Managerial Economics Unit Titles 1 Introduction to Managerial Economics 2 The Theory of the Consumer 3 The Theory of the Firm 4 Competitive and Monopolistic Markets 5 Strategic Behaviour and Oligopoly 6 Bargaining and Private Information 7 The Optimal Provision of Incentives 8 Financial Investment, Capital Structure and Corporate Control Managerial Economics Unit 1 Introduction to Managerial Economics Contents Page What this unit is about 2 1 Introduction to Managerial Economics 3 2 The Main Concepts in Microeconomics 5 3 Optimisation in Economic Analysis 6 4 Properties of Objective Functions and Feasible Sets 7 5 Properties of Solutions 11 6 Constrained Optimisation: the Lagrange Method 12 7 Comparative Statics and the Envelope Theorem 14 8 Conclusions 17 Revision Exercise 17 References 20 2MANAGERIAL ECONOMICS UNIVERSITY OF LONDON What this unit is about This first unit introduces you to the main methods of microeconomics and manage- rial economics. We see how we can formulate problems of optimisation under constraints, which are central to this course. After explaining the language and the main concepts of microeconomics, we look at the role of optimisation in economic analysis. We derive some general methods for solving optimisation problems and for analysing the characteristics of the solutions. This unit lays the foundations for the analysis in the course. What you will learn • The scope of microeconomics; • The nature of managerial economics; • What is meant by adverse selection; • The meaning of moral hazard; • How to define an economic commodity; • What is a price; • Who are economic agents; • The characteristics of a market; • The meaning and properties of objective function; • The definition and use of a feasible set; • When a solution to an optimisation problem exists; • When is the solution a global optimum; • When is the solution unique; • How to use the Lagrange method; • The nature of Lagrange multipliers; • What is meant by comparative statics, or sensitivity analysis; • What is the envelope theorem.  Readings Gravelle and Rees, Microeconomics, Chapter 1 and Appendices A-G, I and J. Milgrom and Roberts, Economics, Organization and Management, Chapter 1 UNIT ONE 3 C ENTRE FOR FINANCIAL AND MANAGEMENT STUDIES 1 Introduction to Managerial Economics Welcome to this course in managerial economics. In this course we will study the way individual economic units – firms, consumers, managers etc. – should go about making their decisions. In order to address this question, we have to be more precise about what the objectives of individual economic units are: what do they seek to achieve, and what are their aims? We also have to be precise about the context in which the economic units operate: what are the variables under their control? And what constraints do they face? Economic agents do not operate in a social vacuum. A crucial aspect of their behaviour includes their interactions with other agents. On the one hand, this can create new opportunities for individuals. Agents must rely on others in pursuing their own interests. This may be achieved either by explicit co-operation or by their understanding of the other agents’ selfish pursuit of their own best interests. On the other hand, the need to interact with other agents can place severe constraints on individual agents’ behaviour. They will not always be able to get their own way and will be forced to accommodate the other agents’ needs. Sometimes, economic agents may try to behave in a strategic fashion. They will try to anticipate the others’ reactions to their own actions, and will therefore endeavour to make decisions which turn to their best advantage, given that their actions could influence the other agents’ choices and behaviour. One way agents can achieve this aim is by entering into some form of contract, which – explicitly or implicitly – takes into account other agents’ motivations and seeks to exploit their economic incentives in order to induce them to perform. In general, thus, we have to examine: • how individual agents behave; • what is their motivation; • what are the constraints they face; and • how they interact with other agents in the economy. An important issue in managerial economics arises when agents have imperfect knowledge of the characteristics of the other agents (adverse selection), or when they cannot compel the other agents to behave in a given way (moral hazard). For instance, an insurance company may be unable to observe the exact class of risk of its prospective customers. If it were to offer a standard contract to all its prospective clients, high-risk individuals might form a disproportionate number of its customers. This would be a case of adverse selection. A possible way out is for the insurance company to offer a range of different contracts to its customers, with different premia and penalty structures. If the range of contracts has been optimally designed, high-risk customers will prefer one type of contract, and low-risk customers another. The insurance company will therefore be able to separate high- from low-risk customers by offering a range of contracts, and by letting customers choose. Another example might be an employer who wants to elicit a high level of effort from its employees. This would be a case of moral hazard. The employer could achieve its aim by creating suitable incentives – in the form of performance-related pay, appropriate promotion schemes, etc. – which reward higher effort. 4MANAGERIAL ECONOMICS UNIVERSITY OF LONDON The approach to managerial economics which we study in this course relies very closely on microeconomic analysis. Indeed, we could define managerial economics as that branch of microeconomics which helps develop a rational decision making approach in management. We deal with individual behaviour and motivation, explore how agents may interact with each other, and analyse how best they could design contracts in order to elicit the desired behaviour from other agents. So, for instance, we look at the optimal production decisions of firms, or at the design of labour contracts between an employer and its employees. 1.1 The Structure of this Course The outline of this course is as follows. This unit illustrates the main ideas in micro- economics and managerial economics and reviews the theory of mathematical optimisation which we use in this course. Unit 2 deals with the theory of the consumer. We look at how rational agents can maximise their individual welfare, given the constraints they face. Unit 3 presents the theory of the firm. We analyse the structure of technology in the short and in the long run, and consider the optimal output supply by firms. In the next units we move on from individual consumers and firms to consider how they interact in markets. In Unit 4 we look at competitive markets and monopoly, and in Unit 5 we explore oligopolistic markets. In dealing with the latter, we make extensive use of game theory, which studies how agents can behave strategically. Unit 6 considers the important issue of how agents should behave when they have imperfect knowledge of the characteristics of other agents or of how they will behave. Unit 7 examines how agents can devise economic mecha- nisms to elicit information from other agents, and how they can design optimal contracts which induce the other agents to provide the required incentives. Unit 8 brings together the methods of the previous units and applies them to issues in financial investment, capital structure and corporate control. You have been given the following textbooks, which constitute the main readings for this course: Hugh Gravelle and Ray Rees (2004) Microeconomics, 3rd edition, Prentice-Hall, Harlow; Paul Milgrom and John Roberts (1992) Economics, Organization and Management, Prentice-Hall, Inc., Englewood Cliffs (New Jersey). Gravelle and Rees cover all the main topics in microeconomics, including the more recent and advanced topics in the economics of imperfect information and incen- tives. Milgrom and Roberts deal specifically with the issues of optimal organisation, co-ordination, motivation, and incentives that are crucial for modern managerial economics. You will see that Gravelle-Rees and Milgrom-Roberts are very different in their approach: the first one is more formal in its arguments and more mathemati- cal, whereas the second makes more use of examples and applications. The two textbooks complement each other quite well, and by studying them both you will experience a useful range of approaches to microeconomics and managerial eco- nomics  It is useful at this point for you to stop and read the first chapter, ‘Does Organization Matter?’ in Milgrom and Roberts. This chapter is an introduction to the problems of business organisation, and explains why the compensation and owner- UNIT ONE 5 C ENTRE FOR FINANCIAL AND MANAGEMENT STUDIES ship structure of firms can be an important determinant of their performance. In this chapter, the authors clearly illustrate the importance of economic decisions in business organisations. They introduce a number of useful concepts: • co-ordination within a company and with outside suppliers; • performance-related pay systems; • the ratchet effect; • the role of information; and • incentives, which will be fundamental to our analysis in the later units of this course. 2 The Main Concepts in Microeconomics This section introduces the main ideas and concepts in microeconomics. The basic notion is that of a commodity, which constitutes the object of production and exchange in economics. The concept of commodity should be interpreted in a broad sense, including both goods and services. It is important to note that the exact definition of commodity must specify its physical characteristics, the location where the commodity is available and the date when it is made available. Thus, a commod- ity could be a car, of a particular make and type, in Paris, on a given date. The same car, on the same date, but in Mexico City, should be regarded as a different com- modity. Another example of a commodity may be given by the consultancy services provided by a financial analyst, with a given educational and professional back- ground, in Hong Kong, on a given date. The consultancy services provided by that same analyst in Hong Kong, but on a different date, should be regarded as a different commodity. The second main concept in microeconomics is price. The price of commodities measures the terms at which the commodities can be traded with one another. It is customary to express prices in terms of monetary units of accounts, such as Singa- pore dollars or South African rands. In microeconomics, the main notion is that of relative price between two commodities – let’s call them commodity A and com- modity B. The relative price between A and B is the number of units of B which have to be given up in order to purchase one unit of A. For example, if the monetary price of commodity A is 200 Singapore dollars, and the monetary price of commod- ity B is 50 Singapore dollars, then the relative price of A in terms of B is 4, since we have to give up 4 units of B in order to purchase one unit of A. An important assumption which is often made in microeconomics is that agents do not suffer from money illusion: if all monetary prices were suddenly to double, the real decisions of agents would be unaffected. This is because the relative prices between commodities would still be the same, reflecting the fact that the terms at which commodities are traded with one another have not changed. The third main concept is that of economic agents. In traditional microeconomics, these are usually classified as consumers and firms. We shall analyse the behaviour of consumers in Unit 2, and the behaviour of firms in Unit 3. Consumers must allocate their limited resources among the different commodities they can purchase, and firms employ inputs such as capital and labour to produce output. In the 6MANAGERIAL ECONOMICS UNIVERSITY OF LONDON traditional analysis, firms are seen as individual decision makers. In the more recent microeconomic theory and in managerial economics, however, it is usually acknowl- edged that firms are complex organisations, and that the individual agents attached to a firm may each have different goals in mind. It is therefore necessary to explore how firms behave, given the possible conflicts of interest between the members of the organisation. We address these and related issues in Units 6, 7 and 8. The fourth main concept is that of a market. By this we mean the place where economic commodities are traded. It is important to note that a market is not necessarily a formal market place. Trade occurs whenever agents engage in an exchange of commodities, irrespective of whether this exchange is regulated or not. Also, trade does not require exchange of money: Barter, for instance, is a form of trade. An important issue in microeconomics is to analyse how markets work, and how agents behave in markets. In markets with a large number of participants, individuals often have very little power to alter the conditions of exchange. A small shopkeeper in a large town may have limited control over the prices charged for its goods, because higher prices could mean losing most of its customers: they could just walk away and buy from the rival shops. By contrast, the only shopkeeper in a remote village could wield some market power, in the sense of enjoying some latitude in setting prices. Its customers would not be able easily to walk away from the shop and purchase the commodities somewhere else, if no rival shop were available. An important component of this course is the analysis of how markets work, and how agents can behave strategically in a market setting. We explore market behaviour in Units 4 and 5.  Please now stop and read pages 1-6 from Gravelle and Rees, Chapter 1, section A. The textbook introduces the main concepts in microeconomic analysis (com- modities, price, economic agents and markets), and illustrates them by means of examples. We shall constantly be referring to these concepts in this course, so it is essential that you are thoroughly familiar with them. In addition, I should like you to pay special attention to the discussion of markets and of economic agents. 3 Optimisation in Economic Analysis In microeconomics, the assumption is often made that agents behave in a rational fashion. This means that, when making their decisions, they consider all the possible alternative courses of action, rank them according to their preferences, and finally choose the action which they prefer best. Thus, a consumer seeking to maximise her utility given her total income will consider all the possible uses of her income, will rank these uses according to the utility she derives from each of them, and finally will choose the use which yields the highest utility (Unit 2). Similarly, a firm might seek to maximise its profit given technology and input prices and given a demand curve for its output or output price, and will decide on the levels of labour and capital it employs (Units 3 and 4). Formally, the process of choice can be modelled as an optimisation problem faced by the economic agent. There is a well-defined objective function that the agent seeks to maximise by optimal choice of the decision variables. The context in which choices take place is modelled as a set of constraints on individual behaviour. Thus, the objective function of consumers is their utility function, which they seek to UNIT ONE 7 C ENTRE FOR FINANCIAL AND MANAGEMENT STUDIES maximise; their choice variables are the quantities of the various commodities which are consumed, and their choice must satisfy the budget constraint which requires that their expenditure cannot exceed their total income. The objective function of the firm is the value of its profits; its choice variables are the quantity of inputs employed (capital and labour), the output supplied and the price of its output (unless the firm is operating under perfect competition), and its constraints are the level of technology and the demand for its output by consumers. The general method of microeconomics is therefore to model individual choice as a problem of optimisation under constraints. This approach is very general, and it is easily extended to the more recent topics in microeconomics and managerial economics, such as the economics of imperfect information. Consider, for example, the case of an employer who wants to elicit a higher level of effort from its employ- ees. Its objective function are its profits, its choice variables the remuneration system offered to its employees, and its constraints the response of its employees (who can be thought of as rational and optimising agents in their turn, seeking to maximise their own welfare given the remuneration scheme offered). The problem can be fairly complicated, but the basic structure is quite straightforward, and always involves optimisation under constraints. Note that optimisation may involve either a maximisation or a minimisation problem. Examples of the latter case are the minimisation of costs of a firm, or the minimisa- tion of the risk faced by a financial investor. In this course we shall encounter many examples of both maximisation and minimisation. The same methods can be applied to both cases.  It is now a good moment to stop and read pages 6-11 from Gravelle and Rees, Chapter 1, sections A and B. Note how these authors pay special attention to the assumption of rationality in economics. Please read these sections carefully, making notes on the important points as you read. Read also with attention the analysis of the economic and social framework of choice theory in section B. The structure of an optimisation problem in economics is explained by Gravelle and Rees in Appendix A, pages 657–59, and you should read these pages as well. Note in particular how the set of constraints is described by Gravelle and Rees as the feasible set. Pay special attention also to the definitions of choice variables and of the objective function, and to the economic examples which are provided. 4 Properties of Objective Functions and Feasible Sets In the previous section, we saw that the general method of microeconomics is to model the choice problem as a programme of optimisation under constraints. It is therefore necessary to be able to establish whether the problem we are considering does have a solution, whether the solution is unique, and how the characteristics of the solution depend on the parameters of the problem. For instance, when we look at consumption behaviour, it is important to establish whether there is a combination of commodities which maximises the utility of the consumer (existence of the solution), and whether other combinations exist which yield the same level of utility so that the 8MANAGERIAL ECONOMICS UNIVERSITY OF LONDON consumer is indifferent between them (uniqueness of the solution). Even without knowing the exact functions involved in the optimisation problem, it is usually possible to say something about the solution. The reason for this is that economic theory suggests that the functional forms in a microeconomic decision problem must satisfy some given properties, and this in turn could lead to guaranteeing that the problem has a unique solution with some important additional characteristics. The main properties we are looking for in the solution to a microeconomic optimisa- tion problem are: • whether it exists; • whether it is a global solution; • whether it is unique.  These properties are explained in the textbook by Gravelle and Rees. Please stop now and read the relevant pages in the book before continuing with the rest of this text. These are pages 660-62 from Appendix B; be sure to make careful notes on these properties as you read this section. Existence of a solution is clearly a crucial feature of the optimisation problem, yet it cannot always be taken for granted. Some mathematical problems simply do not have a solution. Hence, when setting up an economic problem we must always check whether a solution exists. The good news is that sometimes the properties of the objective function and of the constraints do ensure that a solution exists (this will be discussed further in the next section of this unit). But even when a solution exists, we cannot always be sure that it is a global solution, i.e. that it achieves a maximum (or a minimum, depending on the problem) over the whole range of feasible values for the decision variables. Figure B.1 in Gravelle and Rees shows an example of a function f(x) which has a local, but not a global optimum at x**. When solving an optimisation problem, it is therefore necessary to check that the solution is a global, rather than simply a local solution to the problem. Finally, it is important to establish whether the solution to the optimisation problem is unique, or whether there could exist several choices of the decision variables which yield the same value of the objective function, and therefore are equivalent for the optimising agent. Although there are no theoretical problems in principle with the latter case, i.e. when there are multiple solutions, there could be difficulties when it comes to predicting the behaviour of the economic agents. In fact, if the agent is indifferent as between a number of alternative courses of action, it could be impossi- ble to predict with certainty what the outcome of its actions will be. Sometimes it is possible to anticipate that agents will choose one of these actions over the others – for instance, in problems which involve co-ordination by many agents, there could be a focal equilibrium, that is, an action to which all agents co-ordinate their behaviour. Thus, when driving a car, keeping to the right side of the road is the focal equilibrium in France, whereas keeping to the left is the focal equilibrium in the UK. In a number of cases, however, it could be quite difficult to predict the action of agents when there are multiple solutions to the individual optimisation problem. We are going to look at the issues of existence, unicity, and the global property of solutions in the next section. We will see there that, for a large class of problems in [...]... based on the Lagrange function is explained by Gravelle and Rees, pages 679-84 Please read these pages now CENTRE FOR FINANCIAL AND MANAGEMENT STUDIES 14 MANAGERIAL ECONOMICS 7 Comparative Statics and the Envelope Theorem In microeconomics and managerial economics there are two main questions to be addressed when we regard economic choice as a problem of constrained optimisation The first question is:... these are not compulsory reading 8 Conclusions This unit introduces you to the main methods of microeconomics and managerial economics You should now see how to formulate problems of optimisation under constraints, which are central to this course After explaining the language and the main concepts of microeconomics, we looked at the role of optimisation in economic analysis We derived some general methods... + ) + u* =A m ( + ) m + p1 p2 +1 m + + 1 + (1.30a) (1.30b) 1 p1 p2 CENTRE FOR FINANCIAL AND MANAGEMENT STUDIES (1.30c) 20 MANAGERIAL ECONOMICS References Gravelle, Hugh and Ray Rees (2004) Microeconomics, 3rd edition, Prentice-Hall, Harlow Milgrom, Paul and John Roberts (1992) Economics, Organization and Management, Prentice-Hall, Inc: Englewood Cliffs (New Jersey) UNIVERSITY OF LONDON ... or if the commodities prices change? This question is clearly important for our analysis The present section explains how we can address this question, for a fairly general problem in microeconomics or managerial economics The remainder of the course will see many applications of these methods to a variety of examples Suppose that the objective function is: max (x1, x2) y = u(x1, x2) (1.7) where the... problem explicitly and check directly whether a solution exists, whether it is a global rather than a local optimum and whether it is unique Fortunately, in a large number of problems in microeconomics and in managerial economics all the above properties hold We can therefore be confident about the solutions having the desired properties This is a good moment to stop and read Gravelle and Rees, Appendices... further explanations and examples of the above properties It is often possible to verify that these properties are actually satisfied in a large number of problems analysed in applied microeconomics and managerial economics This turns out to be quite useful, since in these cases we can be more precise about the nature of the solutions to the optimisation problem We shall consider this point more fully... (1.10c) to have: 2 u 2 u dx2 x1 x2 p1d = dp1 (1.13a) 2 u u dx1 + 2 dx2 x1 x 2 x2 p2 d = dp2 (1.13b) 2 x1 dx1 + 2 p1dx1 p2 dx2 = x1dp1 + x2 dp2 dm CENTRE FOR FINANCIAL AND MANAGEMENT STUDIES (1.13c) 16 MANAGERIAL ECONOMICS The system (1.13a)-(1.13b) above can be solved by substitution to obtain the desired derivatives For instance, if we are interested in how the quantities consumed x1 and x x x2 change as... (a) gives an example of a concave function, whereas part (b) displays a function which is not concave FIGURE 1.2 CONCAVITY f(x) g(x) x o o (a) CENTRE FOR FINANCIAL AND MANAGEMENT STUDIES x (b) x 10 MANAGERIAL ECONOMICS Finally, part (a) of Figure 1.3 shows a quasi-concave function (note that now we have two choice variables, x1 and x2), while part (b) displays a function which is not quasi-concave FIGURE... Find how the optimal values for x1 and x2 vary with p1, p2 and m (c) Find how the maximised value of the objective function varies with p1, p2 and m CENTRE FOR FINANCIAL AND MANAGEMENT STUDIES 18 MANAGERIAL ECONOMICS Solution to the Revision Exercise (a) Write the Lagrangean as: L = Ax1 x2 + (m p1 x1 (1.20) p2 x 2 ) The first-order conditions are: ( x1 ): A x1 1 x2 = p1 ( x2 ): A x1 x2 1 = p2 (1.21a)... authors deal with the topics presented above, and present proofs for the theorems They also discuss the important issue of interior versus boundary CENTRE FOR FINANCIAL AND MANAGEMENT STUDIES 12 MANAGERIAL ECONOMICS optima The latter occur when the optimum lies on the boundary of the feasible set – i.e., on one of the constraints You should read carefully what Gravelle and Rees have to say on this . Control Managerial Economics Unit 1 Introduction to Managerial Economics Contents Page What this unit is about 2 1 Introduction to Managerial Economics 3 2 The Main Concepts in Microeconomics. effort. 4MANAGERIAL ECONOMICS UNIVERSITY OF LONDON The approach to managerial economics which we study in this course relies very closely on microeconomic analysis. Indeed, we could define managerial. 679-84. Please read these pages now. 14 MANAGERIAL ECONOMICS UNIVERSITY OF LONDON 7 Comparative Statics and the Envelope Theorem In microeconomics and managerial economics there are two main questions