## 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

- Keynesian growth model
- Scale of government
- Fiscal deficits
- Cost-minimizing investment

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- 1.
For simplicity, it is assumed that the disutility of labor increases proportionately to the level of dexterity that an employee possesses.

- 2.
- 3.
For a more rigorous solution method, see Chap. 12.

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## Mathematical Appendix

### 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 \(({{\rho }^{*}},{{{\tilde{y}}}^{N*}},{{L}^{s*}})\):

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

If:

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

.

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.

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Otaki, M. (2015). A Keynesian Monetary Growth Model Under Monopolistic Competition: Is Economic Growth Sustainable Without Government Help?. In: Keynesian Economics and Price Theory. Advances in Japanese Business and Economics, vol 7. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55345-8_13

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DOI: https://doi.org/10.1007/978-4-431-55345-8_13

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