Environmental effects of behavior growth under green development

Abstract

This paper introduces the vitality of science and technology innovation and the ability to coordinate science and technology strength of green development, builds green innovation knowledge system, studies the new endogenous growth law driven by green innovation knowledge system under the active, conscious and autonomous practice of green low-carbon behavior has become a common form. This paper constructs a green development equilibrium model of economic system from the aspects of production, household and government intervention and discusses the relationship between economic growth and environmental quality driven by green development behavior. In the production part, the green innovation knowledge system becomes endogenous factor of production under the stimulation of vitality of science and technology innovation and integrates into the production of green low-carbon behavior goods. In the consumption part, the household utility function is given from the aspects of environmental quality, carbon emission and consumption. Through empirical analysis and research, the environmental effects which are cognitive dissonance effect and loss aversion effect can be obtained.

Appendices

Appendix

Appendix 1

According to $K = \int_{0}^{{D_{1} }} {x_{i} di}$ in Eq. (1) and according to symmetrical characteristic that $x_{i} = x,i \in [0,D_{1} ]$, then

$$K = D_{1} x$$

(60)

Substituting Eq. (60) into Eq. (1), this study can get

$$Y = A(N)L_{Y}^{\beta } e^{1 - \alpha - \beta } K^{\phi } x^{\alpha - \phi }$$

(61)

Substituting Eqs. (60) - (61) into Eq. (5), this study can get

$$w_{Y} = \beta (1 - \tau_{T} )(1 - \tau )({Y \mathord{\left/ {\vphantom {Y {L_{Y} )}}} \right. \kern-\nulldelimiterspace} {L_{Y} )}}$$

(62)

Substituting Eqs. (60) - (61) into Eq. (6), this study can get

$$p = \alpha (1 - \tau_{T} )(1 - \tau )({Y \mathord{\left/ {\vphantom {Y K}} \right. \kern-\nulldelimiterspace} K})$$

(63)

Substituting Eqs. (60 - 61) into Eq. (10), this study can get

$$r = \alpha^{2} (1 - \tau_{T} )(1 - \tau )({Y \mathord{\left/ {\vphantom {Y K}} \right. \kern-\nulldelimiterspace} K})$$

(64)

Substituting Eqs. (60 - 61) into Eq. (11), this study can get

$$\pi = (\alpha - \alpha^{2} )(1 - \tau_{T} )(1 - \tau )x({Y \mathord{\left/ {\vphantom {Y {K)}}} \right. \kern-\nulldelimiterspace} {K)}}$$

(65)

In addition, it can be proved that consumption, output, capital and technological innovation grow at the same speed in the balanced growth path (BGP).

$${{\dot{C}} \mathord{\left/ {\vphantom {{\dot{C}} C}} \right. \kern-\nulldelimiterspace} C} = {{\dot{K}} \mathord{\left/ {\vphantom {{\dot{K}} K}} \right. \kern-\nulldelimiterspace} K} = {{\dot{D}_{1} } \mathord{\left/ {\vphantom {{\dot{D}_{1} } {D_{1} }}} \right. \kern-\nulldelimiterspace} {D_{1} }} = {{\dot{Y}} \mathord{\left/ {\vphantom {{\dot{Y}} Y}} \right. \kern-\nulldelimiterspace} Y} = g$$

(66)

Equation (66) here is Eq. (30).

Appendix 2

According to Eq. (15), this study can get

$$(1 + s)p_{{D_{1} }} D_{1} ({{\dot{D}_{1} } \mathord{\left/ {\vphantom {{\dot{D}_{1} } {D_{1} )}}} \right. \kern-\nulldelimiterspace} {D_{1} )}} = w_{H} H_{1}$$

(67)

From Eq. (17) and the definition of balanced growth path, this study can get

$$r = {\pi \mathord{\left/ {\vphantom {\pi {[p_{{D_{1} }} (D_{1}^{\xi } + p_{h} )}}} \right. \kern-\nulldelimiterspace} {[p_{{D_{1} }} (D_{1}^{\xi } + p_{h} )}}]$$

(68)

Therefore,

$$p_{{D_{1} }} = {\pi \mathord{\left/ {\vphantom {\pi {[r(D_{1}^{\xi } + p_{h} )]}}} \right. \kern-\nulldelimiterspace} {[r(D_{1}^{\xi } + p_{h} )]}}$$

(69)

Substituting Eq. (69) into Eq. (67), this study can get

$$(1 + s)\frac{{\pi D_{1} }}{{r(D_{1}^{\xi } + p_{h} )}}g = w_{H} H_{1}$$

(70)

Combining Eq. (65) and Eq. (70), this study can get

$$\frac{{(1 + s)(\alpha - \alpha^{2} )(1 - \tau_{T} )(1 - \tau )YKg}}{{r(D_{1}^{\xi } + p_{h} )}} = w_{H} H_{1}$$

(71)

Equation (71) here is Eq. (31).

Appendix 3

According to Eq. (12), this study can get:

Per unit of the marginal productivity of human capital invested in emission reduction R & D and technological innovation is

$${{\partial \dot{D}_{1} } \mathord{\left/ {\vphantom {{\partial \dot{D}_{1} } {\partial H_{1} }}} \right. \kern-\nulldelimiterspace} {\partial H_{1} }} = {{\lambda_{1} \dot{D}_{1} } \mathord{\left/ {\vphantom {{\lambda_{1} \dot{D}_{1} } {H_{1} }}} \right. \kern-\nulldelimiterspace} {H_{1} }}$$

(72)

Per unit of the marginal productivity of basic scientific knowledge invested in the basic research sector is

$${{\partial \dot{D}_{1} } \mathord{\left/ {\vphantom {{\partial \dot{D}_{1} } {\partial D_{2} }}} \right. \kern-\nulldelimiterspace} {\partial D_{2} }} = {{\theta_{1} \dot{D}_{1} } \mathord{\left/ {\vphantom {{\theta_{1} \dot{D}_{1} } {D_{2} }}} \right. \kern-\nulldelimiterspace} {D_{2} }}$$

(73)

Per unit of the marginal productivity of applied scientific knowledge invested in the applied research sector is

$${{\partial \dot{D}_{1} } \mathord{\left/ {\vphantom {{\partial \dot{D}_{1} } {\partial D_{3} }}} \right. \kern-\nulldelimiterspace} {\partial D_{3} }} = {{\psi_{1} \dot{D}_{1} } \mathord{\left/ {\vphantom {{\psi_{1} \dot{D}_{1} } {D_{3} }}} \right. \kern-\nulldelimiterspace} {D_{3} }}$$

(74)

According to Eq. (18), this study can get:

Per unit of the marginal productivity of human capital invested in basic research sector is

$${{\partial \dot{D}_{2} } \mathord{\left/ {\vphantom {{\partial \dot{D}_{2} } {\partial H_{2} }}} \right. \kern-\nulldelimiterspace} {\partial H_{2} }} = {{\lambda_{2} \dot{D}_{2} } \mathord{\left/ {\vphantom {{\lambda_{2} \dot{D}_{2} } {H_{2} }}} \right. \kern-\nulldelimiterspace} {H_{2} }}$$

(75)

According to Eq. (19), this study can get:

Per unit of the marginal productivity of human capital invested in applied research sector is

$${{\partial \dot{D}_{3} } \mathord{\left/ {\vphantom {{\partial \dot{D}_{3} } {\partial H_{3} }}} \right. \kern-\nulldelimiterspace} {\partial H_{3} }} = {{\lambda_{3} \dot{D}_{3} } \mathord{\left/ {\vphantom {{\lambda_{3} \dot{D}_{3} } {H_{3} }}} \right. \kern-\nulldelimiterspace} {H_{3} }}$$

(76)

Per unit of the marginal productivity of basic scientific knowledge invested in the applied research sector is

$${{\partial \dot{D}_{3} } \mathord{\left/ {\vphantom {{\partial \dot{D}_{3} } {\partial D_{2} }}} \right. \kern-\nulldelimiterspace} {\partial D_{2} }} = {{\theta_{3} \dot{D}_{3} } \mathord{\left/ {\vphantom {{\theta_{3} \dot{D}_{3} } {D_{2} }}} \right. \kern-\nulldelimiterspace} {D_{2} }}$$

(77)

When the market is balanced, the marginal productivity of basic research sector, applied research sector, G-behavior R&D should be equal. Combining Eqs. (72 – 77), this study can get

$$\frac{{\lambda_{1} }}{{H_{1} }} = \frac{{\theta_{1} \lambda_{2} }}{{H_{2} }}\frac{{\dot{D}_{2} }}{{D_{2} }} = \frac{{\lambda_{3} \psi_{1} }}{{H_{3} }}\frac{{\dot{D}_{3} }}{{D_{3} }}$$

(78)

Eq. (78) here is Eq. (35).