part of answering “how much” questions, but it is not the only part. Marginal analysis finds a local optimum, but the answer to the “how much” question is a global optimum, that is, a level of activity such that there is no other level of activity that generates strictly higher net benefit. If an activity level is a global optimum it must also be a local optimum, because if it is true that no other level of activity anywhere generates higher net benefit, then it must also be true that there is no nearby activity level that generates higher net benefit. But a local optimum may not be a global optimum. Figure 2.2 shows a case where the local optimum found by marginal analysis is also a global optimum. We can tell by looking at the cost and benefit curves. The global optimum is the point where the benefit curve is the farthest above the cost curve. In the figure, the benefit curve rises at a decreasing rate, which is consistent with a downward- sloping marginal benefit curve (recall that one finds a marginal curve by graphing the slope of the original curve), and the cost curve rises at an increasing rate, which is consistent with an upward-sloping marginal cost curve, exactly as in Figure 2.1. The local optimum a* is found where MB = MC. Since marginal benefit is the slope of the benefit curve and marginal cost is the slope of the cost curve, the local optimum is where the two curves in Figure 2.2 have the same slope. As one can see in the figure, there is no other point where the benefit curve is farther above the cost curve, and a* is indeed a global optimum. Figure 2.3 shows a case where the local optimum found by marginal analysis is not a global optimum. The cost curve has the same shape as before, but the benefit curve is different. This time the benefit curve is horizontal when the activity level is between CH. 2: OPTIMIZATION 7 PERSONNEL ECONOMICS W. NEILSON zero and a0, and then it is an upward-sloping line when the activity level is above a0. Marginal analysis identifies the local optimum a* where the two curves have the same slope. However, the vertical distance between the two curves is greater when the activity level is zero than when the activity level is a*. So, the global optimum is zero, and it is labeled a** in the figure. The benefit curve in Figure 2.3 can occur in the following scenario. Suppose that a salesperson receives a salary of B0, and gets no additional pay unless he reaches his quota of a0 units. After he sells a0 units, he receives a commission of b for every additional unit he sells, where b is the slope of the benefit curve above a0. Selling is costly to the salesperson because it requires time and effort. According to the figure, he is best off taking his salary and selling nothing, since that is where his benefit curve is the farthest above his cost curve. FIGURE 2.2 To find the global optimum, benefit, cost look at the benefit and cost C curves. The global optimum is where the benefit curve is farthest above the cost curve. B The local optimum is where MB = MC, which is where the benefit and cost curves have the same slope, as at point a*. In this figure, the local optimum is also a global optimum, since there is no activity a* other point where the benefit curve is farther above the cost curve. CH. 2: OPTIMIZATION 8 PERSONNEL ECONOMICS W. NEILSON FIGURE 2.3 The marginal benefit curve is benefit, cost horizontal from zero to a0, C and then it is an upward- B sloping line. The local optimum is a*, where the benefit curve and the cost curve have the same slope. However, the vertical distance between the two curves is greater when the activity level B0 is zero than when it is a*, and so a* is not a global optimum. activity a** a0 a* The global optimum is zero, and is denoted a**. Figure 2.4 shows the marginal curves that correspond to the curves in Figure 2.3. When the activity level is below a0, small increases in activity generate no additional benefit, so the marginal benefit is zero. When the activity level is above a0, increasing the activity level by one unit increases benefit by b, and so the marginal benefit curve is horizontal at b. Since the cost curve in Figure 2.3 becomes steeper as the activity level increases, the marginal cost curve is upward sloping. The local optimum is found where the marginal benefit and marginal cost curves intersect. But, as shown in Figure 2.3, this is not the global optimum. CH. 2: OPTIMIZATION 9 PERSONNEL ECONOMICS W. NEILSON FIGURE 2.4 The marginal benefit curve MB, MC shown here is derived from MC the benefit curve in Figure 2.3. Marginal benefit is zero for activity levels below a0, and it is b for activity levels above a0. The local optimum, b MB found where MB = MC, is at activity level a*. This is not a global optimum, though, as shown by Figure 2.4. activity a0 a* Marginal analysis is not always enough. We now have two examples, one in which marginal analysis correctly identifies the global optimum (Figures 2.1 and 2.2) and one in which it does not (Figures 2.3 and 2.4). Figuring this out took two graphs for each example. It would be nice if there was a way to tell from the marginal graph whether or not the second graph is needed, because then we could save some trouble. It turns out that there is a way to tell. Compare the marginal curves in Figure 2.1, where marginal analysis identified the global optimum, and in Figure 2.4 where it did not. In Figure 2.1 the marginal benefit curve crosses the marginal cost curve only once, and from above, while in Figure 2.4 the marginal benefit curve crosses the marginal cost curve, the first time from below. This turns out to be a general rule: if the marginal benefit curve crosses the marginal cost curve only once, and from above, then marginal analysis identifies the global optimum. If the marginal benefit curve ever crosses the marginal cost curve from below, it is necessary to look at the benefit and cost curves to find the global optimum. 3. GENERAL LESSONS We can now identify some general rules for optimization. 1. If the question begins with the words “How much,” the answer involves marginal analysis. “How much” questions are central in economics, and one of the things that makes economics different from the other social sciences is our reliance on marginal analysis to answer questions. CH. 2: OPTIMIZATION 10 PERSONNEL ECONOMICS W. NEILSON 2. Marginal analysis identifies the local optimum. If marginal benefit is greater than marginal cost, the individual should increase the activity by a small amount. If marginal benefit is smaller than marginal cost, he should decrease the activity by a small amount. When the two are equal, neither small change increases net benefit, which is the definition of a local optimum. 3. If marginal benefit crosses marginal cost only once and from above, then marginal analysis also identifies a global optimum. If marginal benefit crosses marginal cost only once and from above, there is no need to check the benefit/cost graph to find the global optimum. Marginal analysis is sufficient. 4. If marginal benefit ever crosses marginal cost from below, then marginal analysis may or may not identify the global optimum. If marginal benefit crosses marginal cost from below, it becomes necessary to draw the benefit/cost graph to find the global optimum. The global optimum is the activity level at which the benefit curve is the farthest above the cost curve. Occasionally in this text we will want to derive a marginal benefit function from a total benefit function or a marginal cost function from a total cost function. There are very simple rules for doing so. Suppose that the original function is linear with the form F(x) = a + bx. Then the marginal function is MF(x) = b. Graphically, the function F(x) is a straight line with slope b and vertical intercept a. The marginal function should be the same as the slope, and it is. Now suppose that the original function is quadratic with the form G(x) = a + bx + cx2. In this case the marginal function is MG(x) = b + 2cx. Linear benefit and cost functions yield constant marginal functions, but quadratic benefit and cost functions yield marginal functions that can be either increasing or decreasing. Since we will often want increasing marginal cost functions and decreasing marginal benefit functions, the rule for deriving marginal functions from quadratic functions is extremely useful. 4. A CLASSIC EXAMPLE: THE SHORT-RUN COMPETITIVE FIRM The most common textbook example of a case in which marginal analysis fails to generate a global optimum is the profit-maximization problem faced by a competitive firm in the short run. A competitive firm is one that is small enough relative to the market that its actions have no effect on the market price, so that it can sell as much or as little as it wants without causing the price of the good to rise or fall. The short run is a period of time long enough for the firm to change the amounts of some of its inputs but CH. 2: OPTIMIZATION 11 PERSONNEL ECONOMICS W. NEILSON not all of them. In the short run some inputs are fixed and some are variable, leading to fixed and variable costs. FIGURE 2.5 In the case of a short-run $/unit competitive firm, marginal MC analysis identifies the local optimum q* where MR ATC crosses MC. But, since MR AVC crosses MC twice, the first time from below, the local optimum may not be a global p MR optimum. Since at q* the firm does not output q** q* cover its variable costs, the firm should produce nothing. The local optimum is not a global optimum. Figure 2.5 should be familiar, since it is found in virtually every introductory economics text. The firm’s average total and average variable costs are shown by the curves ATC and AVC, respectively, and MC denotes marginal cost. Since the firm can sell as much as it wants at price p, its marginal revenue is equal to p no matter how much output it sells. Marginal analysis identifies a local optimum where the marginal revenue curve crosses the marginal cost curve at point q*. The only issue is whether or not this is also a global optimum. Notice that in the drawing the marginal revenue curve crosses the marginal cost curve twice, first from below and then from above. As we saw in previous sections, this means that the local optimum might not be a global optimum, and we should graph the benefit and cost curves to decide. Actually, Figure 2.5 contains enough information to determine whether or not the local optimum q* is also a global optimum. The firm must pay its fixed costs no matter how much it produces, so those costs are irrelevant to the analysis. The firm covers its variable costs if the price is above average variable costs, otherwise it loses additional money on every unit it sells. If the price is strictly above average variable cost, every CH. 2: OPTIMIZATION 12 PERSONNEL ECONOMICS W. NEILSON unit sold contributes to profit. So, the firm should produce q* if the price is above average variable cost at q*, and it should produce nothing at all if the price is below average variable cost at q*. The way Figure 2.5 is drawn, the price is below average variable cost, so the firm should produce nothing. It is informative to look at the corresponding benefit/cost diagram. Figure 2.6 has two cost curves, a variable cost curve labeled TVC and a total cost curve labeled TC. The TC curve is obtained from the TVC curve by shifting the TVC curve upward by the amount of fixed costs. The total revenue curve is labeled TR and it linear with slope p since the firm’s revenue is p∙q, where p is the price and q is the amount sold. As stated above, the firm should produce if it covers its variable costs, and it should shut down otherwise. In Figure 2.6 the total revenue curve is always below the total variable cost curve, so the firm should not produce any output at all. FIGURE 2.6 TC The local optimum identified $ by marginal analysis is q*, where the TC, TVC, and TR TVC curves all have the same slope. However, since total revenue is not enough to TR cover total variable costs, the firm loses money on every unit it sells and would be FC better off producing zero, p which is the global optimum q**. output q** q* PROBLEMS 1. Explain the difference between a local optimum and a global optimum. 2. Consider a firm that negotiates a lower price for a critical input. Assuming that no other prices change, use a marginal benefit/marginal cost diagram to determine whether the firm will produce more or less output. CH. 2: OPTIMIZATION 13 PERSONNEL ECONOMICS W. NEILSON 3. The benefit function is given by B(x) = 4 + 12x – 2x2, with marginal benefit function MB(x) = 12 – 4x. The cost function is given by x2 + 6x + 2, with marginal cost function MC(x) = 2x + 6. Find the optimal value of x. 4. Explain how one can tell by looking at a marginal benefit/marginal cost diagram whether or not a local optimum might not be global optimum. 5. A hairdresser faces two types of costs: She must pay $400 per month to rent a chair at a local salon, and she must bear the cost of her own effort from cutting hair. Her marginal effort cost increases with the number of haircuts. Once she pays to rent the chair, she gets to keep the $40 per haircut she charges her customers. Draw benefit and cost curves corresponding to the case in which it is worthwhile to pay to rent the chair, and show the optimal number of haircuts per month. 6. The cost function is C(x) = x2 + 2, with marginal cost function MC(x) = 2x. The benefit function is given by  60 0 x5  B( x )   if 12x x5  which has marginal benefit given by MB(x) = 0 if 0 ≤ x ≤ 5 and MB(x) = 12 if x ≥ 5. (a) Find the value of x where the marginal condition holds. (b) Find the global optimum. CH. 2: OPTIMIZATION 14  CHAPTER 3 TRADITIONAL LABOR MARKET ANALYSIS Personnel economics is about the employment relationship. So is labor economics. The two fields of economics are concerned with different aspects of the employment relationship, and approach the relationship in different ways. Labor economics is the older of the two fields, and uses more traditional tools. This chapter briefly outlines some of the results from traditional labor market analysis, which can then be used as a point of departure when we delve into personnel economics in the next chapter. 1. THE FIRM’S PROBLEM The first step in analyzing the firm’s problem is to figure out exactly what the firm is doing. More specifically, the firm makes a choice and we must figure out what the firm chooses and what its objective is. The answer is familiar: Firms choose the amounts of inputs to use in order to maximize profit. Typically in economics we look at two inputs, capital and labor. If the firm uses L units of labor, typically measured in hours, and K units of capital, it produces output Q = F(L,K), where F is the production function. The firm also faces a demand curve, and P(Q) is the market-clearing price when the firm tries to sell Q units. Finally, labor costs w per unit, where w is the hourly wage, and the rental price of capital is r per unit. This gives us enough information to write down the firm’s profit function. If the firm uses L units of labor and K units of capital, it produces F(L,K) units of output and sells them at the market-clearing price. The firm’s total revenue is R(Q), and since Q = F(L,K), total revenue can be written R(F(L,K)). The firm’s labor cost is wL, which is the hourly wage times the number of hours of labor employed, and its capital cost is rK, the rental price per unit of capital times the number of units of capital. Profit, then, is given by π = R(F(L,K)) − wL − rK. PERSONNEL ECONOMICS W. NEILSON The firm chooses the amounts of capital and labor to maximize profit. Because this chapter is concerned with labor markets, we will restrict attention to how much labor the firm employs. Since this is a “how much” problem, the answer involves marginal analysis, equating marginal benefit and marginal cost. Begin by looking at marginal benefit. Using labor benefits the firm by increasing revenue, and an additional unit of output increases revenue by MR, marginal revenue. An additional hour of labor increases output by MPL, the marginal product of labor. So, an additional hour of labor increases revenue by MR∙MPL, or MPL units of output which each generate MR dollars of additional revenue. There is also a cost to using labor since workers must be compensated, and each additional hour of labor requires the firm to pay the wage w. The firm’s marginal condition equates the marginal benefit of labor with the marginal cost, or MR∙MPL = w. The left-hand side is the additional revenue generated by a one-hour increase in labor, and the right-hand side is the additional cost. The firm employs labor until the extra revenue generated by an additional unit of labor equals the extra cost of it, which is the hourly wage. The left-hand side is often given a name, and it is the marginal revenue product of labor. The marginal condition states that the firm employs labor until the marginal revenue product of labor equals the wage rate. CH. 3: TRADITIONAL LABOR MARKET ANALYSIS 16 PERSONNEL ECONOMICS W. NEILSON FIGURE 3.1 The firm’s marginal condition $/hour states that it employs labor until the marginal revenue product of labor equals the wage rate, or MR∙MPL = w. The downward-sloping curve is the marginal revenue w product of labor, and it is also the firm’s labor demand curve. The horizontal line MRPL represents the wage. The firm maximizes profit by hours L* employing L* hours of labor, of labor which is where the two curves cross. Figure 3.1 graphs the marginal condition. The horizontal axis measures hours of labor, and the unit for the vertical axis is dollars per hour of labor, which is the appropriate unit for both the wage rate (workers are paid a certain number of dollars per hour) and the marginal revenue product of labor (an additional hour of labor generates a certain number of dollars in revenue). The marginal revenue product curve is downward sloping for two reasons. Each additional unit of output generates less additional revenue than the unit before it, so that marginal revenue is declining in output. Also, each additional unit of labor generates less additional output than the unit before it, holding capital fixed, and so the marginal product of labor is also declining. Both components of marginal revenue product are decreasing functions, and so marginal revenue product is also a decreasing function. The wage curve is a horizontal line at the market wage. The firm employs the amount of labor where the two curves cross, marked L* in the figure. Since the marginal benefit curve (MRPL) crosses the marginal cost curve (w) only once and from above, L* is a global optimum as well as a local optimum. The marginal revenue product curve is the firm’s labor demand curve. It shows how much labor the firm chooses to employ for every given wage rate. Using the components of marginal revenue product it is straightforward to find the factors that cause the firm’s labor demand curve to shift. An increase in the demand for the firm’s output causes prices to rise, which cause marginal revenue to rise, which shifts the labor CH. 3: TRADITIONAL LABOR MARKET ANALYSIS 17 PERSONNEL ECONOMICS W. NEILSON demand curve outward. An increase in worker productivity causes the marginal product of labor to rise, also shifting the labor demand curve outward. 2. THE WORKER’S PROBLEM We now turn to the choices made by workers. Once again we address the problem by first determining what workers choose and what their objective is. Workers maximize their utility, which is the way economists usually discuss the behavior of individual people. What workers choose is a more subtle issue. Since this chapter is about labor markets, we want labor to somehow enter the analysis. But how? Some people really like their jobs and get utility from working. More people, though, only work because it is a source of income, and income allows them to buy things that give them utility. Labor should not be an entry in the worker’s utility function, since work does not provide any utility, but the income generated by work can be an entry in the utility function. We need a second argument, though. If income is the only argument, the worker should work as much as possible to maximize income. But this is not what people do. They work for part of the day, and then enjoy leisure time the rest of the day. We can make leisure be the other argument of the utility function. There are 168 hours in a week. If the worker chooses to work L hours in a week, then he is also choosing to devote 168 − L hours to leisure activities. Leisure time generates utility, and so the second argument of the utility function should be leisure time. The worker chooses the amount of time to spend working to maximize his utility. His utility function can be written U(Z,I), where Z denotes leisure and I denotes income. Working provides a benefit in the form of increased income, but it also imposes a cost in the form of lost leisure time. Working for one additional hour generates an additional hour’s pay, w, and each additional dollar of income increases utility by MUI, the marginal utility of income. Therefore, the worker’s marginal benefit of labor is w∙MUI, the additional utility from the income generated by working for another hour. Working for another hour reduces leisure time by one hour, and that causes utility to fall by MUZ, the marginal utility of leisure. The worker’s marginal cost of labor, then, is MUZ. The marginal condition can be written w∙MUI = MUZ. The marginal condition states that the worker spends time at work until the marginal benefit in terms of increased income is equal to the marginal cost in terms of decreased leisure time. Put another way, the worker spends time at work until he is indifferent between spending one more hour at work to earn additional income and spending one more hour of leisure time. It is customary to rearrange the above expression by dividing both sides by MUI: CH. 3: TRADITIONAL LABOR MARKET ANALYSIS 18 PERSONNEL ECONOMICS W. NEILSON MU Z w. (*) MU I The right-hand side is the marginal rate of substitution of income for leisure. To interpret it, think about the units in which the two terms are measured. MUZ is utility per hour of leisure, and MUI is utility per dollar of income. Consequently, MUZ/MUI is (utility/hour of leisure)/(utility/dollar) which reduces to dollars per hour of leisure. Consequently, the right-hand side of expression (*) is the number of dollars the worker is just willing to give up to get one more hour of leisure. The left-hand side is the wage, which is the number of dollars the worker has to give up to get one more hour of leisure. The marginal condition states that the amount of money the worker is just willing to forego for an hour of leisure is equal to the amount he must forego to get it. FIGURE 3.2 The worker’s marginal $/hour condition states that he works until the marginal rate of substitution of income for labor equals the wage rate, or MUZ/MUI = w. The upward- sloping curve is the marginal w rate of substitution curve, and it is also the worker’s labor supply curve. The horizontal line represents the wage. The worker maximizes utility by hours L* working for L* hours, which of labor is where the two lines cross. Figure 3.2 graphs the marginal condition w = MUZ/MUI. As the worker works more, he earns more income which makes the marginal utility of income fall, and he has less leisure time which makes the marginal utility of leisure rise. Accordingly, as he works more MUZ/MUI rises, since the numerator gets larger and the denominator gets smaller. The curve is upward-sloping in the figure. The marginal condition is satisfied where the marginal rate of substitution curve crosses the horizontal line through the wage CH. 3: TRADITIONAL LABOR MARKET ANALYSIS 19 PERSONNEL ECONOMICS W. NEILSON w, and the worker chooses to work for L* hours. Since the marginal benefit curve (w) crosses the marginal cost curve (MUZ/MUI) only once and from above, L* is also a global optimum. The upward-sloping curve in Figure 3.2 is also the worker’s labor supply curve. Since it is a supply curve, we are interested in the factors that cause it to shift. Constructing the supply curve from the worker’s utility maximization problem makes this straightforward. Anything that causes the worker to desire income more causes MUI to rise, which in turn shifts the upward-sloping curve in Figure 3.2 downward. This downward shift is also a rightward shift (draw it to see this), so anything that causes the worker to desire income more causes the labor supply curve to shift to the right. Examples of things that might cause the worker to desire income more would be having to pay for some large expense, like college or braces or a new vehicle. Anything that causes the worker to desire leisure more causes MUZ to rise, which in turn shifts the curve in Figure 3.2 upward, which is also a shift to the left. So, for example, as the worker becomes older he values his leisure time more, and this causes his labor supply curve to shift to the left. AN ALTERNATIVE APPROACH Most intermediate microeconomics courses take an alternative approach to analyzing the worker’s labor-supply decision. The alternative approach uses indifference curves, and it yields some additional insight into the problem, and also leads to a more complicated shape for the labor supply curve. Figure 3.3 shows a budget line/indifference curve diagram. The axes measure the two variables that generate utility for the worker, leisure and income, with leisure on the horizontal axis and income on the vertical axis. There are 168 hours in a week, and so the most leisure the worker can consume in a week is 168 hours. The most income he can earn comes from working for a full 168 hours, which is 168w. The budget line connects the two points (168,0) and (0,168w). The slope of the budget line is −w, the negative of the wage rate. CH. 3: TRADITIONAL LABOR MARKET ANALYSIS 20 PERSONNEL ECONOMICS W. NEILSON FIGURE 3.3 The worker’s budget line is income downward sloping, and he can get a maximum of 168 hours of leisure if he does not work at all, or a maximum of 168w in income if he works 168w every hour of the week. His * indifference curve is downward-sloping, reflecting I* the tradeoff between income u0 and leisure. leisure Z* 168 The worker maximizes utility by choosing the point on the budget line that is on the highest indifference curve. An indifference curve is the set of points that all generate the same amount of utility. The worker can get additional utility from either more income or more leisure. To keep the level of utility fixed, then, if he consumes more leisure he must also consume less income. Similarly, if he consumes more income, to stay indifferent he must consume less leisure. This makes the indifference curves downward-sloping. Higher indifference curves have higher levels of both income and leisure, which means that higher indifference curves correspond to higher levels of utility. The slope of the indifference curve is the negative of the marginal rate of substitution, −MUZ/MUI. The worker maximizes utility by finding the point on the budget line that is on the highest indifference curve, which is the point where the indifference curve is just tangent to the budget line, as shown in the figure. The tangency condition is that the budget line and the indifference curve have the same slope. Since the slope of the budget line is −w, and the slope of the indifference curve is −MUZ/MUI, the tangency condition is MU Z w , MU I which is exactly the condition (*) we found using marginal analysis. CH. 3: TRADITIONAL LABOR MARKET ANALYSIS 21 PERSONNEL ECONOMICS W. NEILSON FIGURE 3.4 As the wage rate rises, the income budget lines become steeper. When the wage rate is low, and the budget line is flat, the worker chooses to consume a large amount of leisure. As the wage rate rises the worker works more and consumes less leisure up to a certain point. Eventually the wage rate becomes high enough that the worker responds to leisure 168 further increases by consuming more leisure. Figure 3.4 repeats this procedure for many different wage rates, allowing us to see how the worker’s choice of how much leisure to consume depends on the wage rate. When the wage rate starts out low, the worker chooses to consume less leisure as the wage rises. This makes sense, since the wage is the price of leisure, and as the price goes up, people consume less. As the wage rate continues to rise, though, something different happens. For high wage rates, increases in the wage lead to increases in the amount of leisure consumed. Since L = 168 − Z, a one-hour increase in leisure corresponds to a one-hour decrease in labor, and vice versa. So, when the wage rate is low, increases in the wage lead to increases in the amount of labor supplied. But, when the wage rate is high, further increases in the wage lead to decreases in the amount of labor supplied. The corresponding labor supply curve is shown in Figure 3.5. It is upward-sloping for low wage rates but downward-sloping (or backward-bending) for high wage rates. CH. 3: TRADITIONAL LABOR MARKET ANALYSIS 22 PERSONNEL ECONOMICS W. NEILSON FIGURE 3.5 Figure 3.4 shows that as the $/hour wage rate rises, the worker labor first decreases leisure supply consumption and then increases it. Since a decrease in leisure is an increase in labor, as the wage rate rises the worker first supplies more labor and then supplies less, and the labor supply curve is upward-sloping for low wages and backward-bending hours for high wages. of labor Figure 3.2 and Figure 3.5 do not match. Why not? Figure 3.2 draws the labor supply curve assuming that MUZ/MUI increases as the wage increases. This is a sensible first approximation because when the wage increases the worker’s income increases, causing the marginal utility of income to fall. Since Figure 3.5 does not match Figure 3.2, though, there must be something wrong with this first approximation. The problem is that an increase in income also makes leisure more valuable, because increased income expands the possible uses of leisure time. A worker with more income can travel more, see more movies, watch TV using a better video system, and so on. The impact of increased income on the value of leisure can make the marginal utility of income rise, which means that the curve MUZ/MUI can bend backward, just as in Figure 3.5. 3. LABOR MARKETS The primary contribution of the last two sections was to construct supply and demand curves for labor in ways that allow us to determine what causes the curves to shift. The most important use of supply and demand curves is to determine the effects of changes in either the workers’ or the firms’ circumstances on the amount of labor employed and the equilibrium wage. Figure 3.6 shows a supply/demand graph, assuming for the sake of simplicity that the supply curve is upward-sloping. The two curves cross where the quantity of labor demanded by firms and the quantity of labor supplied by workers are the same at L*, and the corresponding wage is w*. CH. 3: TRADITIONAL LABOR MARKET ANALYSIS 23 PERSONNEL ECONOMICS W. NEILSON FIGURE 3.6 When workers must pay $/hour higher property taxes, the marginal utility of income S rises and the labor supply S’ curve shifts to the right from S to S’. In the ensuing equilibrium the amount of w* labor employed rises from L* to L’ and the equilibrium w’ wage rate falls from w* to w’. D hours L* L’ of labor FIGURE 3.7 When demand for the firm’s $/hour product falls, its marginal revenue also falls and it S demands less labor. The labor demand curve shifts leftward from D to D’. The w* amount of labor employed w’ falls from L* to L’ and the equilibrium wage falls from w* to w’. D D’ hours L’ L* of labor Suppose that there is an increase on the property tax on homes. What happens to the amount of labor and the equilibrium wage? Workers who own their own homes will find income more valuable than before because they must now pay additional property taxes. When income becomes more valuable the marginal utility of income increases, CH. 3: TRADITIONAL LABOR MARKET ANALYSIS 24 PERSONNEL ECONOMICS W. NEILSON which in turn shifts the labor supply curve to the right from curve S to S’. The amount of labor employed rises from L* to L’, which makes sense because workers want to work more so that they can pay the extra taxes, and the equilibrium wage falls from w* to w’, which makes sense because firms only employ more labor if the wage falls. Now consider a different example. A wireless phone service provider is the worst in the industry, with terrible customer satisfaction, and the only customers it manages to hold onto are the ones who find it too costly to change their phone numbers when they switch carriers. As a result of a new law that allows customers to keep their phone numbers when they switch wireless providers, the wireless phone company suffers a large drop in the demand for its output. This reduces the firm’s marginal revenue, which in turn shifts the labor demand curve to the left. Figure 3.7 shows the resulting equilibrium in which the firm employs less labor and the wage falls. 4. LABOR MARKET ANALYSIS AND PERSONNEL ECONOMICS Traditional labor market analysis is quite useful for determining how changes in the circumstances of workers or firms affect the equilibrium wage and the amount of labor employed. It leaves two important issues unaddressed, though. In the traditional labor market model, a worker chooses to go to work for a certain amount of time, and the firm pays the worker for the amount of time spent at work. Somehow during that time the worker produces some output. Why? More to the point, how does the firm motivate the worker to actually do something while at work? It is certainly possible to spend time at work without doing anything productive. The traditional labor market model makes no distinction between time at work and effort at work. Personnel economics is concerned with how the firm motivates workers to produce output. Time and effort are not treated as interchangeable, and the firm must design its compensation scheme in a way that gets workers to exert effort. The next several chapters will look at how the firm designs compensation schemes to get workers to work. In the traditional labor market model, all workers are the same and a unit of labor is a unit of labor no matter who provides it. In real life, though, some workers are more productive than others, and workers often know more about what makes them different than firms do. The firm would like to use this information to hire the right workers, but unless it can get prospective employees to reveal information about themselves, it cannot use the information. This can cause problems for hiring and also for the ways in which the firm motivates workers. Personnel economics is also concerned with how firms respond to this information that workers have but do not necessarily share with prospective employers. CH. 3: TRADITIONAL LABOR MARKET ANALYSIS 25 PERSONNEL ECONOMICS W. NEILSON PROBLEMS 1. What do firms choose and what do they maximize in the traditional labor market model? What do workers choose and what do they maximize in the traditional labor market model? 2. Explain why the wage is the firm’s marginal cost of labor but not the worker’s marginal benefit from labor. 3. Using a graph like the one in Figure 3.1, show the effect on hours of labor demanded when consumers boycott the firm’s output. 4. Using a graph like those in Figure 3.3 and 3.4, show the effect on hours worked of an increase in the income tax. 5. A firm’s labor demand function is given by its marginal revenue product of labor. Explain how the formula changes and how the demand curve shifts when the firm expands its market by exporting its product to another country. 6. A worker chooses the amount of labor that makes MUZ/MUI = w. Explain how this expression changes when a person gets married to a spouse with a high income. What happens to that person’s labor supply curve after they get married? CH. 3: TRADITIONAL LABOR MARKET ANALYSIS 26  CHAPTER 4 COMPENSATION AND MOTIVATION Getting paid is great. It provides one with money to spend on things that the worker likes. However, getting paid also requires work, and work is often not so great. While some people are self-motivated and/or really like their jobs, it is uncommon for workers to enjoy every aspect of their jobs. Those unenjoyable tasks only get done because the worker is paid to do them. Firms must pay workers to perform tasks that they would not otherwise perform. This is not as straightforward as it seems. One can readily observe a wide variety of compensation schemes that firms use to induce their workers to perform. Some pay a fixed amount per unit of time, such as a monthly salary or an hourly wage, while others pay a salary plus a bonus, or some amount per unit of output, or some amount per dollar of revenue produced, such as a commission. Some firms only pay workers if they reach some quota or other output standard. In this and the next several chapters, we will explore how the firm's compensation scheme motivates workers to perform tasks they do not enjoy. In this chapter we look at a very simple employment relationship and look at the effectiveness of different compensation schemes. 1. WORKER EFFORT AND EFFICIENCY In this chapter we restrict attention to an extremely simplified work relationship. The employee has only one task, and must decide how much effort to devote to that task. The task results in output for the firm, which it can then sell at the going market price. The worker finds exerting effort on the task to be unpleasant, which we interpret as being costly. The purpose of this section is to illustrate how effort affects the worker and the firm, and to determine the optimal level of effort. The worker's cost of effort is given in Table 4.1. The worker can exert up to ten units of effort. Effort is unpleasant, reducing his utility, and the cost of effort can be interpreted as the dollar loss that gives him the same utility loss. So, for example, the utility loss from exerting 4 units of effort equals the utility loss from foregoing $320 in income. Exerting 7 units of effort leads to the same utility loss as foregoing $980. PERSONNEL ECONOMICS W. NEILSON TABLE 4.1 Worker's cost of effort Units of effort Cost 0 $0 1 20 2 80 3 180 4 320 5 500 6 720 7 980 8 1280 9 1620 10 2000 Each unit of effort produces one unit of output for the firm. The firm sells each unit of output for $800. However, the firm has some costs besides labor costs. Each unit of output also requires $560 worth of materials, so each unit of output generates $240 net revenue for the firm, where the term “net revenue” will always mean revenue minus all non-labor costs in this book. Is there a “best” or “right” level of effort in this context? Exerting effort helps the firm but is costly to the worker. Exerting more effort helps the firm even more, but is even more costly to the worker. How do we know how much effort the worker should exert in this situation, and how do we know how much effort is too little or too much? Economists use the concept of Pareto efficiency in situations like this. An allocation is Pareto efficient if there is no other allocation that makes one party better off without making the other party worse off. If the worker exerts effort, he is obviously made worse off than not exerting any effort at all. But, if he exerts effort, he produces output that the firm can sell. The proceeds from the sale can be used to compensate the worker. For example, if the worker exerts one unit of effort, he incurs a $20 effort cost. One unit of output is produced, which the firm sells for $800. After paying the $560 in materials cost, the firm has $240 left over. Since the increase in net revenue outweighs the cost increase, there is a gain to be shared. The firm could pay the worker, say, $30, and both the firm and the worker would be better off than they would be if the worker exerted no effort. So, we can determine that zero units of effort does not lead to a Pareto efficient allocation because it is possible to make both parties better off. It is also not Pareto efficient for the worker to exert 10 units of effort. With 10 units of effort, the worker's cost is $2000, but the firm sells the 10 units of output for a CH. 4: COMPENSATION AND MOTIVATION 28 PERSONNEL ECONOMICS W. NEILSON total of $2400 in net revenue ($240 net revenue per unit of output). The firm could pay the worker, say, $2010 to compensate for the effort and still have $230 in profit, so both parties can be better off with 10 units of effort than with zero. This is not the only comparison, though, and it is not the right one. Suppose that the worker exerted 9 units of effort instead. His effort cost would fall by $2000 – $1620 = $380, while the firm's net revenue would fall by $240. The cost saving outweighs the net revenue loss, so there is a gain to be shared. So, both parties could benefit if the worker reduced his effort level. The first example showed that an effort level could not lead to a Pareto efficient allocation if the net revenue gain from increasing effort outweighs the increase in costs. The second example showed that an effort level could not lead to a Pareto efficient allocation if the reduction in costs from decreasing effort outweighs the loss in net revenue. We say that an effort level is Pareto efficient if it can lead to a Pareto efficient allocation. We also sometimes call this the socially efficient or simply the efficient effort level. For an effort level to be Pareto efficient, then, it must be the case that the net revenue gains from increasing effort do not outweigh the costs, and that the cost reductions from decreasing effort do not outweigh the losses in net revenue. In economic terms, this translates into a comparison of the marginal net revenue to the firm and the marginal cost of effort to the worker. The firm's marginal net revenue is the same for every level of output, since the firm receives $240 in additional net revenue for each additional unit of output. The worker's marginal cost of effort must be calculated, and these calculations are found in Table 4.2. We compute marginal cost as the cost of the last unit of effort, so that the marginal cost of the nth unit of effort is simply the total cost of the nth unit minus the total cost of the (n−1)st unit. This formula does not yield a value for zero units of effort, because the formula requires subtracting the cost of unit −1 from the cost of unit 0, and there is no unit −1. Consequently we place a − in the table for unit zero. Using Table 4.2, the Pareto efficient level of effort is 6 units. The marginal cost of the sixth unit of effort is $220, while the marginal net revenue is $240. Since marginal net revenue exceeds marginal cost the sixth unit of effort should be exerted. The marginal cost of exerting the seventh unit of effort, though, is $260, which exceeds the $240 net revenue it generates. There is no way to make both parties (strictly) better off by increasing the effort level beyond 6, and consequently 6 units is the Pareto efficient effort level. CH. 4: COMPENSATION AND MOTIVATION 29 PERSONNEL ECONOMICS W. NEILSON TABLE 4.2 Marginal cost of effort and the Pareto efficient effort level Units of Marginal effort Effort cost effort cost 0 $0 − 1 20 20 2 80 60 3 180 100 4 320 140 5 500 180 6 720 220 7 980 260 8 1280 300 9 1620 340 10 2000 380 The same effort level would be chosen if the worker owned the firm. In that case, all of the net revenue would go to the worker, and so he would choose the Pareto efficient effort level automatically. As the owner of the firm, the worker would choose to maximize profit, which would be net revenue minus effort cost. As discussed in Chapter 2, the solution to this problem is to exert effort as long as the marginal net revenue exceeds the marginal effort cost, which is what was done in Table 4.2 in choosing 6 units of effort. Net revenue minus effort cost can also be considered a measure of social welfare. Net revenue is a gain to the firm, while effort cost is a loss to the worker. Combining the two yields net revenue minus effort cost, a quantity we call total surplus. In general, total surplus is the sum of all benefits minus the sum of all costs for all parties involved in the transaction, which in this case includes the worker and the firm but not consumers. According to standard marginal analysis, the effort level that maximizes total surplus is the one at which marginal net revenue equals marginal effort cost. Consequently, we have three interpretations of the Pareto efficient effort level. The first is the effort level that can lead to a Pareto efficient allocation. The second is the effort level the worker would choose if he owned the firm. The third is the effort level that maximizes total surplus, a measure of social welfare. The first is the definition we began with, while the second works because it makes the same individual act as both the worker and the firm, so of course he will exploit all gains. The third one works because CH. 4: COMPENSATION AND MOTIVATION 30 PERSONNEL ECONOMICS W. NEILSON maximizing total surplus gives the same marginal condition as with the worker-owned firm. 2. COMPENSATION SCHEMES AND EFFORT CHOICES We have now found the level of effort that is “best” in the sense of both Pareto efficiency and maximizing total surplus. If the firm wants the worker to exert that level of effort, though, it must pay him to do so. The worker is selfish, and will behave in his own best interest, not necessarily in the best interest of the firm or social welfare. The purpose of this section is to explore some common compensation schemes and see if they are able to entice the worker to exert the Pareto efficient level of effort. For each compensation scheme there are two issues to explore. First, what level of effort will the worker choose? The worker chooses the effort level that maximizes his compensation from the firm minus his effort cost. Second, does the firm gain or lose from the compensation scheme? The firm will not use a compensation scheme that leads to negative profit. The compensation schemes considered here are commonly found in the real world. They include paying the worker per unit of output, commonly called a piece rate; paying the worker a straight salary; paying the worker after he meets a production quota; and paying the worker a percentage of the revenue he generates, commonly called a commission. PIECE RATES In a piece rate compensation system, the firm pays the worker a fixed amount for each unit of output produced. The piece rate is the amount paid per unit of output. For example, migrant farm workers are often paid by the amount of fruit picked, rather than the time spent picking. Some automobile windshield replacement companies pay installers by the number of installations they make, instead of by the hour. To analyze such a compensation system, we must choose a piece rate to analyze. Start with a piece rate of $120. The worker receives $120 for each additional unit of effort, so his marginal benefit of effort is $120. His marginal cost is given in Table 4.2. The marginal benefit of effort exceeds the marginal cost at 3 units of effort, but marginal cost exceeds marginal benefit at 4 units of effort, and the worker exerts 3 units of effort. Obviously, this does not yield the efficient level of effort, so we need to find the right piece rate. Since the piece rate is the worker's marginal benefit, and since the worker exerts effort as long as the marginal benefit exceeds the marginal cost, to get the efficient level of 6 units of effort the piece rate must lie between $220, the marginal cost of the 6th unit of effort, and $260, the marginal cost of the 7th unit of effort. For example, if the piece rate is $230 the worker will exert 6 units of effort, earning a total of 6 x $230 = CH. 4: COMPENSATION AND MOTIVATION 31 PERSONNEL ECONOMICS W. NEILSON $1380. His effort cost is $720, so he earns a net benefit of $660 from the employment relationship. What about the firm? The firm earns $240 before labor costs for each unit, but pays $230 in labor costs for each unit. Consequently, the firm earns profit of 6 x ($240 − 230) = $60. The worker earns a net benefit of $660, but the firm only earns $60. This piece rate system does much better for the worker than the firm. In fact, the very best the firm can do is by setting a piece rate of $221, which is the lowest piece rate it can set and still be sure that the worker exerts 6 units of effort. In this case the worker earns income of 6 x $221 = $1326, yielding a net benefit of $1326 − 720 = $606. The firm earns $240 − 221 = $19 per unit for a total profit of $114. The firm would actually be better off with a lower piece rate. If the piece rate is $181, Table 4.2 shows that the worker exerts 5 units of effort. The worker earns a total of 5 x $181 = $905, and incurs an effort cost of $500, for a net benefit of $405. The firm earns 5 x $240 = $1200 in net revenue, and pays $905 to the worker, for a profit of $295. The firm earns higher profit by inducing the worker to exert less than the socially efficient level of effort. This raises the question of whether it is possible for the firm to earn more than $114 in profit while still getting the worker to exert 6 units of effort. One method that is used in many industries is to have the worker pay a fee to the firm at the start and then earn a piece rate. For example, hair stylists rent their spaces from the owner of the shop, and then keep all of the proceeds from haircuts. Some cabbies rent their cars from the cab company and then keep all of the proceeds from passengers. Accordingly, suppose that the firm charges the worker a $500 up-front fee, and then pays a piece rate of $230. A comparison of marginal benefit and marginal effort cost using Table 4.2 suggests that the worker exerts 6 units of effort. The worker earns (6 x $230) – $500 = $880, and his effort cost is $720, for a net benefit of $160. Since this amount is positive, the worker is willing to take the job and exert 6 units of effort. The firm earns net revenue of 6 x $240 = $1440 and its net payment to the worker is $880, for a profit of $560. By charging the up-front fee the firm is able to extract more of the surplus from the worker. Of course, if the firm charges an up-front fee that is too high, the worker will choose not to work for the firm. Suppose, for example, that the firm charges a fee of $700 at the start and then pays a piece rate of $230. Comparing the worker's marginal benefit and marginal effort cost still suggest exerting 6 units of effort, but this time the worker's income of (6  $230) – $700 = $680 does not cover his effort cost of $720, for a net benefit of –$40. If he refuses to take the job he exerts no effort at all and does not pay the up-front fee, in which case his income is $0 but so is his effort cost, yielding a net benefit of $0. He is better off not working when the up-front fee is too large. CH. 4: COMPENSATION AND MOTIVATION 32 PERSONNEL ECONOMICS W. NEILSON STRAIGHT SALARY Firms often pay their workers a straight salary. Sometimes it takes the form of a fixed amount per month, and sometimes it takes the form of a fixed amount per hour, otherwise known as an hourly wage. Either way, it is based on time, not effort or output. Let's see if a straight salary can induce the worker to exert the Pareto efficient level of effort. To ensure that the worker's effort costs are covered at the efficient level of effort, set the salary at $800. So, the worker is paid $800 no matter what, and the firm asks him to produce 6 units of effort. How much will the worker produce? The answer is nothing at all. If he exerts 6 units of effort, his income is $800. If he exerts 5 units of effort, his income is still $800. If he exerts no effort at all, his income is still $800. No matter how much effort he exerts, his income is $800. Since additional effort does not yield additional income, his marginal benefit from exerting effort is zero, and so he will not exert any. The worker benefits greatly from this compensation scheme. His pay is $800, but he exerts no effort and his effort cost is $0. His net benefit is $800. On the other hand, the firm loses from this compensation scheme. It earns no revenue, but still pays $800 in labor costs. The firm would not find a straight salary compensation scheme profitable. Nevertheless, we see firms offering straight salary all the time, and you might object to the conclusion that workers do no work under this compensation scheme. And, in fact, workers on salary do work. Why? According to this analysis, there must be some other motivating factor. The most likely candidates involve consideration of the future: the worker works so he does not get fired or so that he does not earn a bad reputation. We explore these issues further in Chapter 10. The scenario considered here has no future incorporated into it, so there is no motivation for the worker to exert any effort. He gets his salary whether he exerts any effort or not, and he gets nothing extra for exerting effort, so he exerts no effort. CH. 4: COMPENSATION AND MOTIVATION 33 PERSONNEL ECONOMICS W. NEILSON DO WORKERS ON SALARY WORK LESS THAN THOSE WHO ARE PAID FOR PERFORMANCE? Harry Paarsh of the University of Iowa and Bruce Shearer of Université Laval in Canada compared the productivity of tree planters in British Columbia under two different pay systems.* In one system the planters were paid by the hour, and in the other they were paid by the number of seedlings planted. Their statistical analysis shows that, on average, the piece rate system induced the average worker to plant about 173 more trees per day than the salary system did, an increase of 23%. However, because the piece rate system induced workers to work more quickly, it also induced them to take less care in planting the trees, and only about 109 of the 173 extra trees were planted well. (The issue of piece rates and the quality of performance is explored more thoroughly in Chapter 6.) There has recently been a move in the legislature of British Columbia, Canada, to require that tree-planters be paid a fixed wage rather than a piece rate. Not surprisingly, tree planting firms have resisted this move. * Paarsh, H. and B. Shearer, “Piece Rates, Fixed Wages, and Incentive Effects: Statistical Evidence from Payroll Records,” International Economic Review 41, February 2000, 59-92. QUOTAS In a quota system, a worker must produce a certain amount before he gets any money, and he gets additional money for producing more than the required minimum. So, a quota system is similar to a piece rate system for high amounts of effort. As already discussed, in order to get the efficient amount of effort, the firm should set a piece rate between $220 (to guarantee that the worker exerts 6 units of effort) and $240 (so that the firm does not spend more than marginal net revenue on the 6th unit of output). Taking this as given, all we have left to specify is the quota and the payment made when the quota is reached. First look at a compensation system in which the worker is paid nothing for the first five units of output and $230 per unit for every unit beyond the fifth. So, the quota is 6 units, and the payment for meeting the quota is the same as the payment for additional units, $230. The relevant information for analyzing the worker's response is contained in Table 4.3. The benefit the worker derives from effort is income. When he exerts 6 units of effort marginal income exceeds the marginal cost of effort, as desired. However, at that level of effort, the worker's cost of effort is $720, but his income is only $230, for a net benefit of –$490. If, instead, the worker chooses not to exert any effort at all, his income and effort cost are both zero, for a net benefit of $0. Under this compensation scheme, then, the worker will choose to exert no effort. CH. 4: COMPENSATION AND MOTIVATION 34 PERSONNEL ECONOMICS W. NEILSON TABLE 4.3 Worker costs and benefits under a simple quota system: Quota is 6 units, pay is $230 per unit for the 6th and every additional unit Units of Effort Marginal Marginal effort cost effort cost Income income 0 $0 − $0 − 1 20 20 0