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194 L. Bretschger Fig. 1 Trust and cycle Learning-by doing spillovers Trust 1 Capital so that the additional productivity deteriorates. Thus while the economic upswing is achieved through an increasing trust in the new paradigm, the economic downturn is due to learning about problems and misjudgements of the paradigm. Possibly, new cycles emerge during or after this process. Figure 1 shows the relationship between capital and learning graphically, during one cycle. In the following, B j denotes the size of trust in the j th cycle; it is determined by positive spillovers from capital accumulation. We have B j = 0 until a technology or policy shock occurs (which happens at K = K ¯ j). The development of B j is determined by the “trust dissemination rate” κ and the “maximum obtainable” trust ¯B j. κ reflects communication within the business community and the political sector (e.g. electronic media are assumed to increase κ). ¯B j depends on the perceived potential of the new paradigm, i.e. the productivity enhancing effect of the new cycle. κ and ¯B j together determine when the cycle ends (which happens at K = ¯K j). For simplicity, we assume B ≥ 1 below. 4 Adopting a logistic form for trust building through capital accumulation we get: so that B j(t) = max{κ · K(t) � 1 − K (t) / ¯K j (t) � , 0}+1 (12) ¯K j (t) = � 4 ¯B j − 1 � /κ + K ¯ j(t) (13) which determines the end point of cycle j and its length, see the Appendix for the derivation. In the medium run, energy and capital are assumed to be pure complements. However, energy-saving investments are now feasible. We define ˜K as: ˜K(t) = min {B(t) · K(t), D(t) · E(t)} (14) where B is given by (12) and j is omitted from now on because there is no ambiguity. D is a partial energy efficiency parameter (note that in general D �= x). With given technology (fixed D), E and B(t)K(t) are pure complements. However, substitution between D and E is possible, the substitution elasticity is unity, as usual. ˜K increases with K when E and/or D rise(s). D(t) can be increased by research investments. 4 To take B positive but smaller than unity would be feasible as well.
Sustainability economics, resource efficiency, and the Green New Deal 195 Moreover, we assume for simplicity in the medium-run analysis that the production technologies of Y and K are symmetric and of the Cobb-Douglas form. In this way, (3) can be simplified and K accumulates according to: where s is the savings rate. A(t) now reads: ¨K(t) η A(t) = Ã Z (t) 1−α ˙K(t) = s · Y(t) − δK(t) (15) (16) where ¨K is actually used capital ( ¨K < K when BK < DE) and we again divide by Z 1−α to eliminate the scale effect. During a cycle, maximum output is obtained with B(t) · K(t) = D(t) · E(t), which applies when energy supply is fully elastic. Then, the model predicts cyclical energy use. Regarding the supply of energy we argue along two possible scenarios. In regime 1 (“affluent energy”), energy supply is fully elastic at given energy prices ¯pE: pE = ¯pE (17) Growth in regime 1 is then determined by BK = DE, ˜K = BK, and ¨K = K so that we obtain: Y = ÃB α K α+η (18) ˆK = sÃB α K α+η−1 − δ (19) In regime 2 (“limiting energy”), energy supply is restricted according to: E = Ē The geometrical loci labelled with Y denote output with Y = ÃB α K α+η in regime 1 and Y depending on E in regime 2. The case for regime 1 with α + η0) shift development upward, i.e. Y = ÃB α K α+η > Y = Ã (BK) α . The cyclical impact of trust is added by the dotted semicircles above the curve. If positive learning effects are strong we may have α + η = 1 and get constant returns to capital, which leads to the solid straight line for Ys. 5 If energy is the limiting factor as in regime 2, output becomes lower (an example is given with the dashed line for Yd), with fading energy input and constant D it even approaches zero in the long run. When, in addition, temporary energy shocks in form of intensified shortages hit the economy (like in the 1970s), output 5 Trust is not added in this case but used in the following figures.
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252 R. Walz In addition to exports,
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260 R. Walz Fig. 10 Specialization
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