Producción Científica Integrated Assessment Models provide a framework to study sustainability transitions and their economic impacts. Models seldom consider energy constraints, taking supply availability for granted and thus suggesting a mere change in the energy mix from non-renewables to renewables. In order to address these limitations, a macro-economic module within a broader system dynamics model (MEDEAS) has been developed. The model has been run for the whole world from 1995 to 2050 under three different scenarios: Business as Usual (BAU), considering no further transition policies and keeping current trends; Green Growth (GG), undertaking the low-carbon transition according to the Paris Agreement set of policies and with high GDP growth standards; and Post-Growth (PG), testing the sustainability transition under a GDP non-growth/degrowth approach. The results reveal the conflict between economic growth, climate policy and the sustainability of resources. Whereas a BAU approach would not even be an option to achieve climate goals, a GG view would not only face the downsizing of economic output, but neither would it be able to achieve the 2 °C objective. The success of the PG approach in meeting emissions objectives suggests a redirection from economic growth policies to an industrial policy that incorporates efficiency and redistribution. European project H2020-LCE-2015-2 (691287) Ministerio de Economía, Industria y Competitividad (Project ECO2017-85110-R)