A Malthusian Model with Endogenous Productivity Growth (60 points) following equation: Let us consider that the law of motion of the aggregate...

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I.A Malthusian Model with Endogenous Productivity Growth (60 points)following equation:Let us consider that the law of motion of the aggregate population can be described by theNI+1 = () NEwhere o > 0 and EE(0,1) are parameters, N, represents the aggregate population at time t, andy, denotes the income per capita at time t defined as:yt =N.The aggregate level of output at time t can be described by the following aggregate Cobb-Douglas production function:Yt = AtX*<Lt-oxwhere @=(0,1), At stands for the productivity level at time t, X denotes a fixed stock of land usedin agriculture and Lt represents the aggregate population of worker which is a fraction BE(0,1) ofthe aggregate population:Lt = BN.Let x, stand for the land per capita at time t defined as:XProductivity depends on the size of the aggregate population:At = ZN!