Figure 2: Dynamics of τ and k when σ < 1
The sign of this derivative depends on σ. If σ < 1, then the derivative is negative. It is
positive otherwise.
Hence, the function (24) is increasing in kt and the function (25) is decreasing in kt
if σ < 1 and increasing if σ > 1. Knowing these two functions, we can proceed to a
graphical exposition with a few examples. These examples will illustrate the dynamics of
the economy depending on different types of dictatorships.
3.3.1 Dynamics when σ < 1
If σ < 1, then the function (24) is increasing and the function (25) is decreasing. They
intersect only once at the interior steady state. This steady state is a saddle point.
24
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