Abstract
The relationship between economic growth and environmental degradation has been central to the debate over sustainable growth. This paper uses utility growth as an index of sustainable growth, which is positively related to economic growth and negatively related to environmental degradation. Skilled and unskilled labor are used in this economy and the population is growing over time generating growth without scale effects. The pollution growth rate is higher in a decentralized economy, whereas the sustainable growth rate is higher in an economy with a social planner. An increased rate of population growth is associated with a higher sustainable growth rate in both economies. A higher share of skilled labor is associated with a higher sustainable growth rate in a decentralized economy, while the effect of a higher share of skilled labor is ambiguous in an economy with a social planner.
Funding statement: This work was supported by the Beijing Social Science Fund; [14JGC119].
Acknowledgments
We are indebted to two anonymous referees for valuable comments and suggestions. Xiangbo Liu acknowledges the research support by the Beijing Social Science Fund (Grant no. 14JGC119).
Appendix
A Equilibrium Solution
The current-value Hamiltonian function is:
where
The first-order conditions are:
The growth rate of technology
Substituting
B First-Best Solution
Consider the current-value Hamiltonian:
where
The first-order conditions are:
and,
The growth rates of technology, consumption and pollution emissions are constant along the balanced growth path. Taking logarithms and differentiating eqs (62) and (63) with respect to time, we have
C Second-Best Solution
Consider the current-value Hamiltonian:
where
The first-order conditions are:
and,
Using these first-order conditions, we can solve for eqs (47)–(51).
D Comparative Statics
We have derived the long-run growth rate of technology growth, the growth rate of pollution emissions and the sustainable growth rate of the economy under three different settings: the equilibrium, the first-best and the second-best. Table 1 can be used to show the effects on these growth rates when population and skilled labor change.
Growth Effects of Changes in Population and Skilled Labor
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