Open Access Open Access  Restricted Access Subscription Access

Multiplier-accelerator Models on Time Scales

Martin Bohner, Gregory Gelles, Julius Heim


In this work we derive a linear second-order dynamic equation which describes multiplier accelerator models on time scales. After we provide the general form of the dynamic equation, which considers both taxes and foreign trade, i.e., imports and exports, we give four special cases of this general multiplier-accelerator model: (1) Samuelson’s basic multiplier accelerator model. (2) We extend this model with the assumption that taxes are raised by the government and that these taxes are immediately reinvested by the government. (3) We give Hicks’ extension of the basic multiplier-accelerator model as an example and (4) extend this model by allowing foreign trade in the next step. For each of these models we present the dynamic equation in both expanded and self-adjoint form and give examples for particular time scales.


Time scales, multiplier–accelerator, dynamic equation, self-adjoint, economics

Full Text:


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information.