By Dr. Shinichiro Nakamura (auth.)
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Additional info for An Inter-Industry Translog Model of Prices and Technical Change for the West German Economy
2). 26). 25) are necessary and sufficient for the consistency of the three stage optimization procedure. 2. 31c) XX sj = (xXm+e+1j, ... 32) i,jE I, , , where Vj = (Pmj'Pej,Psj,Pkj,Plj) (PPm+1 j , .. 29). One remarkable feature of this three stage optimization procedure is that with the advance of stages (from the first to the second, and from the second to the third stage) the degree of decentralization and the number of parameters used in solving the optimization procedure increases 1 ). 30» the degree of decentralization is null and the number of parameters is six (five elements of V, and x,).
4 price aggregator functions are indicated below the lines connecting aggregates and variables to be aggregated. 8] has shown that homothetic weak separability of fj with respect to Nand N is necessary and sufficient for the price aggregates, PP1j,···,PPnj' Pmj' Pej' Psj' and the quantity aggregates, xx 1 ]" ••• ,xxn]" xmj ' x ej ' x sj ' derived above to satisfy the condition of additive price aggregation (APA). 4 The Dual Structure of Production Pmj Gmj PP1j g1j PP 2 j g2j PPmj gmj PPm+1 j Pj Q.
M]. ]_o Cl 2lnQJ' dlnG. dIng k . ·x. 38e) v lj = Psj °Xsj pjOX j PkjOXkj pjOX j PljOX lj p. ox. J J CllnQ. = Clln J P sj , CllnQ. = Clln J Pkj , alnQ. = Clln J P lj , j E I. 39) B1ij - ~ , iEJ, jEI. We refer to B1 .. as the bias of technical change for ~J input i at the first stage. If B1 .. > 0, the value share ~J of aggregate input i increases at constant prices of five aggregates: technical change at the first stage is input i-using. If B1ij <0, the value share of aggregate input i decreases at constant prices of five aggregates: technical change at the first stage is input i-saving.