The paper presents the positive and normative analysis of endogenous R&D investment on two types of resources: renewable and non-renewable. The specificity of the paper has to be found in the following assumption: resource-specific R&D investment allows to increase the efficiency of re- source exploitation, but the feasible efficiency improvements are globally bounded from above. We make this crucial assumption to take into ac- count the second principle of thermodynamics. It has important implica- tions for the analysis. First, the system does not admit any balanced path for the decentral- ized economy, because the growth rate in the efficiency of exploitation of any resource cannot be constant. Both effort in R&D sectors is decreasing since the marginal reward to R&D activity declines as the upper bound approaches. Second, in the decentralized economy, R&D effort is decreas- ing in the resource-specific efficiency level, because the marginal reward to R&D activity declines as the upper bound approaches. As a consequence, the share of resources devoted to R&D falls asymptotically towards zero. Third, the finiteness of efficiency improvements together with that of the non-renewable resource supply, imply that the initial conditions deter- mine the qualitative feature of the transition path. In this case, R&D firms make choices taking into account a limited time horizon since suc- cessive innovations make patents obsolete. R&D tends to concentrate in the resource sector where the demand is the largest and where the scope for efficiency improvement is the highest. When the first effect dominates, the technological gap increases, giving rise to possible unbalanced rushes of R&D on one resource. When the initial efficiency gap is favorable to the non-renewable resource, our model pre- dicts that R&D activity focuses on this resource first, causing the gap to increase. Eventually, as the growth of the resource rent reduces the com- petitiveness of the non-renewable resource, R&D focuses gradually and eventually exclusively on the renewable substitute. This development is in contrast with the qualitative features of the optimal path of technological change. Because of the limited availability of the non renewable resource, whenever efficiency improvement on this resource is worth, it is preferable from a social point of view to obtain it as soon as possible. In fact, the improved efficiency can be applied to a larger resource stock if it is obtained early rather than late. The timing and the relative size of R&D effort are typically different in the decentralized and the centralized economies.