Multiplier-accelerator Models on Time Scales

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.