In this chapter, we will branch out from sparse signals to a broader class of models: the low-rank matrices. Similar to the problem of recovering sparse signals, we consider how to recover a matrix

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.

Chapter 4 presents the basic formulation of the structural reliability problem. It starts with the so-called R-S problem with R denoting a capacity (resistance, supply, strength, etc.) value and S denoting a measure of the corresponding demand (load, stress, etc.), both modeled as random variables. Solutions in integral form are presented for the failure probability by conditioning on R or S, or using formulations in terms of the safety margin or safety factor that lead to the introduction of the concept of reliability index. Exact solutions are presented for specific distributions of R or S. This allows examination of the so-called tail-sensitivity problem, i.e., the sensitivity of the failure probability to the selected probability distributions. It is shown that small failure probabilities are sensitive to the shape of the selected distributions in the tail. The formulation of the structural reliability problem is then generalized and presented in terms of a limit-state function of basic random variables. Using this formulation, the probability of failure is expressed as a multifold integral over the outcome space of the basic random variables. Descriptions of several example applications of the generalized structural reliability formulation conclude the chapter.

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.

Another useful transform related to the Fourier and Laplace transforms is the Z-transform, which, like the Laplace transform, converts a time-domain function into a frequency-domain function of a generalized complex frequency parameter. But the Z-transform operates on sampled (or “discrete-time”) functions, often called “sequences” while the Laplace transform operates on continuous-time functions. Thus the relationship between the Z-transform and the Laplace transform parallels the relationship between the discrete-time Fourier transform and the continuous-time Fourier transform. Understanding the concepts and mathematics of discrete-time transforms such as the Z-transform is especially important for solving problems and designing devices and systems using digital computers, in which differential equations become difference equations and signals are represented by sequences of data values.