In this chapter, we proveKakutani's Fixed Point Theorem, which is an extension of Brouwer's Fixed Point Theoremto correspondences (set-valued mappings). We then define the concept of $\lambda$-discounted equilibrium, and using Kakutani's Fixed Point Theorem we prove that every multiplayer stochastic game admits a stationary $\lambda$-discounted equilibrium, for every discount factor $\lambda \in (0,1]$.

This topic relates to capital budgeting. The starting point is an explanation of why investment analysis is important in managerial economics, and the different types of investment and investment decision. Cash flow analysis and the principles involved in identifying and measuring relevant cash flows is discussed. The concept of risk and types of risk, stand-alone risk, within-firm risk and market risk, are discussed. The security market line (SML), beta coefficients and the capital asset pricing model (CAPM) are explained. The cost of capital is examined, explaining the calculation of the cost of debt, the cost of equity and the weighted average cost of capital (WACC). Methods of evaluation of individual projects are discussed, with a focus on net present value (NPV) and internal rate of return (IRR). There is a discussion of the determination of the optimal capital budget for a firm, in terms of the investment opportunity schedule (IOS) and the marginal cost of capital (MCC), with the distinction between mutually exclusive projects and independent projects. Case studies include two resource-heavy situations: the HS2 rail link and 5G telecommunications.

This final chapter does not cover any new principles; instead it presents case studies that have a huge global impact in terms of both managerial and government decision making. These case studies relate to: the role of big tech firms in the economy and the opportunities and threats that they present; the problems that the Covid-19 pandemic has posed for governments at the global level; and the problems that climate change is posing for both governments and firms, again at the global level. The last two cases involve geopolitical issues that go beyond the scope of the text, but it is important for managers to have a general appreciation of these issues in order to anticipate government policy and respond appropriately. The questions at the end of the case studies are intended to prompt students to utilize principles explained throughout the text to develop an understanding of the relevant issues and determine optimal courses of action.

This topic examines government policy and regulation. The starting point is the objectives of government regulation and market failure. The implications for managerial decision making are outlined. The nature of market failure and its different aspects are discussed. Externalities are discussed, and the policy implications. Public goods, and their nature and policy implications, are examined. Imperfect information and the policy implications are discussed. Transaction costs are discussed. Monopoly and the nature of market power and its consequences are examined. Strategic behaviour, such as collusion, predatory pricing and exclusive dealing, is discussed. The distinction between structural and strategic barriers to entry and their different policy implications is explained. Aspects of new technology are discussed, such as network effects and the ‘winner-takes-most’ phenomenon. Various policy approaches and their costs and benefits are examined. Case studies involve two situations in the UK where governments may have made errors of policy. A final case study relates to the global phenomenon of increasing concentration and its consequences.

Cost estimation – this topic parallels the topic of demand estimation in many ways, in terms of examining the nature of the process involved in cost estimation. Different types of cost scenario are described, explaining the differences between short-run, long-run and learning curve situations. The implications for appropriate model specification are explained, along with the interpretation of different mathematical forms. Cost elasticities and their relationship to returns to scale are discussed. For different scenarios the nature of empirical studies is described, the method of estimation using regression analysis is explained, and the problems of estimation and the implications in terms of managerial decision making are discussed. As with other topics, case studies are important in illustrating the application of principles to real-life situations. Three case studies are presented, all involving recent data from major industries where digital applications are important: banking, airlines and electricity generation.

Managerial economics provides a toolbox for solving problems that managers frequently face. It addresses issues relating to any aspect of decision making that ultimately affects the profit of a firm. Although the general methodology of managerial economics has not changed over the decades, there have been rapid and significant changes in the business environment in the last ten years or so, and three new themes have become increasingly important: digitization; behavioural aspects; and globalization. The first of these developments involves aspects of big data and advanced data analytics, the human-machine interface and the interconnectedness of electronic devices. The second relates to psychological aspects of decision making that cause both consumers and managers to engage in behaviour normally referred to as ‘irrational’. The third development is that improvements in technology relating to digitization have made the business world more interconnected. The text makes heavy use of recent case studies involving these three themes, for example on tech firms, Covid-19 and climate change, so students can see how the tools of managerial economics can be applied in real-life situations.

This chapter examines two fundamental issues regarding the nature of firms. First, why are they necessary in the business environment? Second, what are their objectives? Addressing these issues involves various aspects of theory which are not always associated with economics: transaction cost theory, property rights theory, motivation theory, information theory and agency theory. Regarding the first issue, the necessity for the existence of firms may appear to be self-evident, but on closer examination we can see that many transactions can be performed between individuals without firms existing at all. The problem is that with complex activities the transaction cost of engagement as individuals can be high, whereas internalizing transactions within firms can reduce this cost. The second issue regarding objectives begins with the concept of profit maximization, and then examines the various assumptions underlying it. Various problem areas related to these assumptions are identified, in particular: the existence of agency problems, the measurement of profit, risk and uncertainty, and multi-product firms. The impact of these problems on firms’ objectives is discussed.

This topic examines the nature of game theory, why it is relevant for managerial decision making, and how it determines decisions. The starting point is an explanation of the nature of game theory in terms of the inter-dependence of decision making, and its wide range of applications in real life. Different types of game and their elements are described. The prisoner’s dilemma illustrates some of the counterintuitive aspects of game theory. Static and dynamic games are analysed, and the different types of equilibrium: dominant strategy equilibrium, iterated dominant strategy equilibrium, Nash equilibrium, subgame perfect Nash equilibrium and mixed strategy equilibrium. Cournot, Bertrand and Stackelberg types of oligopoly and their strategy implications are analysed, and comparisons are drawn between them and with perfect competition and monopoly. Games with uncertain outcomes and repeated games are discussed, along with commitment strategies and credibility. Limitations of standard game theory are discussed, such as the existence of bounded rationality and social preferences. Aspects of behavioural game theory are introduced to account for these factors.

This topic examines the nature of factors that affect what people buy and how much. These factors can be categorised into controllable and uncontrollable by managers. The first category relates to internal factors to the firm and involves the marketing mix. The second category relates to external factors in the business environment. A mathematical framework of analysis is required to quantify the effects of the different variables. This involves the use of demand functions or equations, which are often in a linear or power form. The linear form entails the coefficients of explanatory variables representing the marginal effects of those variables. The power form entails the coefficients or powers of the variables representing elasticities. There is a discussion of the factors determining various elasticities and their interpretation. The importance of elasticities in economic analysis is explained, in terms of managerial decision making and forecasting. The focus is on the application of concepts in demand theory to real-life situations, and the performance of the necessary calculations to make decisions and forecasts. Many solved problems are presented as an aid to this process.

This topic examines the nature of market structure, its characteristics and implications for managerial strategy and industrial structure, conduct and performance. The starting point is a discussion of markets and the characteristics that are relevant in terms of determining structure and strategy, in particular pricing. These characteristics relate to number of sellers, type of product, barriers to entry, pricing power and the importance of non-price competition. The four main types of structure, perfect competition, monopoly, monopolistic competition and oligopoly, are described in terms of these characteristics, and in each case both a graphical and algebraic analysis of the equilibrium is presented for both short-run and long-run situations. The different types of structure are compared in terms of price, output, profit, efficiency and welfare. The relationships between structure, conduct and performance are discussed in the light of recent empirical studies, along with some implications for government policy which are examined further in Chapter 14. Case studies illustrate the application of theoretical concepts in practice, particularly in the presence of Covid-19.