1 A Recursive Dynamic Computable General Equilibrium Model For ...

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Xj,k V1,j,k………………. Vn,j,k Figure B1: Schematic representation of the production nest. Mathematical derivations of linearised nested demand functions Composite Input Nest This appendix is based on the mathematical techniques provided in Dixon et al., (1992). The top nest in the tree is by definition a single production process Leontief structure. Hence, assuming rationality on the part of producers, levels demands for composite inputs are restricted by a fixed share coefficient. Composite intermediate and primary factor demands are given in equation B1: Y j, k γ j, k Z k X j, k = γ j, k = Z (B1) k where γ j,k are the fixed input-output coefficients. Linearised Leontief demands are given as: y = Zk σ Cobb-Douglas (σ=1) σ σ j, k = zk x j, k zk (B2) 56 Leontief (σ=0) Yj,k T1,j,k………………. Tn,j,k CES
Note that the absence of any price effects is due to the zero value of the elasticity of substitution. Hence, increases in output are translated as equiproportional changes in demands for each composite intermediate input which implies CRS. Assuming zero profit: P k Z k W j, kY j, k + U j, k X j, k = (B3) Substituting demands in (B1) into (B3) and simplifying: P k γ j, kW j, k + γ j, kU j, k = (B4) Linearising gives a composite price of: p k S1 , k w j, k + S2, ku 2, k = (B5) where S j,k is an output share weighted by price, where for the composite intermediate input: S γ W 1, k 1, k 1, k = (B6) γ 1, kW1, k + γ 2, kU 2, k Primary Factor Nest In the primary factor nest, production is characterised by a CRS CES function: 1 − ρ ⎡ −ρ ⎤ , = , ⎢∑δ , , , , ⎥ ⎣ = 1 ⎦ n X j k Aj k i j kVi j k (B7) i where A j,k is a scale parameter, δ i,j,k is a distribution share parameter and ρ is an elasticity parameter. Minimising cost subject to (B7) gives first order conditions: 1+ ρ − ρ n ⎡ −ρ ⎤ −( 1+ ρ ) R i, j, k = ΛAj , k ⎢∑δ i, j, kVi, j, k ⎥ δ i, j, kVi, j, k (B8) ⎣ i= 1 ⎦ 57
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A Recursive Dynamic Computable Gene
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Figure 5: The Private consumption n
Page 5 and 6: which the commodity is purchased. I
Page 7 and 8: 1.1.2 Private Final Demand In ORANI
Page 9 and 10: capital goods in industry ‘i’ i
Page 11 and 12: nesting to incorporate energy deman
Page 13 and 14: Note, that the values of the capita
Page 15 and 16: disposable income grouping. 11 Once
Page 17 and 18: equal for each using industry ‘i
Page 19 and 20: modelled as sector-wide output cons
Page 21 and 22: Spain on (i) the biophysical charac
Page 23 and 24: the crops for which data on ‘gros
Page 25 and 26: ⎡ B ⎤ AREA = 1 − ⎢ ρ ⎣C
Page 27 and 28: qo(i,r) q1lnd(FCP) q1lnd(other agri
Page 29 and 30: Given that set-aside is mainly comp
Page 31 and 32: Price Pm Pfob Expenditure E1 E0 Q m
Page 33 and 34: household income is simply the addi
Page 35 and 36: G t = I/K (22) Relating changes in
Page 37 and 38: An additional extension of this dyn
Page 39 and 40: pick up) rather than a long term st
Page 41 and 42: A proportional link between househo
Page 43 and 44: (TRANSFER(“spend”)), less socia
Page 45 and 46: downward (negative) shock in the ex
Page 47 and 48: the data base and model structure a
Page 49 and 50: Harrison, W. J., and K. R. Pearson
Page 51 and 52: Appendix A: Nesting The choice of f
Page 53 and 54: The second condition is that the ag
Page 55: Appendix B: A Linearised representa
Page 59 and 60: Rearrange (B14) in terms of v i,j,k
Page 61 and 62: t n ⎡ = y j, k − ⎢ f n, j, k
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1 A Recursive Dynamic Computable General Equilibrium Model For ...

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