A Keynesian Monetary Growth Model Under Monopolistic Competition: Is Economic Growth Sustainable Without Government Help?

Abstract

Almost every developed country experiences serious enlargement of the scale of government, specifically in the expansion of fiscal deficit s. This chapter outlines why such a phenomenon is so prominent, based on a Keynesian growth model entirely compatible with standard neoclassical microeconomics. Cost-minimizing investment plays a key role. Whenever the demand that each firm faces is constraint by effective demand (cases include the situation of monopolistic competition ), a firm strives to raise the productivity of labor and save its production costs. Since such a process continues only until costs are completely minimized, human capital investment is gradually reduced as the improvement in the production process advances. Thus, this form of investment cannot become a driving force for economic growth. As a result, and differing from the case for perfect competition analyzed in Chap. 12, ceaseless expansionary aggregate demand policy is inevitably required when seeking sustainable economic growth under monopolistic competition.

Keywords

Mathematical Appendix

This appendix establishes the local stability of the economy around a stationary state. On the aggregate demand curve (Eq. 13.18), the following relationship holds at the vicinity of a stationary state $({{\rho }^{*}},{{{\tilde{y}}}^{N*}},{{L}^{s*}})$:

$$ \begin{aligned}<Para>& [s(\rho)\tilde{y}_{t}^{N}-m ]-[s({{\rho }^{*}}){{{\tilde{y}}}^{N*}}-m ]={{I}_{t}}\\ <Para>& =\left[L_{t}^{S}-{{L}^{s*}}\right]-[L_{t-1}^{S}-{{L}^{s*}}]=\left[\frac{\partial I}{\partial \rho }\frac{\partial \rho }{\partial L_{t-1}^{S}}+\frac{\partial I}{\partial \tilde{y}_{t+1}^{N}}\frac{\partial \tilde{y}_{t+1}^{N}}{\partial L_{t-1}^{S}}+\frac{\partial I}{\partial L_{t-1}^{S}}\right][L_{t-1}^{S}-{{L}^{s*}}]+o[[L_{t-1}^{S}-{{L}^{s*}}] ]. \\ <Para>\end{aligned} $$

Note that $I(\cdot)$ is equal to zero at any stationary equilibrium.

If:

$$ -1<\frac{\partial I}{\partial \rho }\frac{\partial \rho }{\partial L_{t-1}^{S}}+\frac{\partial I}{\partial \tilde{y}_{t+1}^{N}}\frac{\partial \tilde{y}_{t+1}^{N}}{\partial L_{t-1}^{S}}+\frac{\partial I}{\partial L_{t-1}^{S}}<0, $$

(13.20)

then also from Fig. 13.3 it is clear that $L_{t}^{S}\to {{L}^{S*}}$ when $t\to \infty$. This implies that:

$$ s(\rho)\tilde{y}_{t}^{N}\to s({{\rho }^{*}}){{\tilde{y}}^{N*}},{{I}_{t}}\to 0 $$

.

Thus $s(\rho)\frac{\tilde{y}_{t}^{N}}{L_{t}^{S}}+{{I}_{t}}\to s({{\rho }^{*}})\frac{{{{\tilde{y}}}^{N*}}}{L_{{}}^{S*}},$ when: $t\to \infty$.

That is, Eq. (13.20) is the local stability condition of a stationary equilibrium. The condition in Eq. (13.20) implies that although the indirect effects of a change in the dexterity via the inflation rate, $\rho$ and real NDP, ${{\tilde{y}}^{N*}}$, exist, the direct effect is that the efficiency of cost-reduction measures declines along with progress in developing dexterity, $\frac{\partial I}{\partial L_{t}^{S}}$, dominating the aforementioned effects.