Let us consider a Malthusian economy in which the aggregate level of output at time t can be described by the following aggregate Cobb-Douglas production function: Yt = At X* N] -x where aE (0,1), At denotes the productivity level at time t, X > 0 stands for a fixed aggregate stock of land used in agriculture and Nt represents the aggregate population. Let us assume that productivity grows at a constant rate ac (0, 1). At+1 - At _ a At Let xt stand for the land per capita at time t defined as: X Xt = 7 Nt At time t, let us consider that the birth rate: bt and the death rate: dt can be written as: bt = B ( yt ) = dt = 1 - 8(yt) where B, 8 > 0, EE (0,1) are parameters and yt denotes the output per capita at time t defined as: Yt yt = Nt