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Fundamental Concepts of Microeconomics
6.1 Objectives and Methods of Microeconomics
Microeconomics is an impressive (and bold) architecture of thought. Its objective is most ambitious: it attempts to describe, explain and evaluate almost everything that is going on in the world as far as human behaviour is concerned. 1 To achieve this goal (or to at least come as close as possible) microeconomics takes a multi dimensional approach providing
- a theory of rational individual decisions,
- a theory of conflict resolution and coordination,
- a theory of the evaluation of resource allocation,
- a theory of public regulation. Given this set of dimensions, microeconomics is fairly comprehensive. It is also quite general. Let us see what the term “general” means in this context, and take the first of the four bullet points presented above, the dimension of individual decision making, as the example for our explanation. The decisions of a baker are certainly different from the decisions of the manager of a basket ball team, and the two afore mentioned decisions are certainly different from the decision of a couple to get married. However, when we said that microeconomics attempts to provide a theory of individual decisions, above, we did not mean that microeconomics provides different theories for the decisions of bakers, sports club managers and fiance´s. On the contrary, microeconomics tries to identify features of decision making that are general in the sense that they are common to all kinds of rational decision making, irrespective of who the decision maker is and what the decision is about. Based on this general approach microeco- nomics serves as the basis of many different fields of applied economics, such as environmental economics, industrial organisation or the economics of the family.
(^1) Describing and explaining constitute the positive, evaluating the normative part of microeco-
nomics. See Sect. 3.4, above.
43
Let us now elaborate on each of the four dimensions of microeconomic theory mentioned above.
- Microeconomics as a theory of rational individual decisions It is an essential feature of human life that each autonomous individual takes many decisions every day. This is a burden and a privilege, at the same time. There are fundamental and trivial decisions. An example (of the former) is that most of the honourable readers of this text, at a certain point in their lives, may have decided to enrol on an environmental studies programme of a university. Instead, they could have decided to enrol on a different programme or not to go to university at all. Another example is a family deciding on whether to buy a new car instead of travelling abroad in their vacations. 2 These decisions (and all others), have an important feature in common: the decision maker must choose between alternatives. “Alternatives” means that realising one possibility implies that the other possibility cannot be chosen. The decision in favour of a new car, for example, implies that the vacations abroad cannot be realized. (At least, this is so in the case of the family playing its part in our example.) As regards the decision to enrol in a certain university program the possibilities to do the one and leave the other are rather limited. Some people might go for two university degrees, simultaneously, but this is the maximum you can do, in most cases. The reason for the necessity to choose and therefore being forced to decide is that the realisation of an alternative uses up resources. Once these resources are consumed for one alternative they cannot be used for the realisation of the other alternative. It is impossible “to have your cake and eat it”. These resources can be of completely different kinds for different decisions. For example, the resource that forces you to decide between buying the car and going away for vacation is money. The resource that forces you to decide between different university programmes is money too, but in addition, it is time. 3 Of course, the fact that the decision in favour of a certain alternative uses up resources wouldn’t be worth mentioning if resources were abundant. It is the scarcity of resources, as discussed in Sect. 2.4, above, that adds a painful touch to decision making: realizing one alternative comes at the cost of not being able to realize the other alternative. The alternative foregone is interpreted to be the cost of the alternative chosen, in economics.^4 It is called “opportunity cost”. So if microeconomics is a theory of individual decision making, this is a consequence of the central theme of scarcity that we have discussed in Part I, above. Since economics focuses on the painful aspect that the decision to realize a
(^2) The wish to have a new car, and to travel abroad in the vacations are “needs” in the sense of Sect.
2.1, above. (^3) These two resources are related to each other, even if the saying “time is money!” somewhat
overstates the case. (^4) If there are several alternatives forgone, it is the best of these which counts as the opportunity
cost.
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Art work 1 David Dalla Venezia, No. 269, Oil on Canvas, 2000 This might be the illustration of three economics textbook authors (they all look alike!) struggling on whose name will appear first on the cover. Obviously, they are using brute force as a means of conflict resolution. Alternative mechanisms of conflict resolution would be the seniority principle, or – sometimes it’s as simple as that – the alphabet. An alternative (and possibly more serious) interpretation would be that the painting illustrates the internal creative struggle of the artist. Interestingly, this kind of a conflict, the conflict within one and the same person, is dealt with in the arts, philosophy, as well as in poetry and prose, but not in mainstream economics. In economics, it is assumed that the decision making process of any individual does not use up emotional (or any other) resources, but is conducted “costlessly”. When we talk about “conflict”, in economics, we are most certainly referring to conflict between different individuals
Conflict resolution and coordination were no hot topics for Robinson Crusoe, at least in the time before he met Friday. Sparse as the resources on his island were, they were all his – at least that’s what he thought, initially. However, there was no one with whom he could share the tasks of life. Modern societies are designed in sharp contrast to the Robinson Crusoe scheme. People compete with each other for all kinds of objects of desire, like consumer products, jobs, organ transplantations, and grants to cover the costs of university environmental studies programmes. Moreover, labour is strictly divided between people who specialize in narrowly defined tasks. For example, there are environmental scientists who know most everything about the greenhouse effect but who do not know how to bake a bread, let alone how to drive a nail straight into a piece of wood. This is no problem: working on how to meet the need of society for energy without burdening the earth with excessive greenhouse gas pollution, they earn money. They can use this money to pay people who know to bake bread and to work on the nails if this is what needs to be done. This may sound trivial but it is not. On the contrary, we are talking about a fundamental problem every society must solve. The problem consists of two elements.
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The first is that society must provide a mechanism for the solution of conflicts in cases where the goals of different individuals are not compatible with each other. This is a social “must” no matter what the conflict is about: if two people want to have a unit of a certain good, it must be decided who prevails, no matter whether this unit is the last slice of bread, or the last student slot in an environmental studies programme. The second aspect of the problem with which we are dealing here is that where ever the goals of different individuals are compatible with each other, society must provide a mechanism which makes people cooperate together like the different organs in a healthy body. This means, for example, that the decision of a consumer to buy a certain good can only be realized if this decision is complemented by firms (or other institutions) producing this good. Your decision to learn about environmental sciences and to get a qualification which makes you fit to enter the labour market for environ- mental specialists leads to nothing, except your frustration, if your decision is not complemented by universities’ decisions to offer environmental studies programmes.
Art work 2 Theater Bonn, Germany, FRIDA KAHLO, 2003. Director and Choreographer: Johann Kresnik (Photo: Thilo Beu). There are many wonderful photos particularly from Dance and Opera on Thilo Beu’s webpage, http://www.thilo-beu.de/ In economics, we certainly acknowledge the utmost importance of coordination among individuals for their well-being. However, we take a rather prosaic look at it. The scene from the ballet shown above reminds us that there are poetic (if not romantic) alternatives. Here’s the authors’ understanding of utmost romance: we believe the photo shows a (somewhat farsighted) couple coordinating in jointly reading Economics for Environmental Studies. And don’t they look happy?!
The problems we are dealing with are about how scarce goods are assigned among the people who want to lay their hands on them: is David’s or Susan’s application successful when the last student slot in the prestigious environmental
6.1 Objectives and Methods of Microeconomics 47
coordination. We will elaborate on this in Sect. 6.4, below, dealing with “the market”. In the present section we make some general observations on how the market mechanism might be able to meet the need for coordination and for the solution of conflicts. To do so we will consider an extremely simple example. Imagine that the firms in a certain market have decided to produce 50 units of a certain good, X. We won’t worry about how this decision was made. This kind of a question is postponed to Sect. 6.3 on “the firm”, below. On the other side of the market there are assumed to be 100 consumers and each of them would love to have exactly one unit of this product. Of course, this example is highly artificial. This might be considered to be a drawback. On the other hand, it has the advantage of being most simple. It is the simplest means of demonstrating the point at issue here: how the market mechanism can contribute to solving the two problems involved here, the one of coordination and the one of conflict resolution. 8 In the context of this example, the coordination problem is restricting the total quantity demanded by the consumers to the total quantity of supply provided by the firms. The aspect of conflict regulation is how to decide which ones among the 100 consumers are the “lucky winners” who will receive the unit of the product in question. In a market system, the issue is not decided by a lottery but by the market price. We are looking for the level of the price for good X which cuts back the aggregate demand of the consumers to 50 units and simultaneously identifies the 50 consumers who will buy the product. This special price which equates the total quantity demanded to the total quantity supplied is called the equilibrium price in economics. Obviously, this price cannot be 0. As the example has been constructed, each consumer would want one unit if the product was given away for free and then the total demanded quantity would be in excess of the total quantity supplied. Excess demand is at a level of 50 units in our example if the price is 0. Let us assume the price is one monetary unit (dollar, euro, yen.. .). Then, each consumer is forced to think about it thoroughly (or fulfil the task using his/her intuition). Since the budget from which the monetary unit (let it be dollar hereafter) must be taken is limited, the question is: is a unit of good X worth the dollar? To answer this question the consumer must consider other possibilities to spend the dollar and compare the utility that this dollar generates if spent on good X with the utility this dollar provides if spent on any other good, Y.^9 On the basis of this kind of an internal evaluation process, a certain number of consumers (say, five consumers) may decide not to spend the dollar on good X but instead on an other good (or put it away into a savings account). Then, the
(^8) Choosing the simplest way to make our point meets the requirement of efficiency, one of the most
important concepts in economics, as explained in Sect. 3.1, above: we choose the way in which we achieve our didactical goal such that it confines the time our readers must devote to this issue to its minimum level. You see: we treat your time budget as a scarce resource which has to be allocated efficiently. So the rule for prudent decision making that has been explained in the previous subsection also holds for decisions in the process of economic theory building, and of textbook writing. (^9) Not being able to buy a dollar’s worth of Y is the opportunity cost of buying a dollar’s worth of X.
6.1 Objectives and Methods of Microeconomics 49
discrepancy between the quantity demanded and the quantity supplied has already somewhat narrowed compared to the situation with a price of 0, but is still at 45 units. Obviously the equilibrium price for X is higher than 1 dollar. Assume that at a price of 43.50 dollars there are 51 consumers left who think, based on an assessment of their needs and their budgets, that good X is worth buying. Then, the equilibrium price is the lowest price at which one additional consumer can be induced to refrain from buying X. If at 44 dollars just one of the remaining 51 consumers decides to leave the market, then 44 dollars is the equilib- rium price: at that price, the total quantity demanded is exactly equal to the total quantity supplied. At the same time this price draws the line according to which it is decided which of the 100 people interested in X, in the first place, actually receive it and which don’t. Obviously, the people who prevail are the ones who are able to demonstrate the intensity of their needs for X by paying the equilibrium price. If all consumers had a budget of the same size, then the people with the highest intensity of need for X would be the ones who in fact received a unit of X. If different people have different sized budgets, this is not so simple. The willingness to pay depends on both, the intensity of the preference for the good and the size of the budget. Of course, a prerequisite for the workability of the mechanism described above is that all people participating in the process respect the rules of the market mechanism as a means of coordination and conflict resolution. There must be a consensus in the society that scarce goods are allocated using the price mechanism, at least as far as goods like X are concerned. An alternative would be that goods are stolen. Another possibility is that they are distributed by the government according to a catalogue of criteria defined by a bureaucracy. A third possibility would be allocation by waiting in line. All of these procedures play a certain role in most societies. Microeconomics can be applied to analyse what’s going on if any of these allocative schemes is applied. However, the focus of microeconomics is on the market mechanism (and on governmental intervention).
- Microeconomics as a theory of evaluation of resource allocation Under the first bullet point of this introduction into the objectives and methods of microeconomics, we presented some observations on how microeconomics stylizes individual decisions: economic agents are taken to choose among alternatives, striving to achieve their goals as well as they can in light of the fact that their resources are limited. We call this behaviour rational, in microeconomics. What these goals are is left (almost^10 ) completely down to the individual decision makers themselves.
(^10) There are some basic requirements on the preferences of individual decision makers which
somewhat attenuate the generality of the observation made above. However, we do not follow this line of thought here. See, e.g., Varian (2010), p. 35/36. Moreover, not all individual goals are socially accepted. There are certain constraints on individual goals defined by the law, but also by ethical principles, as well as the customs of a particular society. Notably, microeconomic analysis can also be applied to illegal behaviour. See the groundbreaking (1968) work of Economics Nobel Prize Laureate Gary Becker and, for a more recent exposition, Chaps. 11 and 12 in Cooter and Ulen (2004).
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view of society as a whole. It is this issue which we courageously tackle in this subsection. Compare two different allocations a certain society might be able to realize, A and B. To illustrate this, imagine that society enjoys a certain provision of con- sumption goods which are sold in private markets and also enjoys a certain level of environmental quality, in allocation A. In allocation B, consumption is a little lower than in A and environmental quality is somewhat higher. The question is: which allocation is better for society? In the common terminology of microeconomics you could reformulate this question to ask: is the welfare of society higher or lower in A than it is in B? A subsequent question is: in which situation (A, B or a third alternative C) is the welfare of society maximal? The allocation for which the welfare of society is maximal is called the “socially optimal” allocation. Microeconomists have been working on these questions for quite a while (and very hard too). We will deal with the answers they have come up with in subsection 6.5.1, below. In this introductory section we work with the idea that good old Jeremy Bentham proposed in 1776, and which was referred to in Sect. 3.4, above. According to this somewhat cryptic but also plausible concept, an allocation is socially optimal if it provides the greatest happiness to the greatest number of members of the society under consideration. This leads us to the fourth (and last) dimension of microeconomics.
- Microeconomics as a theory of public regulation Microeconomics uses the idea of social optimality to assess the results that are produced if a society uses a certain allocation mechanism, e.g., the market mecha- nism. If this mechanism produced results (“equilibria”) that were socially optimal, this would be a strong case in favour of the allocation mechanism under consider- ation leaving things as they are. On the other hand, if the equilibria produced by the allocative mechanism a society applies do not meet the criterion of social optimal- ity, the question arises as to whether the welfare of society can be improved by governmental intervention. It is important to note, however, that “governmental intervention” is a very comprehensive term, incorporating many forms of govern- mental intervention. Microeconomics tries to analyse the properties of different forms of governmental intervention and to find designs that best meet the objective of maximizing social welfare. Ooophs! This sounds awfully philosophical. Is it still economics? Yes, it is, as will become apparent when we apply these concepts in the subsequent sections. To give you a preliminary idea of how this might work, consider environmental problems. A doctoral degree in environmental economics is not needed in order to observe that an unregulated market mechanism will not be able to secure natural resources for this and future generations. It is a safe guess that governmental intervention will be needed to protect the natural environment, and that this protection will improve social welfare. However, there are obviously different forms of governmental intervention that benefit the environment and society. Wherever the readers of this book may be located, each will know – from their home country – examples of different kinds of environmental policy instruments.
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These include environmental taxes, environmental subsidies, various emissions trading programmes, requirements to apply environmentally sound technologies, and many other forms of environmental regulation. An important economic ques- tion is to evaluate these different kinds of environmental policy instruments in terms of their effectiveness and their potential to enhance social welfare. We will briefly deal with these issues in Chap. 7, below, where we discuss the microeco- nomics of environmental policy.
6.2 The Consumer
We will turn now to one of the main actors of any market economy: the consumer. The consumer is an economic agent, supplying such things as labour and capital in the market for productive factors, as well as demanding in the market for consumer goods items such as refrigerators and haircuts.^12 In discussing the economics of the consumer we apply microeconomics predominantly as a theory of rational individ- ual decisions, in the sense explained in the preceding section. In this section we identified the scarcity of resources to be the reason for the necessity to decide among alternatives. Let us apply this idea to the role of a consumer supplying labour. The resource which is scarce in this context is time. Each consumer must decide how to allocate his/her time budget to alternative activities all of which need time to be performed. Economically, the most crucial of these activities are work, leisure, and education. The most important benefit from work is money (as far as traditional microeconomic theory is concerned). The most important benefit from leisure is fun, hopefully.^13 The most important benefit from education is to improve the chances of making more money by working in the future.^14 Microeconomics stylizes the decisions of consumers to divide their scarce time budget optimally among the three competing uses in the sense that the total utility derived from spending the time is maximized. The situation in which a consumer spends his/her time in the utility maximizing manner is called the equilibrium use of time. Naturally, this equilibrium may look different for different consumers. It depends upon the relative utility a consumer
(^12) Additionally, a consumer might operate in money markets, borrowing and lending. However, we do not pay very much attention to this dimension of consumer decisions. In the context of environmental issues it is not as consequential as the activities of consumers in markets for physical resources. The present textbook is designed to present economics as it is most useful to environmental studies. (^13) The German philosopher Johann Friedrich Herbart (1776–1841) said: “Boredom is the biggest
sin!”. This is understandable from the point of view of microeconomics because a lifetime is definitely limited. Interestingly, the economic quest for efficiency, often sneered at to be a low “purely mercantile” issue, can be interpreted as a high moral obligation. (^14) Most of our readers know that education is a lot of fun, too – isn’t it? However, we do not deal
with this aspect in the above brief exposition.
6.2 The Consumer 53
utility maximizing bundle of consumption goods constitutes the equilibrium demand of a consumer. Of course, the structure of equilibrium demand is generally different for different consumers. This is so, because the preferences of different consumers differ. Some consumers are prepared to pay up to 200 dollars to see a soccer match, others couldn’t care less. Moreover, the budgets of different consumers differ widely.
Calculus Club: Session 1 In this digression we address those of our readers who are familiar with the mathematical method of calculus. Occasionally during our exposition we call this subset of readership together to an imaginary “club session”, where we use some mathematical language to make the point. So this section is more appropriately geared to people who take the environmental engineering perspective as the focus of their environmental studies, rather than to those predominantly interested in environmental law or philosophy. We hope that the members of the latter group share our assessment that the discrimination we practise hereby is a mild and tolerable one. The contents of the “calculus club sessions” are strictly supplementary (and thereby optional). The argu- ment can be fully understood by everyone skipping the sessions. However, mainstream economics is a social science that heavily relies on the use of mathematical methods. In the main parts of this book we do without but it would be unwise to completely ignore the didactical potential of mathemati- cal methods; thus, we address those readers who are somewhat familiar with this language. Having said that, the members of the Calculus Club may consider a consumer buying two goods X and Y with quantities x and y. The utility he/she derives from consuming these goods is represented by a twice differ- entiable utility function
U ¼ Uðx; yÞ:
According to an intuitive (even if somewhat old fashioned) interpretation, this function quantifies the satisfaction the consumer derives from consuming the goods. According to a modern (and somewhat prosaic) interpretation, U is just an index function attributing the higher numbers to the dependent variable the more the consumer under consideration likes the bundle of goods, which is represented by the independent variables. So if a consumer prefers a certain bundle ðx, yÞ to a bundle ð^x, ^yÞ, then
Uðx; yÞ > Uð^x; y^Þ
follows. (continued)
6.2 The Consumer 55
The first partial derivative of this function for any of the two variables is assumed to be positive, the second derivative for any of the two variables is assumed to be negative. The second cross derivative may be positive, nega- tive, or zero. The first partial derivative is called marginal utility, in econom- ics. Its economic interpretation is the utility generated by the consumption of a small additional amount of the product under consideration. Strictly speaking (after all, we are talking calculus here), the unit is indefinitely small. Assume that the amount of money the consumer spends for consumption is m and the prices of the two goods are p (^) X; p (^) Y. Then, all the combinations of x,y the consumer might buy are given by the equation
p (^) X x þ p (^) Y y ¼ m:
We call this equation the consumer’s “budget constraint”. From all the combinations of the two goods for which the consumer is able to pay with his/her budget, he/she is assumed to choose the one providing the highest utility. This decision rule is formalized by maximizing the utility function under the budget constraint.
Uðx; yÞ ¼ max!
s:t:
p (^) X x þ p (^) Y y ¼ m
The tuple of consumption quantities solving this constrained optimization problem (let us call it ðx; y^ Þ) constitutes the equilibrium demand of the consumer under consideration.
Above we have characterized the concept of equilibrium supply (of labour) and demand (of commodities and services) of a consumer, as stylized by microeconomic theory. This has been done verbally for all of our readers and in somewhat more formal terms for the subset of our readers familiar with calculus (confined to the case of demand). We have also argued that the structure of equilibrium supply and demand might vary with the level of all kinds of determinants. In the case of equilibrium demand, the consumer’s preferences and budget as well as the product prices have been mentioned. Above, we tacitly assumed that these determinants do not change. We did not introduce any movement in terms of salary, prices of other goods, etc. This kind of an approach, describing equilibria under the assumption that the determinants of those equilibria are unchanged, is called static analysis.
56 6 Fundamental Concepts of Microeconomics
m
equilibrium cannot be upheld. The income is just not high enough to pay for the initial consumption bundle after the price of one of the elements of this bundle has gone up. It is unavoidable that the consumption level of at least one of the goods purchased by the consumer must go down, given that the price of one of the goods goes up. It is most plausible that the equilibrium quantity of the good whose price has risen actually decreases as a reaction. For example, if you imagine that the price of apples in the market increases, with all other prices remaining as they are, it is quite plausible that many consumers may revise their consumption plans: some might buy pears instead. This inverse relationship between the price of a good and the quantity of this purchased good is often referred to as the law of demand. However, this is neither a law from which no deviation is possible – as is the case with natural laws – nor is it a law in the sense that deviators are punished (in the sense of criminal law). The law in the economic sense is a general observation which holds true in most cases but from which there are occasional deviations. Of course, what has been said above for an increase in the price of a certain good can be generalized for any price change in any good. A graphical illustration of this idea is the demand curve of an individual consumer, d. For every given price the curve indicates the corresponding quantity that the consumer under consideration demands in equilibrium. It is presented in Fig. 6.1. For any given price observable from the ordinate of the graph, the curve shows the quantity demanded by the consumer for which this demand curve holds at the abscissa. 22 In the example, at a price of $0.50 the consumer purchases 120 units of the good X in equilibrium. In case of a price increase to $0.70 the quantity demanded drops to 100 units.
Fig. 6.1 The individual demand curve
(^22) The abscissa is the horizontal, the ordinate is the vertical axis.
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Putting it in more general terms you might say that at a price of p the equilibrium quantity demanded by the consumer under consideration is x. If the price increases to p, equilibrium demanded quantity drops to x. The law of demand is respected in that p > p and x<x hold. The demand curve is the graphical representation of the demand function, x ¼ dðpÞ. The equation for the demand function is illustrated in Fig. 6.1 as x ¼ 170 100 p. From the way we wrote this equation and the way we interpreted the demand curve, we note p is the independent variable and x the dependent. Considering this, the illustration of the demand function in Fig. 6.1 is somewhat unusual, because it would be more conventional to plot the independent variable on the abscissa, and the dependent on the ordinate. Well, economists sometimes make an exception. The exposition presented here is very traditional, and economists have gotten so used to it that they do not even realize anymore that it is unconven- tional. As long as the curve is monotonically decreasing, however, it doesn’t really matter which way you position the independent and the dependent variable. 23 Indeed we will use an interpretation below where the quantity is understood to be the independent variable of the demand function and the price to be the dependent. In our example, the demand curve is assumed to be linear. This is done solely for convenience. The demand curve can take any shape: all that is required is that it is downward sloping, obeying the “law of demand”, as was discussed above. There are two points on the demand curve that are immediately eye-catching: these are the points at which the curve intersects the abscissa and the ordinate, respectively. Each of the two has its own economic interpretation which might be worth noting. Consider the intersection of the demand curve with the ordinate first, a. If the price is at a level of a, the quantity demanded is 0 (and stays at 0 for any price higher than a). Since a is the lowest price that prevents the consumer from buying X, a is called the “prohibitive price”. At the other end of the demand curve you find the quantity, b, where d intersects the abscissa. b is the quantity the consumer demands if X is given away for free. (In order to make the consumer ask for more, you would have to pay him/her!) Quite descriptively, b is called the “satiation quantity”. Interpreting the demand curve, you should always keep in mind that illustrating how the quantity demanded of a certain good depends upon the price of this good does not say that this price is the only determinant of this quantity. Instead, all other determinants are assumed to be constant in the process of interpreting the demand curve. 24
(^23) Please remember that the property of being monotonically decreasing is assured by the law of
demand. (^24) Academic economists sometimes love to show off their high level of education. A well
established trick to make an impression is to occasionally intersperse some Latin terminology. So instead of saying “all other determinants assumed to be unchanged”, you might say “ceteris paribus”.
6.2 The Consumer 59
In Fig. 6.2, for any price of p, the demand is at x given income is at m and at x^0 if income is at m^0. m^0 > m and x^0 > x hold. Above, we have presented a little exercise in comparative static analysis: one of the determinants assumed as being constant in the static analysis of the demand curve has been allowed to vary. This determinant is income. Of course, analogous comparative static analyses can be applied with respect to all other determinants of the quantity demanded which are assumed to be constant in the consideration of a demand curve. An issue very often discussed in economics is what happens to the demand curve of a certain good X, if the price of another good, Y changes. Depending on how the two goods are related to each other in terms of their suitability for satisfying the consumer’s needs, an increase in the price of Y may stimulate or attenuate the demand for X. In the former case the demand curve of X would shift outward (to the north-east), whereas in the latter case it would shift inward (to the south- west). A case where the demand for X increases as the price of Y increases might be observed if X and Y are two different kinds of TV sets with comparable quality. Then, X and Y are said to be substitutes in microeconomic terminology. A case where the demand for X decreases if the price of Y goes up might be observed if Xand Y are hardware and software. (An old-fashioned example is bread (popcorn!) and butter.) In this case, X and Y are called, in microeconomics, complements. 26 For now, we will take a hiatus from comparative static analysis and return presently to the static analysis of the demand curve, taking a look at it from a different perspective. In the interpretation of the demand curve, presented above, we have always taken the price to be the independent variable and the equilibrium quantity demanded to be the dependent variable: given a certain price the consumer wants to buy a certain quantity. So the curve was read “from the ordinate to abscissa”. This is appropriate in the present context, explaining the decisions of a consumer as an important agent in the market. However, it is also possible to interpret the demand curve by reading it “from the abscissa to the ordinate”. This is a nice little exercise in mental flexibility. More- over, it will turn out to be useful in Sect. 6.5. There, we proceed from describing what is going on in the market (positive analysis, see Sect. 3.4, above) to its evaluation (normative analysis, as is also dealt with in the section referred to above). Consider the point on the demand curve shown in Fig. 6.1, as has been interpreted above, with the price being 0.50 and the quantity 120. (In more general terms the price/quantity combination is (p; x).)
(^26) Our honourable readers are invited to graphically illustrate the comparative static analysis of
demand for X as the price of Y increases. They might proceed analogously to what we have done in Fig. 6.2 referring to an increase of income. They might also distinguish the case of substitutes from the case of complements.
6.2 The Consumer 61
How about letting price and quantity switch the roles as independent and dependent variables? Then, we arrive at the following interpretation: if the con- sumer has bought a quantity of 120 (x), then the price he/she has been willing to pay for the last unit of X is 0.50 (p). Why? Try to prove the opposite: to do that, claim first that the willingness to pay for the last unit is lower than 0.50 (p). Wrong! If it were true that the consumer was not willing to pay 0.50 (p) for the last unit, then he/ she would not have bought it. After all, we assume that the consumer strives for utility maximization. Second, what if one claims that the willingness to pay for the last unit is higher than 0.50 (p), at a quantity of 120 (x). Wrong! If the willingness to pay were higher than 0.50 (p) at a quantity of 120 (x), then a consumer would still buy this last unit at a price which is a little higher than 0.50 (p). However, he/she doesn’t, which can be seen in Fig. 6.1. If you observe a price which is a little higher than 0.50 (p), then equilibrium demanded quantity drops below 120 (x). It can’t be otherwise because the consumer operates under the law of demand. Of course, what we have argued for one point on the demand curve (0.50, 120), (p,x) can be just as easily argued for any point on that curve. For each predetermined quantity you can read the consumer’s willingness to pay for the last unit consumed from the demand curve. In the usual microeconomic terminol- ogy (inspired by calculus) we call the last unit the marginal unit. So the demand curve can be interpreted as the marginal willingness to pay-curve. It must be mentioned that our little mental exercise of exchanging the roles of p and x as the independent and dependent variables, respectively, was made possible courtesy of the law of demand: if the curves were not running monotonically you could not transform the unique mapping of prices into quantities into a unique mapping of quantities into prices. 27 For the benefit of terminological clarity economists do not shy away from any effort and thereby created a special word for the demand curve as interpreted above: if we read the demand curve such that the quantity is the independent and the price the dependent variable we speak of the inverse demand curve. Take the example we used above. If x ¼ 170 100 p is the initial demand curve, 28 then p ¼ 1 : 7 x= 100 is the inverse demand curve. In general terms, if the direct demand curve is x ¼ dðpÞ, then the inverse demand curve is p ¼ d^1 ðxÞ. Very often, however, the “ 1” in the exponent of the symbol of the function, “d”, is not written. There, the authors trust that the readers will understand from the context, whether it is the direct demand curve or the inverse demand curve that is referred to. We partake in this tradition of “expository sloppiness” in the notation of graphs. There, a curve labelled “d” might sometimes be interpreted as being the direct demand curve, and sometimes to be the inverse demand curve. We do that in order to economize in
(^27) To see why, imagine that the demand curve is U-shaped instead of being monotonically
downward sloping. After completing this exercise, you might immediately forget about u-shaped demand curves; they violate the law of demand! (^28) The initial demand curve (the one where p is the independent and x the dependent variable) is
sometimes called the direct demand curve.
62 6 Fundamental Concepts of Microeconomics
