Fig. 1

Efficient schedules when technologies progress once. Note that $\delta =0.05$, ${\lambda }_{30}^1=5$, $k=0.5$, $a=25$, $b=0.5$, $A=250$, $\alpha =2$, $\beta =0.5$, $\gamma =0.5$ for all scenarios. a Time paths for the resource price when technology changes once every 15 years. In the no progress scenario, $z_t^1=z_t^2=1$ for $t\in [0,29]$. In the extraction progress scenario, $z_t^1=1$ for $t\in [0,14]$, $z_t^1=10$ for $t\in [15,29]$ and $z_t^2=1$ for $t\in [0,29]$. In the exploration progress scenario, $z_t^1=1$ for $t\in [0,29]$, $z_t^2=1$ for $t\in [0,14]$ and $z_1^2=10$ for $t\in [15,29]$. b Time paths for the marginal revenue of resource extraction for the same parameters as used in a. c Time paths for explorative efforts for the same parameters as used in a