Appendix A Relevant Fundamental Principles of Welfare Economics: Efficiency, Equity, Social Welfare.

Appendix A Relevant Fundamental Principles of Welfare Economics: Efficiency, Equity, Social Welfare. Introduction A1 Economics as a discipline is essentially concerned about choices. More specifically, it considers how unlimited human wants can best be satisfied through the use of scarce resources. Given this subject domain, key economic choices which are addressed include: what types of goods should be produced.what volume of each good should be produced what techniques should be used to produce the goods who should receive the goods actually produced A2 If the word goods in each of the above is replaced with the phrase HEI outputs, it is immediately clear that these choice questions apply directly to the economic evaluation of Higher Education. A3 Before presenting a formal presentation of how economists utilise the concepts of efficiency and equity to analyse choice issues, it is useful to comment briefly on the assumed motivations of economic agents, since it transpires that these are of some importance in considering specifically Higher Education (HE) choices. A4 Specifically, it is assumed that, in making their choices, individuals and organisations are economically rational; that is, they minimise the resource cost of achieving a desired benefit or they maximise the benefits from the use of a given i

volume of resources. Put simply, it is assumed that agents make the best of what they have. It is important to note that the assumption of economic rationality does not imply that agents are omniscient, in the sense that they always choose the actual best course of action; rather, it is assumed that they always choose the course of action which they think is best. However, it is acknowledged that they may make some choices based on imperfect or false information, for example. A5 In fact, this apparently small philosophical distinction raises some profound issues of an ethical/moral nature. In particular, should individuals be allowed to make choices which someone else (a parent? government? society?) knows to be poor for the individual him/her self. The arguments for intervention are particularly strong if the someone else has superior information, which, if it could somehow be effectively transmitted to the individual, would cause him/her to change choices. A6 In the real world, questions of this type seem to arise more in some areas of economic activity than others; notably and relevantly, in Education and Health. Specifically for HE, these issues are considered in the main text under the headings of market failures. A7 Two other features of assumed agent behaviour of relevance to the current study may be noted: Firstly, in making choices relating to consumption/saving/production/investment, individuals and firms will generally make their decisions based on an assessment only of their own private costs and benefits. However, in certain areas of economic activity ( including education ), it is argued that the actions of individuals affect members of society other than themselves, and that these effects should be accounted for in a holistic economic evaluation of the actions. In the context of HE, these extra-individual effects are discussed under the heading of externalities ii

Second, in improving their economic welfare, most economic agents will wish to exchange some of their initial endowments of goods and resources for others. This implies the existence of markets in some form or other in which agents can trade. However, in the real world of the UK HE system, there are elements of Higher Education Institution (HEI) activities for which, at least apparently, markets do not exist. In such circumstances, how can agents possibly maximise their welfare? 1 Issues relating to the existence or otherwise of markets for the products of Scottish HEIs, and the appropriate methods for valuing non-marketed outputs, are fundamental to the present study s economic evaluation of the Scottish HE sector, and hence are considered extensively in the main text. A8: From the preceding discussion, it will be clear that consideration of economic welfare leads into some deep and important areas, both with respect to the individual member of society and with respect to society as a whole. The latter perspective in particular raises issues regarding the formulation, implementation and evaluation of public policy. From the point of view of the present study, it is also clear that a number of difficult questions will have to addressed in undertaking an economic evaluation of the Scottish HEI sector. A9: However, to set the agenda for the theoretical discussion to follow, the key topics to be considered can be summarised in the form of three questions: How can an individual economic agent maximise his/her private welfare? Does maximisation of individual private welfare automatically maximise social welfare? What market structures, if any, maximise social welfare. The provision of logically rigorous answers to these questions is the objective of welfare micro-economic theory, to which we now turn. 1 Equally, if there is no market for an HEI s product, there is no price for that product. If there no prices for its products, then how can a monetary value be put on the HEI s output? iii

Primer on the fundamentals of welfare economic theory (Pareto Optimality and the Pareto Principle. A10 In evaluating alternative choices facing society, a fundamental criterion adopted in welfare economics is that of Pareto optimality, also termed Pareto efficiency. 2 2 When an economy s allocation of resources is such that no individual agent can be made better off without making another worse off by any further re-allocations, then that economy is in a Pareto optimal state. Suppose that, in evaluating a single choice ( such as spending more on HE), society finds that it would benefit some individuals and would harm no one, then that choice is said to be a Pareto improvement. The recommendation that Pareto improvement changes should in fact be implemented is termed the Pareto Principle. A11 In a formal logical sense, adoption of the Pareto Principle as a choice evaluation criterion can fairly be described as non-controversial: by definition, adoption of a Pareto improvement choice unambiguously improves society s welfare ( through the individual members who benefit) and moves society as whole towards a Pareto optimal state. Given this logical impeccability, it is unfortunate that the Pareto Principal is severely restricted in the range of choice issues to which it can be applied. A12 Firstly, in the real world (and reflecting the ultimate scarcity of resources referred to earlier), many, possibly most, choices involve changes which will make some members of society better off and others worse off. Such choices cannot be avoided, but the Pareto Principal cannot be used to select among the various alternatives available. A13 Secondly, the concept of Pareto optimality itself embodies an individualistic approach to the evaluation of welfare in the sense that it is the person s perception of his/her own welfare which counts; i.e. everyone knows what is in their own best interests. As noted earlier, particularly with respect to so-called merit goods, there may be circumstances in which society as a whole believes that this is not the case. 2 Named after the Italian economist Vilfredo Pareto ( 1848-1923) iv

More importantly, Pareto optimality refers to the welfare of individuals on a standalone basis, it is not concerned with the relative welfare levels of different individuals. In reality, this can lead to the recommendation of choice selections which many societies would feel to be unfair or unjust. For example, consider an initial resource allocation in which a very small number of people were very rich and a very large number were very poor. A policy choice which further increased the wealth of the rich but left the poor unaffected would be a Pareto improvement, and that policy should be implemented according to the Pareto Principle. Hence, large and increasing inequalities in resource distribution are not inconsistent with Pareto optimality. An alternative policy choice would transfer some resources from the rich to the poor, but the rich themselves would perceive this transfer as adversely affecting their own welfare. Adoption of this policy would not be a Pareto improvement, and should not implemented according to the Pareto Principle. 3 Hence, policies which societies may feel were equitable could be precluded by strict adherence to Pareto optimality choice criteria. A14 Clearly, welfare economists have had to devise evaluation methods for the very large number of policy choices in which strict application of the Pareto Principle is inappropriate or impossible. Of these, the most important are based on variants of the compensation principle. Very briefly, the compensation principle states that if a policy choice is such that the gainers could compensate the losers and still be better off, then that policy should be adopted. This is described as a potential Pareto improvement policy. 4 It is important to note that adoption of a potential Pareto improvement policy does not require that the gainers actually compensate the losers, only that they could do so in principle. 5 3 Note that if the rich agree that some of their resources should be given to the poor, then they can affect the transfer themselves through altruistic/charitable giving or allow society to do it through taxation. However, in this case the policy is a Pareto improvement and would be adopted according to the Pareto Principle. 4 Of particular relevance to the present study, it is the development of concepts such as the compensation principle that have allowed the translation of welfare theory into real world applications via the applied tool of cost-benefit analysis. 5 In fact, a moment s reflection will indicate that, if compensation were actually paid, then the situation would be one in which some agents were better off and none worse off. This is clearly an actual Pareto improvement and would be adopted according to an unmodified Pareto Principle criterion. v

A15 None of the preceding remarks should be taken to imply that the concept of Pareto Optimality is unimportant or irrelevant to the economic evaluation of Scottish HEIs. On the contrary, the concept provides a core theoretical underpinning to most of the case-specific work reported in the text. In particular, as will be clearer subsequently, (a) Pareto optimal states embody strong and desirable characteristics in terms of various aspects of economic efficiency, against which the efficiency performance of real world entities can be evaluated; (b) a Pareto optimal state provides benchmark reference levels of efficiency and welfare against which potential trade-offs involved in moving to other states (which may or may not be Pareto optimal) can be identified and evaluated. Economic Efficiency. A16 Efficiency is one of the core concepts in economic science. In a broad sense, economists interpretations of efficiency in various contexts are not dissimilar to those found in common parlance; however, economic definitions of the term are more rigorous and detailed than typically are employed in everyday usage. In particular, economists find it valuable for both analytical and applied purposes to distinguish four efficiency concepts, relating to different aspects of economic activity. In summary, these four types of efficiency are as follows: (1) Exchange efficiency. Given an initial allocation of resources/goods, when, through trade (exchange), a situation is reached where further trade could only make one person better off at the expense of another, then that outcome allocation is exchange efficient. (2) Production or Technical efficiency. Given society s state of technology and an available supply of factors of production, technical efficiency is realised when it is not possible to produce more of one good without producing less of another. (3) Cost efficiency. Given the prices of factors of production, cost efficiency occurs when a given quantity of goods is produced at the lowest possible cost outlay. Equivalently, cost efficiency involves producing the maximum quantity of goods for a given budget. A vi

moment s reflection will make it clear that all cost-efficient outcomes will also be technically efficient. (4) Allocative efficiency. An economy which supplies volumes of different goods in the proportions best able to satisfy society s demands ( i.e. the correct product mix ) is allocatively efficient. A17 An economy which satisfies the above four efficiency criteria is Pareto efficient. The outcome situation for a single representative individual in a Pareto efficient economy is shown in Figure A1. 6 P F E U 1 U 2 U 3 P F Y Figure A1: Economy Wide Pareto Efficiency In order to understand how and why the situation depicted in figure A1 represents one of complete Pareto optimality, it is necessary in the first instance to analyse the consumption and production aspects of the economy underlying it. Inter alia, this will also provide an explanation of each of the individual lines and curves contained in Figure A1. 6 In this diagram and others to follow, certain curves are drawn as convex or concave to the origin, as straight lines, etc. There are theoretical justifications for all of these shapes, but it is an unnecessary complication to discuss them here. The reader is assured that all the curves in the text are drawn in the conventional shapes according to mainstream economic theory. vii

The consumption system: Exchange efficiency. A18 The consumption choice set facing an individual in a market consisting of two goods, X and Y, is summarised in Figure A2 7 X P E U 2 U 3 U 1 Y P Figure A2: Utility Maximisation A19 The U curves in Figure A2 are the consumer s indifference curves. Each curve shows different combinations of X and Y which give the consumer the same level of utility ( the economist s traditional term for satisfaction or welfare ). The basic idea is that, since both X and Y are desirable goods, then if the consumer has less of X (say), he/she can be compensated by having some more of Y. The precise shape of the indifference curves derives from fundamental concepts in consumer theory and need not be discussed here. However, it is important to note that the slope of the indifference curve gives the marginal rate of substitution in consumption (MRSC XY ). That is, it gives the exact amount of Y which is required to just compensate the consumer for the loss of a unit of X. It is also important to note that 7 In this exposition, reference is always made to two goods, two consumers, two factors, etc. This is simply for ease of diagrammatic representation. The fundamental points are readily generalisable to the many good, etc. case. viii

indifference curves further from the origin represent higher levels of utility. Thus, in Figure A2, U 3 > U 2 > U 1 The PP line in Figure A2 is the consumer s budget constraint line. Its distance from the origin depends on the volume of goods which the consumer brings to the market to trade and on the prices of goods in the market 8. The slope of the budget line is : -P Y /P X A20 In Figure A2, the consumer will prefer (the consumption basket representing) U 2 to U 1. He/she would prefer U 3 even more, but since it lies above the budget line, it simply cannot be afforded. In fact, it can be seen that U 2, the indifference curve which is just tangent to the budget line, is the highest level of utility which this consumer can achieve. At this point: MRSC XY = -P Y /P X A21 Put in plain language, the consumer maximises satisfaction by trading in the market until the prices he is subjectively willing to pay just equal the prices he objectively has to pay. The sensible householder makes these judgements every day (in the supermarket, for example), without having the slightest knowledge of economic theory. A22 For reference to a subsequent discussion it can be noted that Figure A2 does contain an equity element. Specifically, the highest indifference curve that can be attained does depend on the initial allocation of goods which the consumer commands. If the volume of goods which the consumer has to trade is small, then although U 2 is the best he can do, it may not be very high in some absolute sense. 8 It is perfectly possible for one of the goods to be labour, in which case one the prices would be the wage rate. ix

A23 Figure A2 shows how each consumer attains optimum satisfaction individually; however, in order to establish the conditions for economy-wide exchange efficiency, we need to examine the behaviour of all consumers simultaneously. This is illustrated for a two-consumer, two-good, economy in Figure A3 below. 9 X A P G 0 Y G 1 Y B 1 B 0 A 0 A 1 P B X Figure A3: Exchange Efficiency A24 The bottom left-hand corner of Figure A3 represents the origin for consumer B, while the top right-hand corner is the origin for consumer A. Every point within the diagram represents an allocation of the two goods between the two consumers ( i.e. X A, Y A, X B, Y B ). A25 Suppose the initial pre-trade allocation of goods is at G 0, at which point A has utility level A 0 and B has utility level B 0. It is clear from the diagram that, by trading with each other, both A and B can do better than this. Specifically by exchanging some of his X for some of B s Y, A can ultimately attain the (higher) utility level of A 1 at allocation G 1. Conversely, by exchanging some Y for X, B can achieve utility B 1 9 Formally Figure A3 is known as the Edgeworth-Bowey box Diagram. x

at G 1. At G 1, no further trade can make either A or B better off without making the other worse off ; hence, by definition G 1 represents an economic situation which is Pareto exchange efficient. A26 It can be observed that at G 1 A and B s indifference curves are tangential to one other, i.e. have identical slopes; however, it was noted above that the slope of an indifference curve at a point is the marginal rate of substitution in consumption. Hence at G 1 MRSC A XY = MRSC B XY Thus, the fundamental condition for economy-wide exchange efficiency is that the marginal rates of substitution in consumption across all commodities are the same for all consumers. A27 As is clear from the preceding discussion, this fundamental condition derives most obviously from personal exchange of goods in a barter economy. However, in a modern economy the vast majority of trades are made impersonally through the buying and selling of goods for money in markets. We can see how the fundamental condition translates into a market economy by re-considering Figures A2 and A3. Consider firstly Figure A2 as it applies separately to consumers A and B. Each acting individually and without cognisance of what the other is doing will maximise utility by trading in the market until: (i) for A, MRSC A XY = -P A Y/P A X (ii) for B, MRSC B XY = -P B Y/P B X However, from the discussion of Figure A3, it is clear that (i) and (ii) will not give economy-wide exchange equilibrium unless P A Y/P A X = P B Y/P B X xi

The single slope (-P Y /P X ) of the unique price line PP in Figure A3 satisfies this requirement, being tangential to both A 1 and B 1. Thus it is necessary for all consumers to face the same prices. Given a common set of commodity prices, the fundamental condition for economywide exchange efficiency in a market economy can be expressed as : MRSC A XY = MRSC B XY = -P Y /P X This condition is immediately generalisable to the multi-consumer, multi-commodity case. The production system: technical and cost efficiency A28 In Figure A4, the curve FF is extracted from Figure A1. X F F Y Figure A4: The Production Frontier FF is termed the production frontier. Given the state of underlying technology and given volumes of factor inputs, points on FF show the maximum amount of X which can be produced for a given volume of Y produced and vice-versa. Points inside the frontier show combinations of X and Y which are feasible but inefficient: the best use xii

is not being made of available production resources. Points outside the frontier are infeasible. A29 The precise shape of FF reflects underlying characteristics of production processes which need not be discussed here. However, the slope of FF is important and is termed the marginal rate of transformation of X into Y (MRT XY ). At each point, this gives the volume of X which must be given up to produce one more unit of Y. Of course, alchemy and some nuclear processes aside, X is not directly transformed into Y; rather, production resources are transferred from making X into making Y. To see this, and to define the concepts of cost-efficiency and technical efficiency, it is necessary to examine the relationships between factor inputs and commodity outputs. (It can be noted that the diagrams and discussion that follow closely mirror those above for consumption and hence are given in a little less detail). A30In Figure A5 below, it is assumed there are two factors of production, capital (K) and labour (L), used in the production of good X. An analogous diagram can be drawn for good Y. K C Q 1 X C L Figure A5: Cost-Efficiency A31 In the diagram, the curve Q 1 X is called an isoquant. It shows all the different combinations of K and L which be employed to produce the single quantity of X, Q 1. xiii

Though frequently not mentioned, all the points on an isoquant are in fact technically efficient, that is, they are drawn on the premise that there is no deliberate waste of factor inputs. The slope of an isoquant is important and is termed the marginal rate of technical substitution of K for L in the production of X (MRTS X KL). At a point, it indicates by how much Labour must be increased to compensate for the reduction of one unit of Capital in the production of X. An alternative way of defining the MRTS, which turns out to be helpful subsequently is that it is the marginal product of K in the production of X divided by the marginal product of L in the production of X. 10 That is: MRTS X KL = MP K /MP L The line CC in Figure A5 is an isocost line. Analogous to the consumer s budget line, it shows the total cost of various factor combinations according to the equation: C = P K K + P L L The slope of an isocost line is given by the (negative) ratio of the factor prices: -P L /P K A32 As can be seen from the diagram, the least-cost combination of K and L for producing the quantity Q 1 X is given at the point where the isocost line is just tangential to the isoquant 11. At this point, MRTS X KL = - P L /P K This is the condition for cost-efficient production, and as noted earlier, the factor combination used is also technically efficient. A33 Again mirroring the consumer case, economy-wide technical efficiency requires that the MRTS s are the same for all commodities; otherwise it would be possible for 10 The marginal product of K in X is the increase in X resulting from a very small increase in K, with L held constant. MP L is defined analogously. 11 Alternatively, this point gives the maximum output which can be produced given budget factor CC. xiv

producers to exchange factors to increase the production of one good without reducing the volumes of any other other. The equilibrium position is shown in the Edgeworth box Figure A6 below ( with the origin for factors going into X at the bottom left corner and going into Y at the top right corner. L Y C 0 K Y K X Q Y Q X C 0 L x Figure A6: Technical Efficiency A34 The economy-wide efficiency position is shown where the isoquant for Y is just tangential to that for X, at which point: MRTS X KL = MRTS Y KL However, given that producers are all operating independently and do not in fact directly exchange factors bur rather buy them in factor markets, there is no guarantee that the optimum position shown in diagram 6 will actually be attained, unless all firms are facing the same factor prices (as shown by the line CC in the diagram). If this is the case, then from diagram 5, all cost-minimising firms will equate their MRTS s with the common factor price ratio, so that: MRTS X KL = MRTS Y KL = -P L /P K xv

Generalised to the use of all factors in the production of all goods, this is the economy-wide condition for cost-efficiency and technical efficiency. Conjoining the production and consumption systems: Allocative efficiency. A35 We can finally return to Figure A1, which can now be seen to bring together the production (through FF) and consumption ( through the U curves). Also included is PP, a commodity price line. The essence of allocative efficiency requires that technically-efficient producers supply exactly the right basket of goods ( in terms of volumes and proportions) to maximise consumers utility as expressed through their demands for goods. Loosely, produce what people actually want. A36 Inspection of Figure A1 indicates that the allocatively efficient combination of X and Y is at point E, where the production frontier FF is just tangential to the highest possible consumer utility curve U 2. At E, MRT XY = MRSC XY That is at E, the amount of X which has to be sacrificed to obtain one more unit of Y in production is equal to the amount of X which consumers are willing to sacrifice to obtain one more unit of Y in trade. An economy which satisfies this condition is allocatively efficient. A37 There remains the problem that, given each producer and consumer is acting independently and in their own self-interest, there is no guarantee that the economy as a whole will actually arrive at point E. In fact, the preceding discussion makes it clear that this problem is a very real one, for in section (1) it was shown that consumers respond to output prices, while section (2) demonstrated that cost-minimising firms react to input prices. Thus the producer and consumer sides of the economy are optimising according to different price signals. In such circumstances, it is actually very unlikely that allocative efficiency will be achieved. xvi

A38 What is required is a clear link between input and output prices, but we cannot deduce such a link for a cost-minimising firm. However, such a link can be derived for a profit-maximising firm. Specifically, facing a given set of input and output prices, it can be shown that a profit-maximising firm will produce the level of output at which: P(output) = P(factor) X MP(factor) Thus, in our 2-commodity, 2-factor example, production will take place at the levels where: P X = P K MP X K = P L MP X L And P Y = P K MP Y K = P L MP Y L Dividing the second equation into the first, we obtain: P Y /P X = MP Y K/MP X K = MP Y L/MP X L But since everyone is facing the same prices, P Y /P X is the slope (ignoring minus sign) of the PP line in diagram 1. Also, though we shall not prove it, MP Y K/MP X K is definitionally equal to the marginal rate of transformation of X into Y, so that at the profit-maximising level of output: MRT XY = (-)P Y /P X = MRSC XY That is, the economy is at point E in Figure A1 and is allocatively efficient. A39 Furthermore, from the above equations, at the profit-maximising level of outputs for both X and Y, xvii

P L /P K = MP K /MP L which is the MRTS KL. Hence, the economy with profit-maximising producers is also cost-efficient and technically efficient. A40 To summarise this rather lengthy section, we have rigorously defined the various concepts of economic efficiency. We have derived the characteristics of a Pareto efficient economy which embodies allocative, technical, cost and exchange efficiency. We have shown that such an economic state can be realised by each agent in the economy acting individually and independently in their own self interests, in the sense of consumers maximising utility and producers maximising profits. An important requirement we have specified is that all agents must face the same set of input and output prices. Also importantly, we have noted that a Pareto efficient outcome is non-unique, depending as it does on the initial allocation of resources. Market Structure and the Fundamental Theorems of Welfare Economics. A41 As noted immediately above, the nature of Pareto efficiency leaves a number of distributional issues to be addressed (see below). Nevertheless, the Pareto efficient economy exhibits highly attractive characteristics: it represents an optimal way in resources can be utilised to satisfy the demands of the members of the relevant society. In fact, if the economy is in a Pareto efficient state, then no further changes in production or trade can be made which would make someone better off without making someone else worse off. A42 Given that, other things equal, attaining a Pareto efficient state is entirely desirable, the key question becomes: what structure or organisation of the economy (if any) would lead it to achieve this state? A43 From the discussion section (2) it is clear that prices play the crucial role as signalling devices. If all the economic agents face the same set of correct prices, then individual optimising behaviour will tend to move the economy as a whole towards Pareto optimality. xviii

A44 Given this, it is worth considering briefly an economic structure in which all prices were set by a central planning agency. If this agency had access to all the consumer utility (or demand) functions, all the producer production functions, etc, it could undertake the analysis of section (2) in the real world and arrive at the required sets of input and output prices. If necessary, it could also dictate that all firms maximise profits (or, if it owns the means of production, insist that its managers act as profit maximisers). In fact, it has been formally demonstrated in the abstract that such a system can lead to the Pareto optimal outcome depicted in Figure A1. A45 However, at this point economic reality and economic theory begin to diverge sharply. Consider that the agency will have to collect and process a mass of data for each of perhaps millions of consumers, thousands of producers, and on the many millions of transactions among them. It will need to translate this enormous volume of data into a complete set of correct prices for each and every commodity and factor, no matter how finely differentiated one is from another. This price list may therefore contain millions of entries. It must be speedily transmitted throughout the entire economy. The agency must monitor and adjust the price list continuously, being ready to respond to the slightest change in the economic environment. Clearly, the central planning system cannot work in practice 12 Nowadays, the problem is not so much one of raw computing power, rather it is the complete impossibility of constructing a transmission system which can get the information into and out of the central agency as required. A46 If the central planning model is rejected, then an alternative structure of the economy suggested by the writings of Scotland s most famous economist, Adam Smith, can be considered. In The Wealth of Nations(1776), Smith argued that, if markets were competitive, then an individual pursuing private gains would promote the common good: 12 And in countries where it has been attempted, notably the old eastern block, it has demonstrably been seen not to work. xix

He intends only his own gain, and he is in this, as in many other cases, led by an invisible hand to promote an end which was no part of his intention. Nor is it the worse for society that it was no part of it. By pursuing his own interest he frequently promotes that of society more effectually than when he really intends to promote it This of course contains Smith s famous invisible hand analogy, and we shall see shortly just how remarkable his insight has proven to be. A47 Smith does not rigorously define what he means by a competitive market, but he clearly has in mind a structure in which individual agents have little or no market power i.e. they are essentially price takers rather than price makers 13 A48 Subsequently to Smith, economists developed a formal model of an idealised competitive market economy termed perfect competition. Perfect competition is an abstract, theoretical construct whose outcomes derive logically from a number of underlying assumptions. Full details of the perfect competition model need not be discussed here (an exposition can be found in any elementary economics textbook). However it is necessary to highlight a number of the underlying assumptions of particular importance to the analysis of Scottish Higher Education. The key point is that, if these assumptions are invalid in the HE case, then the conclusions and recommendations derived from the model may also be invalid. The most relevant of the perfect competition model assumptions to the study of Scottish HE include the following: No agent in the economy has market power. That is, all agents have to accept and react to a given set of market prices. All agents have perfect information concerning market conditions ( prices, quantities, qualities,etc.). Strictly speaking, this also refers to all future market conditions. There are no externalities in production or consumption. That is, the only agents who accrue a cost or benefit from a transaction are those directly involved in the transaction. 13 Elsewhere in The Wealth of Nations Smith voices his deep suspicions on monopoly power and oligopolistic collusion. Again, this turns out to be truly insightful with regard to economic efficiency. xx

All producers are profit maximisers. A49 Since these assumptions (and others) will never be exactly valid in the real world, it is reasonable to ask why any particular attention should be paid to the perfect competition model. The answer is that, in the 1950 s, economists (Arrow 1951, Debreu 1959) formally proved intimate and powerful relationships between the perfectly competitive market structure and the Pareto efficient economy. These relationships are encapsulated in the two fundamental theorems of welfare economics. A50 The First Fundamental Theorem can be summarised as follows: The equilibrium position of any perfectly competitive economy will be Pareto efficient. That is, if the economy is perfectly competitive, then the market actions of agents acting individually in their own best interests will result in an economy-wide outcome which is allocatively, technical, cost and exchange efficient. A neat comparison of this market approach to attaining efficiency with the central planning method is given in the World Bank manual: no government or central planner, however omniscient and well-intentioned, can improve on the results obtained by the free market system. The best of all possible planners might do as well as competitive firms attempting to maximise their own profits, but they would never do better. The First Fundamental Theorem provides a powerful theoretical argument in favour of free, competitive markets. A51 The Second Fundamental Theorem states that: xxi

Every economy-wide Pareto efficient outcome can be attained through the operation of perfectly competitive markets, depending only on the initial allocation of resources The Second theorem clearly invites consideration of distributional issues, and the way in which a government may address them. In principle, the government need only ensure that the initial allocation of resources conforms to its equity criteria and then allow competitive markets to operate unhindered to take the economy to a Pareto efficient outcome 14.Thus a certain separation between equity and efficiency issues is invited: let the government deal with equity and the markets will deal with efficiency. Crucially, the Second Fundamental Theorem proves that, in theory, it is possible to attain an economic state which is both efficient and equitable. A52 In summary, the two Fundamental Theorems demonstrate the efficacy of competitive markets in achieving Pareto efficient outcomes, which are in and of themselves entirely desirable. There is a role for government, but only in ensuring a fair distribution of resources. These equity considerations can be dealt with separately from efficiency issues. A53 However, as we move from an idealised theoretical construct towards reality, there are important caveats which can modify the story of the preceding paragraph. Firstly, as noted earlier, some of the assumptions of the perfect competition model may be invalid in a real-world economy. If the actual market economy is not perfectly, then there is no guarantee that it will be Pareto efficient. Indeed, it is quite easy to identify some market structures which are definitely not Pareto efficient. Deviations from the assumed conditions of perfect competition are termed market failures. The existence of market failures may justify government intervention in the market on the grounds of improving economic efficiency. There are reasons for believing that, because of particular aspects of its activities, market failures are prevalent in the Higher Education sector. Certainly, the argued existence of market failure significantly influences the policy debate on Higher Education in Scotland. 14 Again in principle, the government could approach this from the other way round. That is, the government could identify the Pareto efficient outcome which it desired, and work backwards through the analysis of section2 to identify and create the consistent initial allocation of resources. xxii

Given this, rather than abstractly summarised here, market failures as they relate to Higher Education are defined and discussed in detail in the main text. Second, in reality in may not be possible for the government to alter the distribution of resources without impacting on market efficiency. In particular, there may be an equity-efficiency trade-off. This is considered in the section immediately below. A54 In reality, all debates on Scottish Higher Education marshal arguments relating to both equity and efficiency, albeit with varying degrees of consistency and coherence. Section (2) has described the economic meaning of efficiency; hence to round off this primer, section (4) discusses the economists treatment of equity and considers the relationship between equity and efficiency. Equity, Efficiency and Social Welfare. A55 Assume there are two consumers in the economy, and refer to point E in Figure A1. At this point, each consumer has a certain level of utility, U E A and U E B respectively. It has been demonstrated that E is Pareto efficient, which means that, at E, it is not possible to increase the utility of A without reducing that of B or viceversa. As such, the utility combination ( U E A, U E B ) represents one point on the utility possibility frontier which is shown in Figure A7 below. For two consumers, the frontier is given by the curve UU. Each point on the frontier shows the maximum level of utility B can attain for a given level of utility of A and vice-versa. Thus, utility combinations ( U A 1, U B 1 ) and ( U A 2, U B 2 ) are on the frontier. ( U A 1, U B 2 ) is feasible, but sub-optimal, and ( U A 2, U B 1 ) is infeasible. xxiii

U B U U 1 U B i U B 2 U 2 U A i U A 2 U A Figure A7: Utility Possibility Frontier A56 Different points on the UU curve represent different initial allocations of resources between A and B. Re-allocating resources between A and B will change supplies of and demands for the various goods and factors, which will in turn change their prices. Effectively, in terms of Figure A1, the price line PP will move round the production frontier FF. Since there are an infinite number of possible initial resource allocations between A and B, there are an infinite number of points on the utility possibility frontier. If society has an active interest in the individual welfare of its members, how can it identify the specific point on UU in Figure A7 which it regards in some sense as the most desirable combination of utilities for A and B? A57 An immediate problem is, that given the Paretian nature of UU, moving from any point on it to another must reduce the utility of at least one member of society. That is, there is an inevitable utility-utility trade-off. Thus, in Figure A7, moving from state U 1 to state U 2 reduces B s utility by B and increases A s utility by A, but given that A and B s utility functions are entirely personal and subjective, how can any third party decide whether this trade- off is fair or not? At some point in xxiv

considering distributional issues, inter-personal comparisons of utility become inevitable, but there is nothing in the analysis to date which allows us to do this. 15 A58 In short, our analysis of the Pareto efficient economy can take us, through Figures A1-A6, to the UU curve in Figure A7. To choose which points on UU society prefers, we require an additional tool, which economists describe as the social welfare function (SWF). A59 Before discussing the SWF and its role, it is useful to consider a particular special case, which turns out to be important in the real-world evaluation of projects and programmes using the techniques of cost-benefit analysis or project appraisal. The case envisaged is summarised in Figure A8 below. U B U U 3 U 1 U 4 U 2 U U A Figure A8: Cost Benefit or Project Appraisal A60 Suppose the economy is initially at position U 1, which is inside the utility possibility frontier. For any of a whole variety of reasons, this economy is clearly inefficient in production and /or trade. Suppose now that we can identify a project which would move the economy from U 1 to U 2. This represents an improvement in 15 Elements of economic theory can provide some guidance. For example, the concept of diminishing marginal utility of income suggests that transferring 1 of resources from a very rich to a very poor person could be a fair trade off. However, this may not be necessarily true: a rich miser may hate parting with 1 of resources and he/she is a member of society. xxv

production/exchange efficiency, which would be revealed by an economic-efficiency appraisal, but does not unambiguously represent an increase in social welfare since B is worse off at U 2. However, we can undertake a thought experiment along the following lines: first, introduce the efficiency enhancing project so that the economy moves to U 2. Then, in principle, it would be possible to transfer goods/resources from A to B to move to U 3, at which both A and B are better off than at U 1. The potential Pareto improvement criterion for project evaluation indicates that a project which moves the economy from U 1 to U 2 should be undertaken on the basis of the compensation principal; that is, that it possible in theory to compensate the losers from the move while still leaving others better off. The key point which widens the range of acceptable projects is that compensation does not actually take place. A61 Unfortunately, this still does not cover all possibilities: for example, choosing between U 1 and U 2 in diagram 7 or between U 1 and U 4 in Figure A8. To make such choices requires the social welfare function referred to above. In most general terms, the SWF can be summarised by the following equation: SW = f ( U A, U B,. U N ) Where the U s represent the utility levels of each of the n members of society. The precise form of the function f will depend on the moral and ethical views underlying it. Whose views underlie it depends on the political system in place. In reality, the operational SWF is the one of the group that has the power to translate its social preferences into actual choices. While economists can and do say a great deal about what the SWF might look like and how it might be revealed by various voting systems, etc. 16, it is fundamentally a deus ex machina in terms of economic analysis, not being derivable from fundamental economic theory. A62 Nevertheless, taking the SWF as given (and all societies do have one, usually implicitly) it can be integrated into the preceding analysis to give further insights into the nature of social choice among alternative economic states. The framework is illustrated in Figure A9, which combines the utilities possibility frontier U P U P with 16 For a good discussion and some examples see Stigltz.J, Public Sector Economics (3 rd ed), Stanford University Press, 2000, Chapter 15. xxvi

social indifference curves derived from the SWF. These indifference curves need not have the shape drawn, but they do have the property that curves further from the origin represent higher levels of social welfare. U B U P X SW 2 Y SW 1 U P U A Figure A9: Social Indifference Suppose that, given an initial allocation of resources, the efficient operation of the perfectly competitive economy leads to an outcome state at point Y. At point Y, the level of social welfare is SW 1. However, it can be seen that society would prefer to be at point X, which, though not more economically efficient than Y, is at the higher level of social welfare, SW 2. For this society, the allocation of goods/resources at X is more equitable than that at Y. A63 How can society move from Y to X? In principle, there are two ways. Firstly, society could redistribute the initial allocation of resources and then allow markets to operate freely to take the economy to X. In the real world, this principle underlies things like inheritance taxes and, more subtly, policies to promote equality of opportunity and access. Secondly, society could allow the entire economic system to operate freely and redistribute the outcome allocation of goods. This principle underlies most income and expenditure taxes. Thus, in theory, society can move to its preferred economic state by introducing a suitable tax/transfer system. Moving from xxvii

Y to X involves a loss of utility of A in favour of B, but this is regarded as socially equitable. However, there is no loss of economic efficiency. A64 Unfortunately, the prescription in the preceding paragraph cannot work in reality. This is because the only tax system which can move the economy from X to Y is an abstract one based on lump sum taxes/transfers. A lump sum tax is one which has the theoretical property that, in the face of it, no agent changes his/her economic behaviour at the margin in any way whatsoever. No real world tax system satisfies this criterion: in the face of inheritance taxes, people will change the disposition of their assets; in the face of income taxes, they will change their propensities to work; in the face of expenditure taxes, they will change their consumption patterns..and so on. A65 Formally, any real tax introduces a wedge between actual market prices and economic efficiency prices. This distortion of prices as a market signalling device means that the economy will not attain Pareto efficiency. The real world situation is summarised in Figure A10. U B U P X U F Z Y SW 2 SW 1 SW 1 U F U P Figure A10: Utility Feasibility Frontier U A xxviii

A66 Suppose that, without any taxes or other interventions, the economy arrives at point Y as before. Since there are no distortions, Y is still Pareto efficient and lies on the utility possibility frontier U P U P. Society would still prefer to move to point X, but since any real tax/transfer system will reduce economic efficiency, point X or any other on U P U P is not attainable. The best that can actually be achieved is some point on the utility feasibility frontier, shown as U F U F in the diagram. U F U F must lie inside U P U P at all points other than Y. For the economy in diagram 10, point Z is attainable and is at a higher level of social welfare ( SW 1 ) than at Y. However, social welfare is clearly lower at Z than at X, and it is also clear that Z is not Pareto efficient in production and/or trade. This illustrates the point, absolutely crucial in policy analysis and discussion, that any real world attempt to redistribute resources in the interests of social welfare will lead to equity-efficiency trade-offs except in special circumstances. Generally, loss of efficiency is the price that must be paid for greater equity. Overall summary. A67 Economics provides rigorous definitions of four economic efficiency concepts: Exchange efficiency Technical efficiency Cost efficiency Allocative efficiency. An economy which exhibits all of these efficiency characteristics is described as Pareto efficient. Such an economy is one where it is not possible through any change in production, trade or consumption to make some members of society better off without making others worse off. A68 In theory, a Pareto efficient economy could be achieved through the operation of a central planning agency, setting, inter alia, the correct prices. In reality, such a system does not work because of the infeasibility of an agency collecting, processing and transmitting the enormous volumes of information required. xxix

A69 Adam Smith s invisible hand suggests an alternative, market-based, solution, and this has been formalised by economic theorists in the Two Fundamental Principles of Welfare Economics. The Principles are founded on the proof that a market structure termed Perfect Competition will always yield an economic outcome which is Pareto efficient. Furthermore, any desired Pareto efficient outcome can be realised through the operation of perfectly competitive markets depending only on the initial allocation of resources ( which does introduce distributional issues).though the Fundamental Principles provide very powerful arguments in favour of free markets, the assumptions of the perfectly competitive model are very stringent. Where these assumptions are not valid, there is market failure and the outcome of the economic system may not be Pareto efficient. A70 The set of Pareto efficient outcomes is in theory infinite, and society is still confronted with the choice of which of these is its preferred outcome. Particularly in terms of individual projects and programmes, welfare economics theory can provide some guidance in the form of various choice criteria; for example: The Pareto Improvement criterion: always implement programmes which yield a Pareto improvement ( that is, at least one person is better off and no one is worse off) The Potential Pareto Improvement criterion: usually implement projects which yield a potential Pareto improvement ( that is, the gainers could theoretically compensate the losers and still be better off). A71 Such criteria tend to be of more assistance in moving towards the production or utilities possibility frontiers ( which actually makes them very useful in real-world analyses), rather than choosing among points on the frontier, and in any event they do not cover all possible circumstances. A72 A complete analysis requires the introduction of a Social Welfare Function. The SWF reflects society s attitude to the differing welfare levels of each of its individual members. The precise form of the SWF cannot be derived from fundamental economic theory, reflecting as it does the moral, social and political characteristics of xxx