This chapter lies the microeconomic foundation to understand consumer demand in the cultural sector. We start out by outlining the assumptions that underlie the economic analysis of consumer choice, followed by a breakdown of how to measure the utility of the consumer, as well as how the consumer maximizes utility. We also show how to derive demand and supply curves which are essential to analyze the market powers at play in the cultural sector. Finally, we will show how to use the market demand and supply curves to determine the market price.

This chapter deals with one of the most important aspects of systems modeling, namely the arrival process. When we say “arrival process” we are referring to the sequence of arrivals into the system. The most widely used arrival process model is the Poisson process. This chapter defines the Poisson process and highlights its properties. Before we dive into the Poisson process, it will be helpful to review the Exponential distribution, which is closely related to the Poisson process.

Richly illustrated in full colour and packed with examples from every major continent and wetland type, this third edition has been completely rewritten to provide undergraduates with a thoroughly accessible introduction to the basic principles. It divides the world’s wetlands into six principal types and presents six major causal environmental factors, arranged by importance and illustrated with clear examples, making it easy for instructors to plan tailored lectures and field trips and avoid overwhelming students with unnecessary detail. It retains its rigour for more advanced students, with sections on research methods and experiments, and over a thousand classic and contemporary references. Each chapter ends with questions that review the content covered and encourage further investigation. With expanded sections on topical issues such as sea level rise, eutrophication, facilitation and the latest approaches to restoration and conservation, the new edition of this prize-winning textbook is a vital resource for wetland ecology courses.

This chapter begins our study of Markov chains, specifically discrete-time Markov chains. In this chapter and the next, we limit our discussion to Markov chains with a finite number of states. Our focus in this chapter will be on understanding how to obtain the limiting distribution for a Markov chain.

Richly illustrated in full colour and packed with examples from every major continent and wetland type, this third edition has been completely rewritten to provide undergraduates with a thoroughly accessible introduction to the basic principles. It divides the world’s wetlands into six principal types and presents six major causal environmental factors, arranged by importance and illustrated with clear examples, making it easy for instructors to plan tailored lectures and field trips and avoid overwhelming students with unnecessary detail. It retains its rigour for more advanced students, with sections on research methods and experiments, and over a thousand classic and contemporary references. Each chapter ends with questions that review the content covered and encourage further investigation. With expanded sections on topical issues such as sea level rise, eutrophication, facilitation and the latest approaches to restoration and conservation, the new edition of this prize-winning textbook is a vital resource for wetland ecology courses.

In the last two chapters we studied many tail bounds, including those from Markov, Chebyshev, Chernoff and Hoeffding. We also studied a tail approximation based on the Central Limit Theorem (CLT). In this chapter we will apply these bounds and approximations to an important problem in computer science: the design of hashing algorithms. In fact, hashing is closely related to the balls-and-bins problem that we recently studied in Chapter 19.

In this chapter, we examine and analyze private support for the arts, mostly in the form of household, corporate, foundation, and other donations. In addition to this, we also explore the role of “indirect” government support in the form of tax forgiveness for private donors. We compare arts support across countries and explain the vastly different levels of private support. Additionally, we discuss the concept of nonmonetary private donations, often in the form of works of art. Finally, we outline the advantages and disadvantages of private and/or public support.

This part of the book is devoted to randomized algorithms. A randomized algorithm is simply an algorithm that uses a source of random bits, allowing it to make random moves. Randomized algorithms are extremely popular in computer science because (1) they are highly efficient (have low runtimes) on every input, and (2) they are often quite simple.

In this chapter, we investigate the economic choices – especially the price-output choices – made by performing arts firms. We cover the factors that help in determining the optimal price–output combination for performing arts firms. Furthermore, we discuss a multitude of market types and how these market types influence the behavior of performing arts firms. We also present the objectives of the performing arts firms, which depend on whether they are in the commercial or the not-for-profit sector of the economy. Ultimately, we end up with a model for the performing arts firm that is able to predict both ticket prices and length of season.

In the previous chapter, we studied individual continuous random variables. We now move on to discussing multiple random variables, which may or may not be independent of each other. Just as in Chapter 3 we used a joint probability mass function (p.m.f.), we now introduce the continuous counterpart, the joint probability density function (joint p.d.f.). We will use the joint p.d.f. to answer questions about the expected value of one random variable, given some information about the other random variable.

Who engages with art? This chapter outlines methods for art companies to gain a better understanding of the socioeconomic background of their audience. We also present a cross-country comparison on participation rates in the arts to illustrate the patterns of cultural consumption around the world. To get a better understanding of the audience characteristics, this chapter also summarizes the findings of several participation studies on the socioeconomic characteristics of art attenders across countries and over time.

This chapter presents the importance of productivity in the growth of the cultural sector. We describe the concept of productivity lag, as explained by Baumol and Bowen, followed by a more formal algebraic analysis of the effects of productivity lag. In addition to a theoretical approach, we provide historical evidence on the productivity lag and its consequences. We also turn to a discussion of the forces that countervail productivity lag. Finally, we outline evidence that growth of the earnings gap has been forestalled by artistic innovation and an increasing artistic deficit.

This final part of the book is devoted to the topic of Markov chains. Markov chains are an extremely powerful tool used to model problems in computer science, statistics, physics, biology, and business – you name it! They are used extensively in AI/machine learning, computer science theory, and in all areas of computer system modeling (analysis of networking protocols, memory management protocols, server performance, capacity provisioning, disk protocols, etc.). Markov chains are also very common in operations research, including supply chain, call center, and inventory management.

We have studied several common continuous distributions: the Uniform, the Exponential, and the Normal. However, if we turn to computer science quantities, such as file sizes, job CPU requirements, IP flow times, and so on, we find that none of these are well represented by the continuous distributions that we’ve studied so far. To understand the type of distributions that come up in computer science, it’s useful to start with a story.