Utility and Production

Microeconomics, also called the science of the markets, is the most productive branch of economics theory and it studies resources allocation and price theory.By economics theory we mean a language or device for deriving and obtaining operationally significant theorems, a way of understanding reality and the behaviour of society. This book actually aims to follow the tradition of other books about the theory of prices, in which prominent authors reflect on the different aspects of pricing in input and output markets. In this book, I have used advanced material for specialised graduate courses in microeconomic theory.

In this section, we begin our study of consumer demand in the context of a market economy referred to as the system in which commodities (goods and services) are available to the consumer for purchase at known prices. Firstly, we study the primal problem of consumer utility maximisation. Secondly, we analyse the dual approach and, fmally, we study indirect utility function, expenditure function, the theoretical restrictions of demand systems, Roy’s Identity, Hotelling’s Theorem, relationships between functions, the Slutsky equation and complementary and substitute goods, and the elasticities of substitution of goods Finally, we offer basic references and further references and readings.

This chapter sets out alternative consumer behaviour models. First, we shall look at the discrete choice model and time allocation models. Next, we shall examine a model synthesising discrete choice and time allocation. Then we shall turn to the characteristics model. This model has been improved by including work and travel time in the utility function and finding a relationship between goods and leisure. Finally, we address a model under conditions of incomplete information and revealed preference theory.

This chapter has been divided into three big sections in which we present the main functional forms of the utility functions: Cobb-Douglas, CES and quasi-linear. Each of these functional forms, and therefore, each section, has been developed according to the exposure in the previous chapter. Thus, firstly, we obtain the Marshallian and Hicksian demand functions in every functional specification, to follow with the indirect and cost utility functions. Moreover, in the Cobb-Douglas functional form, we obtain expenditure-share functions, Engel curves and elasticities. In the CES functional form, we go even further and prove CES demand system restrictions. And finally, in the quasi-linear functional form, a similar exposure to that developed for the CES is presented.

Consumer Marshallian demand functions are obtained by maximising the utility function (objective function) subject to a budget constraint. However, the consumer utility function is not directly observed, while its level of income and the quantities demanded are.

Once we have analysed the consumer equilibrium, we shall put forward the points concerning production, for which a similar method to that employed in chapter 1 will be used. In the first section, a brief introduction to the firm’s conventional theory will be presented. In the second section, we shall study the production possibility set and the existence of production function. In the next section, we shall present the properties of the production function. Then, we shall pose firstly the most genuine profit maximisation problem subject to a technological restriction, to follow with the same problem fixing the costs, that is, the income maximisation problem subject to a level of cost. A particular case of this problem is obtaining a specific level of production, which makes possible the output maximisation subject to a budget constraint on the acquisition of the inputs so that the firm changes only the suitable level of output. We shall pose the loss minimisation problem which is similar to as the profit maximisation problem and which will be presented next fixing the income, that is, the cost minimisation problem subject to a level of income. Finally, we shall study an especially interesting case of this problem, which is that of cost minimisation subject to a level of output; in this case, the firm will change only the level of cost. In the six cases a perfect competition in the input and output markets is assumed, which means that output prices and demand depend on output market conditions, while input prices -rather than the amount-depend on input market conditions.

There are theoretical models of the company other than the neo-classical profit maximiser. Such alternative models are a response to the emergence of companies with more complex aims, the separation between ownership and control and conflict between different interest groups within the company, such as shareholders, management and workers.

As in chapter 2, we present in this chapter the main functional forms in a basically instrumental manner, describing, in two main sections, the Cobb-Douglas and CES functional forms. For such functional forms, the input classic demand, profit and supply functions are obtained from the first and second-order conditions of the profit maximisation problem, as well as the input conditioned demand and cost functions. Moreover, the Hotelling and Shephard theorems are proved and the long-run average and marginal cost curves are obtained. In both functional forms, we perform a duality application at the end.

In order to estimate the production functions of a particular industry the measurements of the inputs and outputs used by its different plants are needed. Unlike the utility function, which is not observed, the production objective function, either output or profit maximisation, or cost minimisation, is directly observed.

A rational individual can choose under conditions of certainty, as we have assumed up until now, or under conditions of uncertainty, as we shall see in this chapter. The key issue is how to order the different alternatives in the presence of uncertainty in accordance with the individual’s preferences. This issue has had three different responses throughout the history of the development of utility. Here they will be summarised in three stages. Later, we shall address a situation in which the company produces under conditions of uncertainty. To end this chapter, we shall set out the main critiques of expected-utility theory and connect such critiques with the theory of limited rationality.