production theory and welfare economics.
4.3.2 Neoclassical economic interpretations of efficiency and insights into eco efficiency
Production theory efficiency concepts
Production theory seeks to describe the relationship between production inputs and outputs. In doing so, a focus on the efficiency of the production process is inevitable (Clarke &
McGuinness, 1987, p. 1 64; van den Broeck, 1988, p. 63). Indeed, Koutsoyiannis (1979, p. 68)
states "the basic theory of production concentrates only on efficient methods. Inefficient methods aren't used by rational entrepreneurs."
The following sections discuss three key efficiency concepts m production theory42 and
highlight their salient characteristics that could be brought to bear on a production-theory perspective of eco-efficiency. A characteristic of production efficiency concepts is that they all draw on the familiar 'useful output to input' ratio of classical thermodynamics.
Technical efficiency in production theory
Technical efficiency is concerned with the utilisation of inputs into the production process (Helm, 1 988). Economists use production functions to describe the relationship between a firm's input of productive resources (defined in contemporary economic texts (see for example Thompson & Formby, 1993) as capital, labour and natural resources) and its output of goods and services per unit time. This relationship can be expressed as:
41 These include: x-efficiency, managerial efficiency, production efficiency, technical efficiency, price efficiency, allocative efficiency, scale efficiency, scope efficiency, competitive efficiency, distributional efficiency, static efficiency, dynamic efficiency, intertemporal efficiency, profit efficiency, cost efficiency and revenue efficiency.
42 Many more efficiency concepts can be found in production theory literature including price efficiency,
managerial efficiency, scale and scope efficiency. In the interests of brevity, only the fundamental concepts of technical, production and x-efficiency will be discussed. For more detail on production theory efficiency concepts refer to Helm (1988).
Where:
l..f3 = an output from the production process;
Xi = inputs to the production process.
Equation 4-13
Technical effici�ncy measures the ratio of all inputs to total output and each input to total
output44 (Caragata, 1989, p. 20). Achieving maximum technical efficiency with a particular
technology or production recipe requires (i) obtaining the maximum output from a given combination of inputs or (ii) minimising the amount of input that is required to produce a
designated amount of output (Thompson & Formby, 1993, p. 140; Koutsoyiannis, 1979).
Consider a production unit employing variable inputs x=(Xj, . . . ,xn)ER+n in the production of outputs u=(Uj, . . . ,un)ER+m. Technology is modelled by an input correspondence u�L(u)bR/ 45
or inversely by an output correspondence X�P(X)b R+ m 46. Consider also the adjusted
production possibilities sets, or the graph of technology of the input-output vector (x,u), as defined as:
GR=[(X,U):XEL(U), uE R+m}={(X,U):UEP(X), xE R/} Equation 4_1447
Now the efficient subset can be defined as:
Eff GR=[(x,U):XEGR, (v,y)�GR, v,?u, ySx) Equation 4-15
Equation 4-1 5 can be interpreted as follows: the efficient production possibilities set Eff GR
exactly equals a situation where, if a company wanted to increase output (i.e. the new output v
was greater than u) with less input (i.e. the new input y is less than the original input, x), it could not because v and y don't belong to EffGR.
Thus, the input-output vector (x, u) is called technically efficient if and only if (x,u)EEff GR (Lovell & Schmidt, 1988, p. 7). Technical efficiency is sometimes used as a synonym for production efficiency. However, the concepts are different because the former ignores input factor costs.
43 'U' is used, rather than the conventional Q notation to avoid confusion with the thermodynamic use of
Q as heat.
44 This is analogous to the thermal efficiency ratio of useful outputs to inputs mentioned above.
45 L(u) is the subset of all input vectors capable of producing at least output vector u.
46 P(x) is the subset of all output vectors obtainable from input vector x.
47 That is, the production possibility sets exactly equals a situation where x (input vector) belongs to L(u) (the subset of all input vectors capable of producing at least output vector u) where u is a positive real
number, or where u (the output vector) belongs to P(x) - the subset of all output vector slot table from an input vector x.
There are several salient characteristics that could be bought to bear on a technical efficiency perspective of eeo-efficiency. Technical efficiency places emphasis on the production process and the importance of technology, as embodied in the production possibility set. Specifically, it focuses on those inputs and outputs that are commodified as part of the production function. A further implication from the production-function focus is its focus on direct inputs to the production process. Indirect inputs would generally not be considered in a technical efficiency analysis.
Production efficiency in production theory
The general principle in production theory is that firms aim to maximise profit (n) given i) the constraint set by factors of production (x), (ii) the production possibility set (GR) and (iii) the prices of commodities P=(PuJ,Pu2)ER+m and prices of factors of production w=(Px]'Pxl) E R/
(Koutsoyiannis, 1979, p. 104) where:
PuJ and Pu2 = the commodity prices of outputs UJ and U2 respectively;
PxJ and P xl = the prices of factors of production XJ and X2 respectively.
Consider a firm producing two products UJ and U2 using two factors XJ and X2. A firm could be said to be production efficient if it allocates its resources such that the ratio of prices of the outputs (P uJ and P u2) equals the marginal rate of product transformation for U J and Uz:
Where:
MP MP P
MRPT = x"u, X" U , =--.& u"u , MP x"U, MP x"U, P u ,
MRPTuJ.u2 is the marginal rate of product transformation of UJ and U2;
MPxJ.uz etc are the marginal products of XJ (say labour) for producing Uz.
Equation 4-16
Graphically, this is shown as the point of tangency (£) of the iso-revenue curve48 (R with slope=Pu/Pu2) and the production possibility frontier (with slope MPxJ.u/MPxJ.uz= MPx2,u/MPxz,u2=MRPTuJ,uz),
48 Locus of points of various combinations of quantities of UJ and U2 whose sale yields the same revenue to the firm.
lso-reveft\le
Figure 4-5: Graphical presentation of production efficiency
In other words, given that (x, u) EEff GR, a firm earns maximum profit (and is called
production49 efficient) if and only if:
and
where:
pT U = price vector multiplied by the outputs (revenue);
wTX = cost vector multiplied by inputs (costs).
Equation 4-17
Equation 4-18
Two key characteristics emerge that would influence a production efficiency perspective of eco efficiency. Production efficiency emphasises the profit motive of the firm engaged in production. There is also a consequent focus on the prices of inputs and outputs.
X-efficiency in production theory
The general concept of x-efficiency is defined by the outermost production possibility frontier (PPF) (Leibenstein, 1966, p. 206). When a firm sits on the outermost PPF, it is said to be x efficient.
X-inefficiency is the estimate of the 'distance' between where a firm currently operates at and the outermost production frontier (DeAlessi, 1983, p. 69; Leibenstein, 1966) (see Figure 4-6).
49 Because at point E: the firm maximises profit, this point is sometimes called profit efficiency (Lovell &
Current operating
position
Figure 4-6: Graph showing x-inefficiency as the distance between the current operating position and the outermost production possibility frontier (PPF)
The x-efficiency concept helps to describe the phenomena of why fIrms do not operate on the outer-bound of their production possibility frontier. In the context of eco-efficiency, the difference between x-efficienc
i
o and x-inefficiency could be due to waste to the environment that has not been eliminated. Such waste reduction depends, in part on managerial effIciency and, in part, on new or enhanced technological inputs (Caragata, 1 989; Helm, 1 988).Welfare economics
Welfare economics is the branch of economics concerned with discovering principles for how to use limited resources to maximise social well-being (or in economic terms, 'efficiency') (Oser
& Brue, 1 988; Stiglitz, 1988). In order to evaluate alternative economic situations, there is a need for some criterion of social well-being or welfare. Economists have suggested various criteria of social welfare at different times. For example, Adam Smith implicitly accepted the growth of GNP as a welfare criterion. Jeremy Bentham argued that welfare is improved when 'the greatest good (is secured) for the greatest number.' Modem welfare economics is mainly concerned with the examination of the allocative-efficienc
i
l criterion (Koutsoyiannis, 1979, p.524).
50 There is now considerable evidence in favour of the existence of x-inefficiency (see Frantz, 1998).
51 Also referred to as Pareto efficiency or Pareto optimality after the famous Italian economist Vilfredo Pareto ( 1 845- 1923) who "did much to help economists understand the conditions for, and the welfare significance of, economic efficiency" (Oser & Brue, 1988, p. 39 1).
Allocative ejficienci2 in welfare economics
According to this criterion, allocative efficienc
/
3 is achieved when resources are arranged such that no rearrangement of those resources can make someone better off without making another worse off (Stiglitz, 1 988, p. 63). Following standard welfare economic theory, it can be shownthat allocative efficiency requires three marginal conditions to be satisfied54:
• the marginal rate of substitution (MRS) between any two goods (Ul and U2) should be equal for all consumers (A, B ., .). That is, MRsAul.u2= MRSBul.u2;
• the marginal rate of technical substitution (MRTS) between any two inputs (Xl (say labour) and X2 (say capital)) should be equal in the production of all commodities (or, MRTSul xl,x2= MRTSu2 xl,x2)55;
• the marginal rate of product transformation (MRPT) should be equal to the MRSul,u2 for any
two goods (or MRPTul,u2= MRsAul,u2= MRSBul,u2).
Allocative efficiency is a broad term and is interlinked with other neoclassical efficiency concepts. It encompasses other notions of efficiency such as technical, production and profit efficiency (Helm, 1 988).
The standard formulation of allocative efficiency can be extended to incorporate environmental costs and benefits (the realm of eco-efficiency). Optimal allocative efficiency implicitly assumes that all benefits and costs to producers and consumers are reflected in market prices and that there is no divergence between private and social costs and benefits (Koutsoyiannis, 1979, p. 496). In other words, no external economies exist. In real world economies, environmental externalities are ubiquitous (Koutsoyiannis, 1 979, p. 541). In this context the
standard allocative efficiency criterion falls down. Economists have defined an alternative approach to addressing these externalities.
This new criterion can be developed by way of an example that demonstrates how the standard formulation breaks down, and how an amended allocative efficiency criterion could rectify the situation. Assume that commodity 'Ul' is petrol, which for simplicity is assumed to be manufactured in a perfectly competitive market. Each finn is in equilibrium when the (private) marginal cost (MCu1) equals price (Pu1)' This does not include the cost of pollution from the
52 Again, welfare economics includes many more efficiency concepts such as static and dynamic
efficiency and intergenerational efficiency in allocation of exhaustible resources. However, in the interests of brevity, only the fundamental allocative efficiency s discussed here. For a discussion of the other concepts please refer to Randall ( 1 987).
53 Allocative efficiency is what economists usually mean when they refer to efficiency (Stiglitz, 1 988). 54 Refer to any standard microeconomic text for the proofs of this (for example, Lipsey, 1983).
55 This is related to production efficiency mentioned above, since the MRTS gives the slope of an isoquant, and isoquants can be used to establish the PPF.
production or use of petrol. Suppose that the Ministry for the Environment obtains an estimate of these pollution costs. The marginal social cost (MSCuJ) is the sum of the private cost (MC�J)
and the marginal external cost (MECu]), that is
Equation 4-19
There is now a divergence between private and social costs of petrol as shown in the diagram below.
Price
Figure 4-7: An allocative efficiency criterion that explicitly accounts for positive and negative environmental externalities
Since MCu]= pu], then PuJ <MSCuJ' This implies that the allocation of resources to the production of petrol is not socially optimal since at PuJ =MCuJ, Xc is being produced rather than
XI (where PuJ=MSCu])'
Even if the price is equal to the MSC there is no guarantee that social welfare is maximised. This is because the price may be different than the social benefit. For example, consider a person using an energy-efficient vehicle and paying pu] for the petrol. By driving an energy efficient vehicle, the person produces less harmful air emissions per km of travel (ceteris paribus), thus creating a benefit to others who breathe in a less-polluted atmosphere. Since they do not pay for this benefit the marginal social benefit (MSB) is greater than pu]' Again, we have a solution that is less than the socially optimal level of petrol consumption.
The marginal social benefit curve is above PuJ at all levels of output. If consumers pay the full
MSBu], the firm would increase its output by the amount XoXz. If external costs of petrol are taken into account, the marginal cost curve would shift to MSCu]. A new equilibrium point would be reached at point E where MSCuJ=MSBuJ'
Thus, when environmental externalities exist, the criterion for allocative efficiency is equality of the MSB and MSC. In a multi-product economy the condition for optimal allocative efficiency is:
MSBu MSBn Equation 4-20
= ' = = ' = 1
MSCu, MSCu, ... MSCm
In sum, when extended to include environmental externalities, an allocative efficiency approach can be said to provide two important foci for eco-efficiency:
• a focus on the importance of allocating resources so as to maximise welfare;
• an emphasis on the importance of internalising environmental externalities into the market mechanism.
lntertemporal efficiency in welfare economics
Intertemporal efficiency addresses the question 'under what conditions do decisions of rational individuals ensure allocative efficiency for the whole economy over time' ? (Randall, 1 987). The concept of intertemporal efficiency is based on the notion that there is a trade-off between current and future consumption, and this trade-off can be shown by the intertemporal indifference curve. The intertemporal indifference curve defines the set of combinations of future and present consumption such that an individual is indifferent between any combination in the set (see Figure 4-8). A higher indifference curve (lz) implies greater satisfaction than (/1)56. Intertemporal efficiency also introduces the idea of an intertemporal budget line (or constraint), which shows the trade-off between income (or consumption) across time. Consider the two-period example in Figure 4-8 below.
o W2 8ud�t cOlISuaint .! slopc;=-( I+r)) � Y, Indirrercncc curvc 11 (stoPc=MRS.,ly2) w, Total consumption (income) in year one
Figure 4-8: Indifference curves and budget constraints used for identifying intertemporal efficiency
56 Generally, intertemporal efficiency is based on the assumption that consumers have positive time preferences (that is, where the present is valued more highly than the future). Individuals can have negative or neutral time preferences, however positive time preferences are generally accepted as the norm in neoclassical economics.
If W,= Wz this would imply that income could be transferred across time on a one for one basis. This is generally not the case because future income undergoes diminution when transferred to the present because the borrower pays interest. The slope of the budget constraint is proportional to the interest rate (the higher the interest rate the steeper the line).
If it is possible to reallocate consumption across periods, individuals would 'do so to achieve the highest indifference curve given the budget constraint. It can be shown that57 an individual will locate the trade-off of consumption at the intersection of the budget line and highest indifference curve. The necessary condition for the intertemporal efficiency of consumption is:
MRSyl.Yz=Py/PY2=( 1 +r)/l= l +r Equation 4-21
Where:
MRSYl,Y2 = the marginal rate of substitution between consumption in year one and , consumption in year two;
PYl and PY2 = the 'prices' of consumption in year one and year two respectively;
r = the interest rate.
Equation 4-2 1 gives the conditions for intertemporal efficiency for an individual transferring income using capital markets. Now consider an individual who transfers income using productive opportunities. The individual may take income and invest in productive opportunities such as land or a factory. It can be shown that the efficiency condition of an individual facing only productive opportunities is given by the intersection of the intertemporal production possibility frontier and the intertemporal indifference curve:
MRSYl.Y2=MRPTy" Y2 Equation 4-22
It follows then, that for an individual enjoying both market and productive opportunities for intertemporal transfer, the intertemporal efficiency condition is:
MRSYI.Y2=MRPTYJ,Y2=1 +r Equation 4-23
for a two-period case. In other words, an individual who enjoys both market and productive opportunities for intertemporal transfer will allocate consumption (income) across time such that their marginal rate of substitution equals their marginal rate of product transformation subject to the interest rate. Equation 4-23 is a special case of the allocative efficiency condition established above.
57 In the interests of brevity, this section does not present the detailed proofs of intertemporal efficiency. For more detail, see any standard economic text (for example Randall, 1987).
The specification of intertemporal efficiency highlights an important insight for eco-efficiency. This concept emphasises that economic agents consider time in their decisions about using natural resources and that these decisions are influenced by the interest rates. The higher the interest rates, the less likely are firms to delay their use of natural capital.
4.3.3 Assumptions underlying neoclassical economic approaches to eco-efficiency