This second chapter on business strategy examines marketing mix decisions. In particular, it focuses on more complex aspects of pricing not covered in the context of Chapter 9 on market structure and pricing. This starts with a discussion of price discrimination, and its various degrees and types. It then moves on to examine multi-product pricing, transfer pricing and dynamic aspects of pricing over the product life cycle (PLC). A detailed discussion of psychological pricing is included, and this covers behavioural aspects not normally considered within the scope of managerial economics, but highly prominent in real-life applications. Advertising decisions are also discussed in the context of the marketing mix, examining the different strategy variables in terms of content and choice of media. Recent trends in strategy related to digital and social media are discussed. There is also a discussion on the controversial topic of the effects of advertising on welfare. Finally, there is an advanced section at the end of the chapter related to optimising the marketing mix, which is mathematical in nature and involves some counterintuitive conclusions.

The Laplace transform is a mathematical operation that converts a function from one domain to another. And why would you want to do that? As you’ll see in this chapter, changing domains can be immensely helpful in extracting information from the mathematical functions and equations that describe the behavior of natural phenomena as well as mechanical and electrical systems. Specifically, when the Laplace transform operates on a function f(t) that depends on the parameter t, the result of the operation is a function F(s) that depends on the parameter s. You’ll learn the meaning of those parameters as well as the details of the mathematical operation that is defined as the Laplace transform in this chapter, and you’ll see why the Fourier transform can be considered to be a special case of the Laplace transform.

In this chapter, we consider a form of low-dimensional structure that arises in many applications in scientific data analysis: we consider datasets consisting of a few basic motifs, repeated at different locations in space and/or time.

This topic examines the various concepts related to the costs of a firm, and in particular relationships between costs and output, and why these relationships are important for managerial decision making. The starting point is a discussion of the types of cost that are relevant, and irrelevant, for decision making. Distinctions are drawn between explicit and implicit costs, historical and current costs, sunk and incremental costs, and private and social costs. Cost relationships with output, and various types of unit cost, are explained, and the reasons for these relationships based on production theory. Distinctions between short-run cost relationships and long-run cost relationships are explained, and factors that can cause costs to change, aided by graphical presentation. Economies and diseconomies of scale, and returns to scale, are explained in cost terms, along with economies of scope. Cost-volume-profit (CVP) analysis is discussed, and its implications for managerial decision making. There is an extensive problem-solving section with many different types of example. More complex CVP problems are presented in case studies, for example battery charging for electric vehicles.

This topic examines how demand relationships can be estimated from empirical data. The whole process of performing an empirical study is explained, starting from model specification, through the collection of data, statistical analysis and interpretation of results. The focus is on statistical analysis and the application of regression analysis using OLS. Different mathematical forms of the regression model are explained, along with the relevant transformations and interpretations. The concept of goodness of fit, and the coefficient of determination, are explained, along with their application in selecting the best model. The advantages of using multiple regression are discussed, and its implementation and interpretation. Analysis of variance (ANOVA) is explained, and how this relates to goodness of fit. The implications of empirical studies are also discussed, and the light they shed on economic theory. More advanced aspects, related to inferential statistics and hypothesis testing, are covered in an appendix, along with the assumptions involved in the classical linear regression model (CLRM) and consequences of the violation of these assumptions.

The value of knowing the Laplace transforms of the basic functions described in the previous chapter is greatly enhanced by certain properties of the Laplace transform. That is because these properties allow you to determine the transform of much more complicated time-domain functions by combining and modifying the transforms of simple functions such as those discussed in .

Magnetic resonance imaging (MRI) is based on the science of nuclear magnetic resonance (NMR). Magnetic resonance states that certain atomic nuclei (such as the protons in water molecules) can absorb and emit radio-frequency energy when placed in an external magnetic field. The emitted energy is proportional to important physical properties of a material such as proton density. Therefore in physics and chemistry, magnetic resonance is an important method for studying structures of chemical substances, and its discoverers were awarded the Nobel Prize in Physics in 1952.

Many problems in structural reliability require the use of a computational platform, such as a finite-element code, to evaluate the limit-state function. Chapter 12 describes the framework for such coupling between a finite-element code and FORM/SORM analysis. The chapter begins with a brief review of the finite-element formulation for inelastic problems. Because FORM requires the gradients of the limit-state function, it is necessary for the finite-element code to compute not only the response vector but also its gradient with respect to selected outcomes of the random variables. The use of finite-differences for this purpose is not practical because of accuracy issues and computational demand. The direct-differentiation method (DDM) presented in this chapter provides an accurate and efficient means for this purpose. It is shown that the DDM requires a linear solution at the convergence of each iterative step in the nonlinear finite-element analysis. Next, a method for discrete representation of random fields of material properties or loads in the context of finite-element analysis is presented. The chapter concludes with a review of alternative approaches for finite-element reliability analysis or uncertainty propagation, including the use of polynomial chaos and various response-surface methods with efficient selection of experimental design points.