Managerial economics doc

manage-What you will learn • The scope of microeconomics; • The nature of managerial economics; • What is meant by adverse selection; • The meaning of moral hazard; • How to define an ec

Unit Titles

1 Introduction to Managerial Economics

2 The Theory of the Consumer

3 The Theory of the Firm

4 Competitive and Monopolistic Markets

5 Strategic Behaviour and Oligopoly

6 Bargaining and Private Information

7 The Optimal Provision of Incentives

8 Financial Investment, Capital Structure and Corporate Control

Unit 1 Introduction to Managerial Economics

What this unit is about

This first unit introduces you to the main methods of microeconomics and rial economics We see how we can formulate problems of optimisation underconstraints, which are central to this course After explaining the language and themain concepts of microeconomics, we look at the role of optimisation in economicanalysis We derive some general methods for solving optimisation problems and foranalysing the characteristics of the solutions This unit lays the foundations for theanalysis in the course

manage-What you will learn

• The scope of microeconomics;

• The nature of managerial economics;

• What is meant by adverse selection;

• The meaning of moral hazard;

• How to define an economic commodity;

• What is a price;

• Who are economic agents;

• The characteristics of a market;

• The meaning and properties of objective function;

• The definition and use of a feasible set;

• When a solution to an optimisation problem exists;

• When is the solution a global optimum;

• When is the solution unique;

• How to use the Lagrange method;

• The nature of Lagrange multipliers;

• What is meant by comparative statics, or sensitivity analysis;

• What is the envelope theorem

Readings

Gravelle and Rees, Microeconomics, Chapter 1 and Appendices A-G, I and J.

Milgrom and Roberts, Economics, Organization and Management, Chapter 1

1 Introduction to Managerial Economics

Welcome to this course in managerial economics In this course we will study the

way individual economic units – firms, consumers, managers etc – should go about

making their decisions In order to address this question, we have to be more preciseabout what the objectives of individual economic units are: what do they seek toachieve, and what are their aims? We also have to be precise about the context inwhich the economic units operate: what are the variables under their control? Andwhat constraints do they face?

Economic agents do not operate in a social vacuum A crucial aspect of their

behaviour includes their interactions with other agents On the one hand, this cancreate new opportunities for individuals Agents must rely on others in pursuing theirown interests This may be achieved either by explicit co-operation or by their

understanding of the other agents’ selfish pursuit of their own best interests

On the other hand, the need to interact with other agents can place severe constraints

on individual agents’ behaviour They will not always be able to get their own wayand will be forced to accommodate the other agents’ needs Sometimes, economicagents may try to behave in a strategic fashion They will try to anticipate the others’reactions to their own actions, and will therefore endeavour to make decisions whichturn to their best advantage, given that their actions could influence the other agents’choices and behaviour One way agents can achieve this aim is by entering into someform of contract, which – explicitly or implicitly – takes into account other agents’motivations and seeks to exploit their economic incentives in order to induce them toperform

In general, thus, we have to examine:

• how individual agents behave;

• what is their motivation;

• what are the constraints they face; and

• how they interact with other agents in the economy

An important issue in managerial economics arises when agents have imperfect

knowledge of the characteristics of the other agents (adverse selection), or when they cannot compel the other agents to behave in a given way (moral hazard) For

instance, an insurance company may be unable to observe the exact class of risk ofits prospective customers If it were to offer a standard contract to all its prospectiveclients, high-risk individuals might form a disproportionate number of its customers

This would be a case of adverse selection A possible way out is for the insurance

company to offer a range of different contracts to its customers, with different

premia and penalty structures If the range of contracts has been optimally designed,high-risk customers will prefer one type of contract, and low-risk customers another.The insurance company will therefore be able to separate high- from low-risk

customers by offering a range of contracts, and by letting customers choose

Another example might be an employer who wants to elicit a high level of effort

from its employees This would be a case of moral hazard The employer could

achieve its aim by creating suitable incentives – in the form of performance-related

pay, appropriate promotion schemes, etc – which reward higher effort.

The approach to managerial economics which we study in this course relies veryclosely on microeconomic analysis Indeed, we could define managerial economics

as that branch of microeconomics which helps develop a rational decision making approach in management We deal with individual behaviour and motivation,

explore how agents may interact with each other, and analyse how best they coulddesign contracts in order to elicit the desired behaviour from other agents So, forinstance, we look at the optimal production decisions of firms, or at the design oflabour contracts between an employer and its employees

1.1 The Structure of this Course

The outline of this course is as follows This unit illustrates the main ideas in economics and managerial economics and reviews the theory of mathematical

micro-optimisation which we use in this course Unit 2 deals with the theory of the

consumer We look at how rational agents can maximise their individual welfare,given the constraints they face Unit 3 presents the theory of the firm We analyse thestructure of technology in the short and in the long run, and consider the optimaloutput supply by firms In the next units we move on from individual consumers andfirms to consider how they interact in markets In Unit 4 we look at competitivemarkets and monopoly, and in Unit 5 we explore oligopolistic markets In dealingwith the latter, we make extensive use of game theory, which studies how agents canbehave strategically Unit 6 considers the important issue of how agents shouldbehave when they have imperfect knowledge of the characteristics of other agents or

of how they will behave Unit 7 examines how agents can devise economic nisms to elicit information from other agents, and how they can design optimalcontracts which induce the other agents to provide the required incentives Unit 8brings together the methods of the previous units and applies them to issues in

mecha-financial investment, capital structure and corporate control

You have been given the following textbooks, which constitute the main readings forthis course:

Hugh Gravelle and Ray Rees (2004) Microeconomics, 3rd edition, Prentice-Hall,

Harlow;

Paul Milgrom and John Roberts (1992) Economics, Organization and Management,

Prentice-Hall, Inc., Englewood Cliffs (New Jersey)

Gravelle and Rees cover all the main topics in microeconomics, including the morerecent and advanced topics in the economics of imperfect information and incen-tives Milgrom and Roberts deal specifically with the issues of optimal organisation,co-ordination, motivation, and incentives that are crucial for modern managerialeconomics You will see that Gravelle-Rees and Milgrom-Roberts are very different

in their approach: the first one is more formal in its arguments and more cal, whereas the second makes more use of examples and applications The twotextbooks complement each other quite well, and by studying them both you willexperience a useful range of approaches to microeconomics and managerial eco-nomics

mathemati-
It is useful at this point for you to stop and read the first chapter, ‘Does

Organization Matter?’ in Milgrom and Roberts This chapter is an introduction to theproblems of business organisation, and explains why the compensation and owner-

ship structure of firms can be an important determinant of their performance In thischapter, the authors clearly illustrate the importance of economic decisions in

business organisations They introduce a number of useful concepts:

• co-ordination within a company and with outside suppliers;

• performance-related pay systems;

• the ratchet effect;

• the role of information; and

• incentives,

which will be fundamental to our analysis in the later units of this course

2 The Main Concepts in Microeconomics

This section introduces the main ideas and concepts in microeconomics The basic

notion is that of a commodity, which constitutes the object of production and

exchange in economics The concept of commodity should be interpreted in a broadsense, including both goods and services It is important to note that the exact

definition of commodity must specify its physical characteristics, the location wherethe commodity is available and the date when it is made available Thus, a commod-ity could be a car, of a particular make and type, in Paris, on a given date The samecar, on the same date, but in Mexico City, should be regarded as a different com-modity

Another example of a commodity may be given by the consultancy services

provided by a financial analyst, with a given educational and professional ground, in Hong Kong, on a given date The consultancy services provided by thatsame analyst in Hong Kong, but on a different date, should be regarded as a differentcommodity

back-The second main concept in microeconomics is price back-The price of commodities

measures the terms at which the commodities can be traded with one another It iscustomary to express prices in terms of monetary units of accounts, such as Singa-pore dollars or South African rands In microeconomics, the main notion is that of

relative price between two commodities – let’s call them commodity A and

com-modity B The relative price between A and B is the number of units of B whichhave to be given up in order to purchase one unit of A For example, if the monetaryprice of commodity A is 200 Singapore dollars, and the monetary price of commod-ity B is 50 Singapore dollars, then the relative price of A in terms of B is 4, since wehave to give up 4 units of B in order to purchase one unit of A

An important assumption which is often made in microeconomics is that agents do

not suffer from money illusion: if all monetary prices were suddenly to double, the real decisions of agents would be unaffected This is because the relative prices

between commodities would still be the same, reflecting the fact that the terms atwhich commodities are traded with one another have not changed

The third main concept is that of economic agents In traditional microeconomics,

these are usually classified as consumers and firms We shall analyse the behaviour

of consumers in Unit 2, and the behaviour of firms in Unit 3 Consumers must

allocate their limited resources among the different commodities they can purchase,and firms employ inputs such as capital and labour to produce output In the

traditional analysis, firms are seen as individual decision makers In the more recentmicroeconomic theory and in managerial economics, however, it is usually acknowl-edged that firms are complex organisations, and that the individual agents attached to

a firm may each have different goals in mind It is therefore necessary to explorehow firms behave, given the possible conflicts of interest between the members ofthe organisation We address these and related issues in Units 6, 7 and 8

The fourth main concept is that of a market By this we mean the place where

economic commodities are traded It is important to note that a market is not

necessarily a formal market place Trade occurs whenever agents engage in anexchange of commodities, irrespective of whether this exchange is regulated or not.Also, trade does not require exchange of money: Barter, for instance, is a form oftrade An important issue in microeconomics is to analyse how markets work, andhow agents behave in markets In markets with a large number of participants,

individuals often have very little power to alter the conditions of exchange A smallshopkeeper in a large town may have limited control over the prices charged for itsgoods, because higher prices could mean losing most of its customers: they couldjust walk away and buy from the rival shops By contrast, the only shopkeeper in aremote village could wield some market power, in the sense of enjoying some

latitude in setting prices Its customers would not be able easily to walk away fromthe shop and purchase the commodities somewhere else, if no rival shop were

available An important component of this course is the analysis of how marketswork, and how agents can behave strategically in a market setting We exploremarket behaviour in Units 4 and 5

Please now stop and read pages 1-6 from Gravelle and Rees, Chapter 1, section

A The textbook introduces the main concepts in microeconomic analysis modities, price, economic agents and markets), and illustrates them by means ofexamples We shall constantly be referring to these concepts in this course, so it isessential that you are thoroughly familiar with them In addition, I should like you topay special attention to the discussion of markets and of economic agents

(com-3 Optimisation in Economic Analysis

In microeconomics, the assumption is often made that agents behave in a rationalfashion This means that, when making their decisions, they consider all the possiblealternative courses of action, rank them according to their preferences, and finallychoose the action which they prefer best Thus, a consumer seeking to maximise herutility given her total income will consider all the possible uses of her income, willrank these uses according to the utility she derives from each of them, and finallywill choose the use which yields the highest utility (Unit 2) Similarly, a firm mightseek to maximise its profit given technology and input prices and given a demandcurve for its output or output price, and will decide on the levels of labour and

capital it employs (Units 3 and 4)

Formally, the process of choice can be modelled as an optimisation problem faced

by the economic agent There is a well-defined objective function that the agent

seeks to maximise by optimal choice of the decision variables The context in whichchoices take place is modelled as a set of constraints on individual behaviour Thus,the objective function of consumers is their utility function, which they seek to

maximise; their choice variables are the quantities of the various commodities whichare consumed, and their choice must satisfy the budget constraint which requires thattheir expenditure cannot exceed their total income The objective function of the firm

is the value of its profits; its choice variables are the quantity of inputs employed(capital and labour), the output supplied and the price of its output (unless the firm isoperating under perfect competition), and its constraints are the level of technologyand the demand for its output by consumers

The general method of microeconomics is therefore to model individual choice

as a problem of optimisation under constraints This approach is very general, and it

is easily extended to the more recent topics in microeconomics and managerial

economics, such as the economics of imperfect information Consider, for example,the case of an employer who wants to elicit a higher level of effort from its employ-ees Its objective function are its profits, its choice variables the remuneration systemoffered to its employees, and its constraints the response of its employees (who can

be thought of as rational and optimising agents in their turn, seeking to maximisetheir own welfare given the remuneration scheme offered) The problem can befairly complicated, but the basic structure is quite straightforward, and always

involves optimisation under constraints

Note that optimisation may involve either a maximisation or a minimisation problem.

Examples of the latter case are the minimisation of costs of a firm, or the tion of the risk faced by a financial investor In this course we shall encounter manyexamples of both maximisation and minimisation The same methods can be applied

minimisa-to both cases

It is now a good moment to stop and read pages 6-11 from Gravelle and Rees,Chapter 1, sections A and B

Note how these authors pay special attention to the assumption of rationality in

economics Please read these sections carefully, making notes on the important

points as you read Read also with attention the analysis of the economic and socialframework of choice theory in section B The structure of an optimisation problem ineconomics is explained by Gravelle and Rees in Appendix A, pages 657–59, and youshould read these pages as well Note in particular how the set of constraints is

described by Gravelle and Rees as the feasible set Pay special attention also to the

definitions of choice variables and of the objective function, and to the economicexamples which are provided

4 Properties of Objective Functions and

Feasible Sets

In the previous section, we saw that the general method of microeconomics is tomodel the choice problem as a programme of optimisation under constraints It istherefore necessary to be able to establish whether the problem we are consideringdoes have a solution, whether the solution is unique, and how the characteristics ofthe solution depend on the parameters of the problem For instance, when we look atconsumption behaviour, it is important to establish whether there is a combination ofcommodities which maximises the utility of the consumer (existence of the solution),and whether other combinations exist which yield the same level of utility so that the

consumer is indifferent between them (uniqueness of the solution) Even withoutknowing the exact functions involved in the optimisation problem, it is usuallypossible to say something about the solution The reason for this is that economictheory suggests that the functional forms in a microeconomic decision problem mustsatisfy some given properties, and this in turn could lead to guaranteeing that theproblem has a unique solution with some important additional characteristics.

The main properties we are looking for in the solution to a microeconomic tion problem are:

Existence of a solution is clearly a crucial feature of the optimisation problem, yet itcannot always be taken for granted Some mathematical problems simply do nothave a solution Hence, when setting up an economic problem we must always checkwhether a solution exists The good news is that sometimes the properties of theobjective function and of the constraints do ensure that a solution exists (this will bediscussed further in the next section of this unit)

But even when a solution exists, we cannot always be sure that it is a global solution,

i.e that it achieves a maximum (or a minimum, depending on the problem) over the

whole range of feasible values for the decision variables Figure B.1 in Gravelle and

Rees shows an example of a function f(x) which has a local, but not a global

optimum at x** When solving an optimisation problem, it is therefore necessary to

check that the solution is a global, rather than simply a local solution to the problem.Finally, it is important to establish whether the solution to the optimisation problem

is unique, or whether there could exist several choices of the decision variableswhich yield the same value of the objective function, and therefore are equivalent forthe optimising agent Although there are no theoretical problems in principle with

the latter case, i.e when there are multiple solutions, there could be difficulties when

it comes to predicting the behaviour of the economic agents In fact, if the agent is

indifferent as between a number of alternative courses of action, it could be ble to predict with certainty what the outcome of its actions will be Sometimes it ispossible to anticipate that agents will choose one of these actions over the others –for instance, in problems which involve co-ordination by many agents, there could

impossi-be a focal equilibrium, that is, an action to which all agents co-ordinate their

behaviour Thus, when driving a car, keeping to the right side of the road is the focalequilibrium in France, whereas keeping to the left is the focal equilibrium in the UK

In a number of cases, however, it could be quite difficult to predict the action ofagents when there are multiple solutions to the individual optimisation problem

We are going to look at the issues of existence, unicity, and the global property ofsolutions in the next section We will see there that, for a large class of problems in

microeconomics, it is possible to prove that a solution exists, is unique, and is indeed

a global optimum The conditions for this to be true lie in the properties of the

objective function and of the set described by the constraints – the feasible set.

The main properties which an objective function can satisfy are:

F IGURE 1.1 C ONTINUITY

Part (a) of Figure 1.1 shows a function f(x) which is continuous, whereas part (b)

shows a discontinuous function In Figure 1.2, part (a) gives an example of a

concave function, whereas part (b) displays a function which is not concave

F IGURE 1.2 C ONCAVITY