Anthropocene Age Economics

Abstract

In this chapter, the book presents the public policy implications of the unified theory. What choices does human society have in the Anthropocene age? In order to answer this question, this chapter constructs a final and policy-oriented evolutionary model (IV). It is also testable. Public policies will be derived from this empirically validated model; hence, they will be science-based policies.

Appendix: The Evolutionary Model IV

The set of relations established in the text can be summarized by the following set of equations. Equations (6.3), (6.4), (6.5), (6.6), and (6.7) are the structural equations of the model, Eq. (6.8) is the reduced form, Eq. (6.9) shows the dynamic trajectory of the endogenous variable, and Eqs. (6.11) and (6.12) resolve the changes in the trajectory due to change in the exogenous variables.

Symbols

QoS: quality of society; y: per capita income or output per worker; D: degree of income inequality; Π: concentration of pollution in atmosphere; r: growth rate of per capita income; λ: parameter of income inequality, increases with income redistribution policies; τ: technology parameter, increases with mineral resource saving innovations.

$$ QoS=F\left(y,D,\varPi \right),{F}_1>0,{F}_2<0,{F}_3<0 $$

(6.3)

$$ D=g\left(y,\lambda \right),{g}_1>0,{g}_2<0 $$

(6.4)

$$ \varPi =h\left(y,\tau \right),{h}_1>0,{h}_2<0 $$

(6.5)

$$ QoS=F\left(y,g\left(y,\lambda \right),h\left(y,\tau \right)\right)=G\left(y,\lambda, \tau \right) $$

(6.6)

$$ y(T)=f\left(T,r,{y}_0\right),{f}_1>0,{f}_2>0,{f}_3>0 $$

(6.7)

$$ QoS(T)=H\left(T,r,\lambda, \tau \right), $$

(6.8)

• H ₁ > 0 for T < T ^′ and H ₁ < 0 for T > T ^′

• H ₂ > 0 for T < T ^′ and H ₂ < 0 for T > T ^′

• H ₃ > 0

• H ₄ > 0

$$ {\displaystyle \begin{array}{c}\partial QoS/\partial T={H}_1=\left[{F}_1+{F}_2\ {g}_1\left(y,\lambda \right)+{F}_3\ {h}_1\left(y,\tau \right)\right]{f}_1\\ {}\kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \ \ \left[\left(+\right)+\left(-\right)\left(+\right)+\left(-\right)\left(+\right)\right]\left(+\right)\end{array}} $$

(6.9)

Thus, H ₁ > 0 for T < T ^′ and H ₁ < 0 for T > T ^′

$$ {\displaystyle \begin{array}{c}\partial {H}_1/\partial r=\left[{F}_1+{F}_2\ {g}_1\left(y,\lambda \right)+{F}_3\ {h}_1\left(y,\tau \right)\right]{f}_{12}\\ {}\kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \left[\left(+\right)+\left(-\right)\left(+\right)+\left(-\right)\left(+\right)\right]\left(+\right)\end{array}} $$

(6.10)

Thus, ∂H ₁/∂r > 0 for T < T ^′ and ∂H ₁/∂r < 0 for T > T ^′

$$ {\displaystyle \begin{array}{l}\partial {H}_1/\partial \lambda ={f}_1\ {F}_2\ {g}_{12}>0\\ {}\kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \left(+\right)\left(-\right)\left(-\right)\end{array}} $$

(6.11)

$$ {\displaystyle \begin{array}{l}\partial {H}_1/\partial \tau ={f}_1\ {F}_3\ {h}_{12}>0\\ {}\kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \left(+\right)\left(-\right)\left(-\right)\end{array}} $$

(6.12)