Scenarios are among the most visible and widely used products of the IPCC. Many kinds of scenarios are used in climate research, but emissions scenarios and the socio-economic assumptions that underpin them have a distinct status because the IPCC orchestrated their development. They have evolved from assessment cycle to assessment cycle and serve as ‘boundary objects’ across Working Groups and as instruments of policy relevance. The field of Integrated Assessment Modelling has emerged to produce these scenarios, thereby taking centre stage within the IPCC assessment process. Because these scenarios harmonise assumptions about the future across disciplines, they are essential tools for the IPCC’s production of a shared assessment of climate research and for ensuring the policy relevance of this assessment. Yet, the reliance on a relatively small set of complex models to generate scenarios spurs concerns about transparency, black-boxed assumptions, and the power of IAMs to define the ‘possibility space’.

This chapter discusses various applications of the analytical framework here. First, we identify the Lindahl tax that serves as the fourth component adding to the triangular equivalence relationship. Under the Lindahl tax scheme, the Cournot-Nash equilibrium of SEEN or DEEN model renders the Lindahl equilibrium without transfers. We examine the quantity tools as well. To showcasing the relevance and importance of the theory in empirical works, we solve the Lindahl equilibrium without transfer and coalitional solutions in the influential RICE model. Lastly, we analyse the one-directional externality problem in a water pollution model. All cases of applications are supplemented with programming codes and/or numerical results.