Film series 1- Mathematical Review In this programme we review some basic ideas in mathematics. You may be familiar with these ideas but you need to be sure about them, as they are fundamental building blocks for what is to follow in a course of mathematics for economists. This programme will review the foundation so that we may develop our understanding of more advanced concepts. But even with just these ideas you will gain some insights into important economic concepts. How do people make choices when they are unsure about the outcome of their decisions? How do governments make decisions about which road-building schemes are worthwhile?

Film series 2 - Linear Equations When we go shopping, we make choices. There are many goods and services competing for our attention – many companies competing for our money. The economist’s perspective in understanding the decisions of consumers is that people bring their preferences to the marketplace and make purchases that will maximise their sense of satisfaction, or utility. But we have to buy subject to a constraint. We are constrained by a limited income and by the price we have to pay to make any purchase. This film uses linear equations to explore constraints in markets.

Film series 3 - Mathematics of Finance and Growth In this programme we examine many circumstances where it is crucial to understand what is happening over a substantial time period. Individuals sometimes have to save for some while in order to finance large expenditures. How quickly do savings grow if the money is saved? Businesses frequently take decisions on whether it is worth borrowing in order to refurbish or to expand. Sometimes people are not incurring debt but trying to get out of it. How do people pay back to banks and building societies the large sums they have borrowed to buy a house? We see how the mathematics of finance can help to give an insight into these questions.

Film series 4 - Linear Programming In the first part of this programme we illustrate how two businesses can make decisions that help maximise profits as a result of using the mathematical technique of linear programming. In the first part we illustrate how two businesses can make decisions that help maximise profits as a result of using the mathematical technique of linear programming. Belgian chocolates are famous the world over. But there are many different kinds of chocolate that can be made. How can the producer pick the best combinations within the various constraints imposed on the business? We see how the mathematics of linear programming can help to give an insight into this question. The second example examines decisions in agriculture. Should a tomato farmer diversify and produce another product entirely? This will depend upon a whole series of factors, including the time it will take to care for a different crop, the limits of greenhouse space and the commitment he has already to supply tomatoes to retail outlets. The use of the mathematical principles of linear programming will enable us to understand the answer to this. In the second part of the film we begin to examine non-linear mathematical techniques. We begin with competitive industries. We will see that many industries have supply and demand curves that cannot realistically be thought of as linear. How can we forecast the price and output of such industries? Then we turn to labour markets. It is often the case here too that we will need non-linear functions to find employment levels and wage rates. The mathematics of non-linear equations will help us arrive at a better understanding of these and related issues that are raised in this film. In the last section of the film we introduce a problem for firms that we solve by differential calculus. We look here at industries where firms have more power to set prices. We then see that calculus can help understand macro issues also. In this case we examine consumption and savings behaviour.

Film series 5 - Differential Equations In the first part of this programme we begin by asking whether American universities are the right size. Would it be cheaper to educate students if universities were larger? We use differentiation to discover the answer. Next we examine what happens to the costs of providing floor space as hotel buildings increase in size, showing how the use of differentiation can help us make sense of these cost decisions that are being made daily in this and other industries all around the world. We then look at supermarkets. Why does the mark-up on products vary so much between the different goods they sell? Why is the size of the mark-up so similar as between the competitors? In the second part of our film we think about the price of wine and meals in a French restaurant to see a simple example of partial differentiation at work. We then look at diversified industries to see how partial differentiation helps us understand the relationship between price, output and profit in multi product firms, where pricing decisions can be more complex than in single product firms. In the final section we discover that integration is a technique that enables us to throw light on one of the most famous paradoxes in economics – the diamond/water paradox. A commodity like diamonds has relatively little usefulness. But it sells for far more than water – a commodity so useful that it can be the difference between life and death. We shall find that integration can help us to resolve this apparent contradiction.