In this paper, a “general equilibrium” (GE) model was developed for the allocation of exhaustible natural resources to examine the impact of different extraction scenarios on intergenerational economic welfare. A stylized GE model was applied to Israel’s natural gas (NG) market to evaluate economic indicators resulting from NG-extraction scenarios: a baseline scenario based on current policy in the NG sector, a conservative scenario based on a lower extraction rate, and an intensive scenario based on a faster extraction rate. The impact of various resource income-allocation strategies on intergenerational economic welfare was examined through the mechanism of a “sovereign wealth fund” (SWF). The results indicate that a higher NG-extraction rate combined with an appropriate investment strategy for NG profits is preferable from an economic perspective compared to a conservative rate. Investment of the government take from the NG market in research and development (R&D) of renewable electricity production can sustainably increase economic welfare.