Transitional dynamics, externalities, optimal subsidy, and growth

Enrique R. Casares; Lucia A. Ruiz-Galindo; María Guadalupe García-Salazar

doi:10.3934/jdg.2018005

Article Contents

2018, Volume 5, Issue 1: 41-59. Doi: 10.3934/jdg.2018005

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Transitional dynamics, externalities, optimal subsidy, and growth

Departamento de Economía, Universidad Autónoma Metropolitana-Azcapotzalco, Av. San Pablo 180, Col. Reynosa Tamaulipas, Delegación Azcapotzalco, 02200, Ciudad de México, México

* Corresponding author: Enrique R. Casares
* Corresponding author: Enrique R. Casares

Received: January 31, 2017

Revised: July 31, 2017

Published: December 2017

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Abstract

We develop an endogenous growth model with two sectors, manufacturing (learning) and non-manufacturing (non-learning). Domestic technological knowledge is only produced in the manufacturing sector through learning by doing. The knowledge produced in the manufacturing sector is available to the non-manufacturing sector. We obtain policy functions for the market economy and the social planner's economy. Thus, with the Pareto-optimal solution, we obtain the path of the optimal investment subsidy rate to the manufacturing sector for the market economy. The optimal investment subsidy rate increases as the market economy moves to the Pareto-optimal steady state.

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Mathematics Subject Classification: Primary: 49J15, 49M30, 91B62; Secondary: 49N90.

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Figure 1. The policy function $n=n(z)$, market economy with $\mu=0$.

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Figure 2. The policy function $v=v(z)$, market economy with $\mu=0$.

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Figure 3. The policy function $n=n(z)$, social planner's economy.

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Figure 4. The policy function $v=v(z)$, social planner's economy.

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Figure 5. The path of the optimal subsidy rate $\mu$.

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Figure 6. Transitional dynamics of $n$ and $z$.

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Figure 7. Transitional dynamics of $v$ and $z$.

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