Wonderland model

Wonderland is an integrated mathematical model used for studying phenomena in sustainable development. First introduced by (Sanderson 1994), there are now several related versions of the model in use. Wonderland allows economists, policy analysts and environmentalist to study the interactionsbetween the economic, demographic and anthropogenic sectors of an idealized world, thereby enabling them to obtain insights transferable to the real world. Wonderland is an integrated mathematical model used for studying phenomena in sustainable development. First introduced by (Sanderson 1994), there are now several related versions of the model in use. Wonderland allows economists, policy analysts and environmentalist to study the interactionsbetween the economic, demographic and anthropogenic sectors of an idealized world, thereby enabling them to obtain insights transferable to the real world. Wonderland is a compact model.In total, there are only four continuous state variables, one each for the economic and demographic sectors and two for the anthropogenic sector; thus making Wonderland more compact and amenable to analysis than larger, more intricate models like World3. For this reason it is often used as an initial testing ground for new techniques in the area of policy analysis (Lempert, et al., 2003). Denote the four state variables as: x ( t ) {displaystyle x(t)}  – population, y ( t ) {displaystyle y(t)}  – per capita output, z ( t ) {displaystyle z(t)}  – stock of natural capital and p ( t ) {displaystyle p(t)}  – pollution flow per unit of output. Let x , y ∈ [ 0 , ∞ ) {displaystyle x,yin [0,infty )} and z , p ∈ [ 0 , 1 ] {displaystyle z,pin } , then the state variables evolve in discrete time, according to the following recurrence relations (Sanderson, 1994).