Political Rents, Promotion Incentives, and Support for a Non-Democratic Regime

At Na = 0, (21) collapses into aLFL/F² and therefore X'(Na) >0 at low levels of Na.. Since the
factor in round brackets is negative and the second term increases in absolute value with an
increase in Na, X"(Na ) < 0.²²

A typical configuration of X(Na) and Y(Na) for this specification is presented in Figure
2. The number of activists in equilibrium is determined by the intersection of the two curves.
A change in the parameters that leads to an increase in N_max = KNT>^r∆R causes a rightward
shift of Y(Na) and consequently an increase in the optimal number of activists. The position of
X(Na) is affected by the changes in labor and capital employed in the economy. To determine
how, let us consider the derivatives of X(Na) with respect to capital and labor. The position of
X(Na) depends on the elasticity of output with respect to labor input FL L/F. If the production
technology has unitary elasticity of substitution between labor and capital, FL L/F does not
depend on factor proportions.²³ If the elasticity of substitution is less than unity, then FL L/F
increases and X(Na) curves fan out as the capital-labor ratio increases. Since less-than-unitary
elasticity of substitution is the only practically relevant possibility on the macroeconomic

level,²⁴ we can expect:

²² The second term may exceed FL to the right of some point N^{^}. In that region, X(Na) bends down.
Alternatively, X'(Na) may remain positive as Na → ∞. In both cases, X(Na) is concave.

²³ X(Na) = aNa (1 - α)∕(1+ aN_a ) in the case of Cobb-Douglas production function, where α is the
capital share.

²⁴ Numerous empirical studies show that the elasticity of substitution between labor and capital is
typically less than one for most modern economies. In particular, this applies to the Soviet economy.
See further discussion in Section 4.1.

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