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Using literature review methodology to analyze the final results and derive the logical development in Acemoglu et al. (2012), this paper is going to present detailed mathematical steps of fundamental equations to obtain the proof of the relation between directed technical change and the environmental quality. The results suggest that government can intervene the development of clean and dirty technology by implementing tax or subsidy policies which induce technology, price and market size effects and lead to the technology shift. Acemoglu et al. (2012) concluded that when the two inputs are strong substitutes and the environmental quality is sufficiently high, subsidy can be used as a temporary intervention to direct scientists towards clean innovations.
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