in this study, i.e., when the food crop yields are perfectly anticipated. Specifically, it shows three scenarios, where the value of the crop technology index corresponds to (i) expected values of the stochastic crop productivity index (deterministic-baseline scenario), (ii) the most pessimistic climate and bad technology states (deterministic-pessimistic scenario), and (iii) the most optimistic climate and good technology states (deterministic-optimistic scenario). The right-hand side of Figure 3 shows the di↵erence range between the 1,000 simulation paths based on di↵erent ex-ante realizations of the stochastic crop productivity index and the deterministic-baseline path. The 10%, 50% and 90% quantile lines represent 10%, 50% and 90% quantiles of 1,000 simulated values respectively at each time, and the average line (the “+” line) represent the average of 1,000 simulated values respectively at each time. The right-hand side of Figure 3 also shows two extreme cases of optimal land-use paths conditional on period _t_ realizations of crop productivity index states _At_ ( _J_ 1 _,t, J_ 2 _,t_ ). The realized crop productivity index always takes the highest possible value in a _stochasticoptimistic_ case (the line of squares), and the lowest possible value in a _stochastic-pessimistic_ case (the line of marks). As future realizations of the stochastic crop productivity index are uncertain, these extreme stochastic solutions are not the same as the corresponding deterministic solutions, where the values of future crop productivity index are known with certainty. In the stochastic-optimistic case, for example, potentially lower realizations of future crop productivity index result in larger current-period agricultural land allocation as compared to the deterministic-optimistic solution. For other model variables, due to resource limits (e.g., the total land area is unchanged over time) and other constraints, the impact of uncertainty is theoretically difficult to assess.

We start with the left-hand side of panels (a)-(e) of Figure 3 that shows the optimal land use paths under the perfect foresight. Beginning with the description of the baseline scenario we see that, in the first half of the coming century, the area dedicated to food crops increases by 350 million hectares or 22 percent compared to 2004, reaching its maximum of 1.88 billion hectares around mid-century (panel a). Continuing population growth, intensification of livestock production, and increasing demand for food, stemming from economic growth are the key drivers for this cropland expansion. In the second half of the coming century, slower population growth, and technology improvements in crop yields and food processing result in a smaller demand for cropland. By 2100 cropland area declines significantly relative to its peak value, falling to 1.45 billion hectares, which is, 6 percent smaller than in 2004. In the first half of the coming century land allocation for the second-generation biofuels is close to zero (panel b). Consistent with the recent analysis of 2G biofuels’ deployment potential (National Research Council, 2011), absent aggressive GHG regulations and biofuels’ policies, this technology is suboptimal because of low extraction and refining costs of fossil fuels and high production and deployment costs of the second-generation biofuels. In the second half of the coming century, the second-generation technology becomes viable, as fossil fuels become scarce and costs of producing the second-generation biofuels decline. This results in greater land requirements for the second-generation biofuels crops. By the end of the coming century, agricultural land dedicated to the second-generation biofuels crops adds 500 million hectares. Consistent with recent trends, global pasture area declines throughout the entire century (panel c), reflecting increased substitution of pasture land for 16