Quantitative Economics How sustainable are our economies by Peter Bartelmus_10

12.1 Environmental Policy Measures in General Equilibrium and Input-Output Analysis 217 Fig. 12.1 Econometric input-output model (Panta Rhei) Source: Meyer (1999), fig. 1, simplified; authorized copyright permission: European Communities. environmental concerns; it ignores produced capital maintenance cost or assumes a constant share of fixed capital consumption in GDP. GDP-based models thus assess the potential economic cost of environmental policy, rather than the sustainability of economic growth (cf. Section 8.3). Figure 12.2 shows a decrease of CO by 17% since the introduction of the eco-tax in 1999. Since 1991, the total reduction amounts to about 25% – in line with governmental targets at the time. The figure also presents a revised baseline scenario, reflecting the policy situation in 2004. This scenario assumes, among others, the introduction of EU-wide trading of capped pollution permits. As a result, Germany should be below the year 2020 target of 800 million tons of emission, set for the country by the Kyoto protocol. One of the modules added in the latest version is the material flow account. Based on export-driven demand for capital goods and diminishing effects of the unification-caused decrease of lignite production (cf. Section 6.3.2), the model predicts a relinkage of TMR with GDP increase. For the period 1991–2020 we might thus see an inverted Kuznets curve, i.e. initially falling and later increasing environmental pressure with continuing economic growth. In Factor-4 terms, the sustainability gap shown in Figure 10.2 would be widening. 218 12 Policy Analysis: Can We Make Growth Sustainable? GDP 3900 3700 3500 3300 3100 2900 2700 2500 Baseline GDP projectionn Eco-taxed GDP 1991 1995 1999 2003 2007 Fig. 12.2 Panta Rhei projections of GDP and CO emissions, Germany 1991–2007/2015 Source: Meyer (1999, 2005); authorized copyright permission: European Communitites. 12.2 Environmental Constraints and Optimality: A Linear Programming Approach The basic input-output model does not leave anything to choice and hence to optimal, cost minimizing or output maximizing, behaviour. As indicated (Section 12.1.1), the introduction of pollution control cost is bound by the (shadow-priced) equality between income and cost. Optimal behaviour is thus ‘locked’ (Dorfman et al., 1958) in the fixed-technology model, where the equality sign of Equation (10.1) ensures that output x is just enough to produce the given bill of final demand y. Relaxing this built-in condition, allows production of more outputs than necessary for predetermined y. This invites inefficiency and at the same time, opens the door 12.2 Environmental Constraints and Optimality: A Linear Programming Approach 219 to the possible increases of y, i.e. higher standards of living – indeed a more realistic assumption. To stem the risk of ‘going wild’ (Chiang, 1984) with (unlimited) final demand maximization one would have to introduce production constraints from limited availability of primary production factors such as labour and/or environ-mental source and sink capacities. This converts the basic input-output analysis into optimization under constraints, i.e. into a linear programming problem [FR 12.2]. Figure 12.3 illustrates the introduction of social and environmental constraints into the model of interdependent economic activities. Two industries of food x and shelter x production face minimum requirements for food and shelter , and maximum environmental limits for the emission of a pollutant and the availabil-ity of a natural resource . Leaving out for now the optimizing function, these lim-its can be expressed as constraints in a linear programming model: (1−a11)x1 −a12 x2 ³c1 −a21x1 +(1−a22 )x2 ³c2 ar1x1 +ar2 x2 £ xr º x− Ax³c,£ x (12.5) ap1x1 +ap2 x2 £ xp x1,x2 ³0 The restrictions delimit a feasibility space (shown in highlighted boundaries in Fig. 12.3) for different production levels and product combinations. Note that labour is not considered a limitation in this particular model. Introducing new environmentally sound technologies would change the pollution and resource use coefficients, turning and further outward. The feasibility space would increase, facilitating a greater scope and level of sustainable economic activity. We can interpret the minimum requirements for food and shelter as basic human needs of development. At the same time development is constrained by environmental Fig. 12.3 Sustainability constraints in a linear programming model Source: Based on Bartelmus (1979), fig. 1, p. 260; with permission by the copyright holder, Elsevier. 220 12 Policy Analysis: Can We Make Growth Sustainable? standards. In practice, interdependent ecological, social and demographic limits are difficult to determine. Consensus on separate limits is only a first step toward rational targets setting as targets might overlap, for instance when determining carry-ing capacities of human populations at different standards of living. The practical use of a feasibility space for economic activity is therefore questionable, especially if many more activities, outputs and standards are included. Still, Fig. 12.3 makes the vision of sustainable development visible in terms of mini-mum inner and maximum outer limits [FR 3.1]. At point N, basic human needs are just met with as the lowest acceptable amounts of total outputs of food and shelter. More importantly, the restrictions for resource availability and emissions turn the original approach of pollution abatement (Equations 12.1) into a precautionary model of producing within preset environmental capacity limits (cf. Section 13.2). The introduction of an optimizing objective function turns the constrained input-output system into a linear programming model. Figure 12.3 shows the maximum net output (for final consumption) value Z* for the (linear) objective function Z =v1x1 +v2 x2 =max (12.6) For given output weights of unit value added generated by the production of food v and shelter v , Z* represents the highest feasible Z value. This value is indeed another version of a maximum greened GDP (total gross value added), where environmental and social (basic human needs) constraints are taken into account. Introducing more than one limiting factor of production, notably produced capi-tal, calls for considering substitution in the production functions. It also opens up the possibility of reserving some output and natural resource reserves for future use, i.e. capital formation and maintenance – the next section’s topic of dynamic modelling. 12.3 Dynamic Analysis: Optimality and Sustainability of Economic Growth 12.3.1 Dynamic Linear Programming Section 12.2 introduced limits in the availability of scarce natural capital in a standard linear programming model. Overuse of natural capital, i.e. either running down natural resource stocks or degrading environmental sinks, threatens the sustainability of economic activities. The key questions, asked repeatedly in this book, are how close are these environmental constraints and when are we running out of environ-mental support functions? The urgency of immediate and radical action, evoked by environmentalists, calls for further scrutiny of the time path towards hitting potential environmental limits. Dynamic linear programming is tailored to answering these questions while adhering to the efficient (optimal) use – now and in the future – of 12.3 Dynamic Analysis: Optimality and Sustainability of Econonic Growth 221 limited produced and natural capital. The challenge is to determine what amount of produced and non-produced goods should be reserved for future use. The basic approach of dynamic linear programming is to allow for future use of outputs in the static system of equation 12.5. In principle, the use of outputs x can then take place either in the current period t or the future period t + 1 as Inputs into different industries j during the current period: x (t), or Net capital formation (including inventories of goods to be used as inputs or final consumption in future periods), increasing the capital stock of industries by K= Ki (+t 1−) Ki (t). Output xi would now have to be large enough to cover both present and future uses: xi (t)³ xij (t)+ Ki (12.7) Further assuming fixed capital requirements b per unit of output of industry j from industry i, and distinguishing final consumption c from capital formation K as components of final demand y, one can describe the dynamics of the two-commodity economy as x1 ³a11x1 +a12 x2 + K+ c1 x2 ³a21x1 +a22 x2 + K+ c2 x³ Ax+ ΔK+ c K1 ³b11x1 +b12 x2 º K³Bx (12.8) K2 ³b21x1 +b22 x2 K1, K2,x1,³x2 0 ΔK³,x 0 Having introduced a new primary factor, capital, the linear programming problem is now maximizing final demand, i.e. final consumption and net capital formation, under the restrictions of (12.8) or as its dual of minimizing capital input costs.3 Textbooks on linear programming [FR 12.2] provide proof and explanation of the weights attached in the objective functions of our model – either as shadow prices of the goods and services of final demand pi with the objective function å pi (ci + Ki )=max (12.9) or as the unit shadow cost or rent r of the use of the limited primary factor (capital) ki with the objective function of the dual årki =min (12.10) subject to prices not exceeding unit factor costs. 3 The dual of a linear programming model yields the same optimal value as the primal (in shadow or accounting prices). The dual changes a maximization problem into a corresponding minimization problem and vice versa. Again, we see here the income (factor cost) = net output identity described in Section 12.1.1 for the basic Leontief model. ... - tailieumienphi.vn