By Prof. Dr. Günter Gabisch, Dr. Hans-Walter Lorenz (auth.)
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Extra resources for Business Cycle Theory: A Survey of Methods and Concepts
Further extensions of these two basic models of the interaction between the multiplier and the accelerator are easy to perform. Possible variations are, among others, the case of growing autonomous investment, If = I8ert, T > 0, extended consumption lags, C t = Co + C1Yt - 1 + C2Yt-2, the introduction of governmental activities, etc. 3. The Influence of Inventories The models of Samuelson and Hicks are definitely very simple macroeconomic models, as they operate only with consumption and net investment in the capital stock.
Let autonomous investment be constant over time: If = Ia = constant. 1 Introductions to the mathematics of difference and differential equations can be found in Allen (1965,1967), Dernburg/Dernburg (1969), and Baumol (1958), who also elaborate on several of the older models presented here. The more mathematically interested reader is referred to Coddington/Levinson (1955) and Boyce/ DiPrima (1977). Chapter 3 38 Induced investment is assumed to behave according to the acceleration principle. e. ) but on the changes of these variables in the past.
Chapter 3 58 The roots are >'12= - a(l - c) + (3 - a(3v ' 2 ± V(a(l- c) + (3 - a(3v)2 - 4a(3(1- c) 2 . 10) such that the roots are either both positive or both negative. 11) holds. 7) converges to the particular solution Y* as long as the real parts of the characteristic roots are negative, it follows as a condition for damped monotonic behavior 16 0> -(a(l - c) + (3 - a(3v) va(3 < a(l - c) ==:;. + (3. Alternatively, as long as va(3 > a(l - c) + (3, the system will monotonically move away from the stationary equilibrium.
Business Cycle Theory: A Survey of Methods and Concepts by Prof. Dr. Günter Gabisch, Dr. Hans-Walter Lorenz (auth.)