The Existence and Persistence of Cycles in a Non-linear Model: Kaldor's 1940 Model Re-examined

Abstract

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Bridging the Gap between Economic Modelling and Simulation: A Simple Dynamic Aggregate Demand-Aggregate Supply Model with Matlab

“…Contrary to many business cycle studies (e.g., [6][7][8][9][10][11][12]), the absence of nonlinearity in our simpler setup rules out the possibility of limit cycles and other more complex economic behaviours (typically, a Hopf bifurcation requires the branching from an equilibrium into a periodic orbit. Here, we use the term "Hopf" just to highlight the fact that a fixed point looses stability as the eigenvalues of the Jacobian at the fixed point cross the imaginary axis of the complex plain).…”

“…After a permanent increase in the government spending and permanent decrease in the tax rate at the initial time 0 , the economy must jump up to a higher level output. This is given by the AD curve in (8). At 0 , real output jumps to a new level 0 = 2.0799 (this result is given by the new initial condition 0 from the output in the command window from Matlab.…”

Continuous Hicksian trade cycle model with consumption and investment time delays

“…Chang and Smyth (1971) applies the Pointcare-Bendixon theorem to prove the existence of a Kaldorian limit cycle. Lorenz (1993) deals with a continuous Kaldor model to obtain a Hopf bifurcation to a limit cycle.…”

First-passage time for stability analysis of the Kaldor model

“…Chang and Smyth [2] and Varian [3] translated KaldorÕs trade cycle model into more rigorous context: the former into a limit cycle and the latter into catastrophe theory. Output, as we saw via the theory of the multiplier, responds to the difference between savings and investment.…”