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1 The rôle of microeconomic principles
CHAPTER 1. INTRODUCTION
Modern microeconomics focuses on the use of abstract models as a means of
pursuing the inner truth of key issues. What are they for? What makes a good
Apart from claims to intrinsic intellectual beauty (and some models do have an
inherent attractiveness all of their own) the quality of a model depends upon
such things as its power to explain the reasons underlying observed economic
phenomena, to make precise the insights born of common sense and to expose erroneous reasoning. It is almost meaningless to describe a microeconomic model
as “good” or “bad” without further quali…cation. Whether or not a particular
model is good depends on the purpose for which it is designed – unless the
model is actually so bad that it violates some fundamental economic principle
(the equivalent, say, of assuming that water can ‡ow uphill).
So, to assess the worth of an economic model we need a speci…c context
in which to place its abstract components and mechanisms. Di¤erent circumstances –but apparently the same economic problem –may demand a di¤erent
type of model. This does not mean that microeconomics is inconsistent or ambiguous, just that we have to be careful to pause and rethink the objectives of
the model, the context in which it is set and the way the model components are
to be implemented. The essential components of a microeconomic model can
be summarised under the following headings:
The economic actors
The economic environment
Assumptions and axioms.
The economic actors
At the heart of the model is the economic actor or agent –someone or something
that is taking economic decisions. It is common practice to speak as though
this entity is just an isolated person –a solitary John Doe acting or reacting in
the arti…cial world of the economic model. However often the same principles
apply whether this actor is considered to be an isolated consumer, a worker, a
representative member of a group or the embodiment of a corporation.
Cynics may say that economics is about greed. In a sense cynics are right:
most microeconomic models assume that somewhere deep in the mechanism is
the driving force of self-interest. Are there useful alternatives? Certainly it is
1.2. MICROECONOMIC MODELS
possible to imagine many cases where self-interest is not well de…ned because
the “self”may be a di¢ cult concept –we shall brie‡y encounter this in chapter
9 where we consider what is meant by “social”choices among alternatives. It is
also possible to consider cases where individuals care about others’consumption
or others’welfare. But in a sense even this can be seen as an extension of the
standard paradigm of sel…shness – I get personal satisfaction from observing
your consumption increase.
The assumption of sel…shness is not essential to economics, but it gets us a
long way in formulating problems precisely and, even though it may go against
the grain of the public-spirited people who study microeconomics, it can be
useful in specifying a well-crafted model.
Where the topic of motivation runs into di¢ culty is in characterising the
content and structure of these sel…sh aspirations. In the matter of specifying
agents’preferences the model-builder usually has to fall back on assertion based
on extrapolation from one’s own preferences and principles or, sometimes, on
mathematical convenience. A special example of this is di¢ culty lies in the
representation of people’s preferences under uncertainty (chapter 8): here strong
far-reaching results can be obtained on the basis of a few elementary assumptions
about preference structure, but it is not at all clear that they are in fact a
suitable way of encapsulating individuals’ motivation when faced with choices
The economic environment
The economic environment may take a variety of forms. The principal form
relevant to our discussion is some sort of market. The market itself could be
represented in a number of ways: obviously it consists of a collection of other
economic actors, but in order to complete its description as the economic environment we need to specify the “rules of the game.”The rules of the game could
refer literally to a game (see chapter 10) but, even in models where game theory
makes no formal appearance, the assumptions about the forms of action and interaction that are admissible in the model are crucial in specifying clearly how
a model is supposed to work and what it can tell us about human behaviour.
This can be illustrated even without using a formal model. We could imagine
three levels of interaction of an individual economic agent with the environment,
in ascending order of complexity:
Agents may just accept the economic environment like we accept the
weather. Just as you cannot change the weather so no agent is large
or in‡uential enough to manipulate the economic environment, so the argument goes.
Maybe agents do not have to accept the economic environment as a given.
Just as some human activities may indeed be big enough to a¤ect the
weather –so some agents’economic activities may big enough to in‡uence
the market price of a product. However, interaction with the environment
CHAPTER 1. INTRODUCTION
is limited: even if you can change the weather it doesn’t try to anticipate
A third view is that the environment in which agents operate is not like
the weather at all. Everyone has to take into consideration the explicit
interaction with everyone else. This interaction will include possible anticipation by one agent of what another agent may do.
Which view of the environment is appropriate clearly depends on the type
of microeconomic model and its purpose.
Assumptions and axioms
Some of the basic ideas about the elements of a model –the nature of preferences,
the structure of organisations, the physical nature of production possibilities –
have to be modelled from scratch. The free hand enjoyed by the model-builder
should be used in a way that well represents the modeller’s craft. The principal
way that this craft is exercised in scratch modelling is known as the axiomatic
Axioms are just formally stated assumptions. They cannot be right or wrong,
although they could be woefully inappropriate, judged by the purpose of the
What is the purpose of this formalisation? Axioms can help us:
carefully develop the ‡ow of an argument,
concentrate on the individual components of key results,
debug a wonky theory.
But they can never substitute for clear thinking about the purpose and
essential functioning of the parent model and about the rôle of the speci…c
model components for which axioms are to be introduced.
“Testing” a model
What is the criterion of “relevance” of an economic model? Clearly it is advantageous if the predictions of the model do not immediately fall over when
confronted with facts. However, this does not mean that all features of a model
should be or could be subjected to rigorous empirical test. The standard methods of quantitative investigation can reveal a lot about the detail of agents’
behavioural responses to the market environment and yet miss the central point
of a model. In some cases, what may be more promising is to turn this connection between theory and empirics around; if the theory predicts a certain
pattern of behaviour by economic agents then use the theoretical predictions
as restrictions on relevant econometric models in order to provide more useful
1.3. EQUILIBRIUM ANALYSIS
Testing a the quality of a theoretical model is a more subtle process than
just confronting it with empirical testing. The model’s quality also depends
on such factors as simplicity of form, clarity of prediction and the absence of
“blind-alley” assumptions (those that leave you with nowhere to go when you
try to relax them).
The importance of economic equilibrium in understanding and applying economic principles cannot be overstated. An equilibrium can be regarded as an
arti…cial construct that allows one to examine the properties of the model in
a situation where every agents’ choices and activities are consistent with each
other and no agent would have an incentive to change its choices or activities.
We can visualise an equilibrium as a posed picture of how a particular piece of
the economic mechanism works.
Equilibrium and economic context
The equilibrium has to be de…ned relative to the economic environment. So if we
make the environment more complicated within the economic model it should
not come as a surprise that we need a more carefully speci…ed de…nition of what
an equilibrium state is. We can imagine this by analogy with a mechanical
model: the more intricate the system of levers, wheels and pulleys, the more
you add on extra subsystems, the more carefully you will need to specify the
conditions for the whole contraption to be in balance.
The comparative statics method
How do things in the model change as things in the environment around it
change? The comparative statics method provides a way of dealing with this
issue. It is built on the concept of equilibrium and focuses on the relationship
between the equilibrium itself and one or more key parameters. It is not a
description of a process but is more like a set of snapshots of di¤erent instances
of equilibrium that leave a trace of a process.
The comparative statics method is sometimes incorporated into speci…c relationships that are used as a shorthand to characterise the behaviour of an
economic agent. The prime example of this is demand and supply functions –
collectively referred to as response functions. A second example is the reaction
function in the analysis of game-theoretic models (chapter 10) –how one player
responds to the actions of another on the assumption of a speci…c form of the
rules of the game.
We use the comparative statics method time and again to get some insight
on where the economic machine might move if certain levers were pulled. How
the machine moves from point to point requires an explicit model of dynamic
CHAPTER 1. INTRODUCTION
Dynamics and stability
With very few exceptions this book does not examine behaviour out of equilibrium. Some of the main issues of disequilibrium arise in the brief discussion
of the stability of a general equilibrium system (subsection 7.4.4 on page 163
onwards). It is important to distinguish between equilibrium itself and the stability of equilibrium.1 We need this notion of stability in order to have some
idea of whether the equilibrium states on which we spend so much intellectual
energy are likely to prove no more than a ephemeral distraction.
Background to this book
This book assumes that you are not coming to the subject with a completely
clean slate. Here is a brief overview of the background that is assumed in order
to pursue the argument.
The opening chapters assume that you have mastered an introductory university course in economics, so that you will already have some familiarity with
production functions, utility, demand and supply curves, the operation of the
market and the nature of equilibrium. However we will reinforce and deepen
understanding of these essential concepts by putting them on a formal basis.
Later developments build on this foundation to introduce more advanced ideas.
This is not a book about mathematical economics nor about mathematics in
economics. But it does not shy away from mathematics. Where a mathematical
explanation could help to make an argument concise, or to give an additional
economic insight that could be lost in the fog of words, we use it. As far
as possible algebraic arguments are backed up with diagrams to present the
The mathematical level does not get harder as the argument of the book
progresses; nor is it the case that the harder economic problems are typically
associated with harder mathematics. The material in Appendix A is intended to
be a statement of fair dealing concerning the technical requirements of the main
text: there are no mathematical surprises in the book that are not brie‡y covered
in that material. Dipping into Appendix A is a way of reassuring yourself of
how far you are expected to go with the mathematics as well as brushing up on
particular technical points.
1 Take an ordinary pencil with a sharpened point and place it on a ‡at table. How many
equilibria does it have? Which of them are stable?
1.5. USING THE BOOK
Using the book
The argument on each topic proceeds by a mixture of narrative and practice.
The narrative is designed to take you briskly through the main themes of modern
microeconomics. The material has been organised in a way that both has an
inner logic to it and that permits extensive re-use of techniques as you progress
through the chapters. To achieve this, I have tried to minimise the interruption
to the ‡ow of narrative by relegating some formal proofs to appendices or to
guided exercises. The practice involves a mixture of examples, exercises and
quick discussion points that you are encouraged to use in order to provide depth
on particular points within the main themes and to develop familiarity with
important solution techniques.
A route map
We begin with each of the two main economic actors –the …rm and the household
–and their relationships to the market. Understanding how these relationships
work is the key to a lot of other interesting microeconomic problems.
The argument naturally moves on to consider how the economic system
works as a whole. This addresses the key question on the rôle of the market in
delivering goods to individual consumers and calling forth resources to produce
the goods. The background message here is “the market works” and can be
used as a method of achieving desirable allocations of goods and services in the
economy. But the discussion moves on to economic reasons why the argument
does not work and why the paradigm of price-taking may be too restrictive.
There is no magic bullet to blow away the market as an institution, but an
understanding of microeconomic principles can help in appraising the various
possibilities for modifying market mechanisms and piecemeal solutions for overriding or replacing particular markets.
You will probably …nd it useful to check through the brief summary of
mathematics in Appendix A. There you will also …nd some suggestions
for further reading if you are a bit rusty on certain techniques. You should
be certain to check carefully the list of symbol conventions used throughout
the book –see page 485.
The proof of some of the results are hived o¤ to Appendix C. This is not
because the results are not interesting, but because the method of proof
is not particularly illuminating or is rather technical.
Throughout each chapter there are footnotes that focus on detailed points
of the argument. These take the form of one-liners or mini-problems that
have suggested answers or outline solutions in Appendix B.
Each chapter has one or two practical illustrative examples drawn from
the relevant applied economics literature.
CHAPTER 1. INTRODUCTION
The bibliographic references for the examples and for further reading are
collected together on pages 484 onwards.
At the end of each chapter there are exercises that are designed to give
you a more serious mental workout than the little footnote questions by
the wayside. Outline answers for these are on the website.
I think business is very simple. Pro…t. Loss. Take the sales, subtract the costs and you get this big positive number. The math is
quite straightforward. –Bill Gates, US News and World Report, 15
We begin with the economic problem of the …rm, partly because an understanding of this subject provides a good basis for several other topics that arise later
in the book, partly because the formal analysis of this problem is quite straightforward and can usually be tied into everyday experience and observation.
We will tackle the issues that arise in the microeconomic analysis of the …rm
in seven stages. The …rst four of these are as follows:
We analyse the structure of production and introduce some basic concepts
that are useful in solving the …rm’s optimisation problem.
We solve the optimisation problem of the price-taking, pro…t-maximising
…rm. Along the way we look at the problem of cost-minimisation.
The solution functions from the optimisation are used to characterise the
…rm’s responses to market stimuli in the long and the short run.
The analysis is extended to consider the problems confronting a multiproduct …rm.
The remaining three topics focus on the …rm’s relationship with the market
and are dealt with in chapter 3.
In this chapter we will …nd in part a review of some standard results that you
may have already encountered in introductory treatments of microeconomics,
and in part introduce a framework for future analysis. I shall give a brief account
CHAPTER 2. THE FIRM
amount used of input i
amount of output
price of input i
price of output
Table 2.1: The Firm: Basic Notation
of the behaviour of a …rm under very special assumptions; we then build on this
by relaxing some of the assumptions and by showing how the main results carry
over to other interesting issues. This follows a strategy that is used throughout
the later chapters – set out the principles in simple cases and then move on
to consider the way the principles need to be modi…ed for more challenging
situations and for other economic settings that lend themselves to the same
type of treatment.
The …rm: basic ingredients
Let us introduce the three main components of the problem, the technology, the
environment, and economic motivation.
You may well be familiar with the idea of a production function. Perhaps the
form you have seen it before is as a simple one-output, two-input equation:
q = F (K; L) (“quantity of output = a function of capital and labour”), which
is a convenient way of picking up some of the features that are essential to
analysing the behaviour of the …rm.
However, we shall express the technological possibilities for a …rm in terms
of a fundamental inequality specifying the relationship between a single output
and a vector of m inputs:
Expression (2.1) allows for a generalisation of the idea of the production relation.
Essentially the function tells us the maximum amount of output q that can
be obtained from the list of inputs z := (z1 ; z2 ; ::; zm ); putting the speci…cation
of technological possibilities given in the form (2.1) allows us to:
handle multiple inputs,
consider the possibility of ine¢ cient production.
On the second point note that if the “=” part of (2.1) holds
production technically e¢ cient –you cannot get any more output
list of inputs z.
The particular properties of the function
about the “facts of life” concerning the production technology
we shall call
for the given
of the …rm.
2.1. BASIC SETTING
Working with the single-product …rm makes description of the “direction of
production” easy. However, sometimes we have to represent multiple outputs,
where this speci…cation will not do –see section 2.5 below where we go further
still in generalising the concept of the production function.
We assume that the …rm operates in a market in which there is pure competition.
The meaning of this in the present context is simply that the …rm takes as given
a price p for its output and a list of prices w := (w1 ; w2 ; ::; wm ) for each of the
m inputs respectively (mnemonic –think of wi as the “wage” of input i).
Of course it may be interesting to consider forms of economic organisation
other than the market, and it may also be reasonable to introduce other constraints in addition to those imposed by a simple speci…cation of market conditions –for example the problem of “short-run” optimisation, or of rationing.
However, the standard competitive, price-taking model provides a solid analytical basis for a careful discussion of these other possibilities for the …rm and for
situations where a …rm has some control over the price of output p or of some
of the input prices wi .
Almost without exception we shall assume that the objective of the …rm is to
maximise pro…ts: this assumes either that the …rm is run by owner-managers
or that the …rm correctly interprets shareholders’interests.1
Within the context of our simpli…ed model we can write down pro…ts in
schematic terms as follows:
More formally, we de…ne the expression for pro…ts as
Before we go any further let us note that it seems reasonable to assume that
in (2.1) has the property:
(0) = 0
which in plain language means both that the …rm cannot make something for
nothing and that it can always decide to shut up shop, use no inputs, produce
no output, and thus make zero pro…ts. Therefore we do not need to concern
ourselves with the possibility of …rms making negative pro…ts (tactful name for
losses) in the pro…t-maximisation problem.2
What alternative to pro…t-maximisation might it be reasonable to consider?
real life we come across …rms reporting losses. In what ways would our simpli…ed
model need to be extended in order to account for this phenomenon?
CHAPTER 2. THE FIRM
Figure 2.1: Input requirement sets for four di¤erent technologies
Properties of the production function
Let us examine more closely the production function given in (2.1) above. We
will call a particular vector of inputs a technique. It is useful to introduce two
concepts relating to the techniques available for a particular output level q:
1. Pick some arbitrary level of output q: then the input-requirement set for
the speci…ed value q is the following set of techniques:
Z(q) := fz : (z)
2. The q-isoquant of the production function
space of inputs
fz : (z) = qg:
is the contour of
Clearly the q-isoquant is just the boundary of Z(q). Although you may
be familiar with the isoquant and the input requirement-set Z may seem to
be a novelty, the set Z is, in fact, useful for characterising the fundamental
properties of the production function and the consequences for the behaviour of
the optimising …rm. Certain features of shape of Z will dictate the general way
in which the …rm responds to market signals as we will see in section 2.3 below.
In a 2-input version of the model Figure 2.1 illustrates four possible shapes
of Z(q) corresponding to di¤erent assumptions about the production function.
Note the following: