The objective of this study is to propose an extension of the Fullerton and Ta (2019) model, who show that their simple general equilibrium model generates comparable results to those yielded by large computable general equilibrium models. We propose key extensions that are relevant for climate policy analysis, in particular, for countries with significant net emissions coming from agriculture. We add timber production as another sector and land as another production factor, and analytically find the closed-form solution for the general equilibrium. We present an application calibrated to 2019 Uruguayan data, and implement the CO-neutral scenario of its 2050 Climate Change Long Term Strategy (LTS) submitted to the UNFCCC, which targets a CO net-zero economy by 2050. It requires a sharp reduction in fossil fuels demand, an increase of electricity demand to compensate the reduction of energy demand, a moderate increase in forestry area driving CO sinks, and a moderate increase in livestock productivity that reduces the CO emissions per unit of output. We assess the impacts on some key macroeconomic variables. Results show that the LTS CO-neutral scenario implies a cumulative impact on GDP level through 2050 of 0.01% or −0.73% depending on the set of policy instruments used. But considering that the time horizon is of about 30 years and assuming that the impact is equally distributed over time, it implies that the GDP growth rate remains almost unchanged relative to the baseline scenario. Therefore, this LTS, which implies drastic changes in the energy supply composition, implies only mild changes in GDP, but strong reductions on net CO emissions.