Consider the simple Solow growth model without techinological progress and without population growth. Assume that the productiou fumetion has the same projerties as we assumed in class. When we look at economic data we usually find that richer individual ave a higher fraction of their income compared to poorer individuals. This problem will ask you to analyze how this will affect Suppose that there is a specific threshold level of the capital stock per worker (Nk)T, belon which individuals save a fraction is and above which individuals save a fraction s2 of their income Mathematically this translates into the following conditions: si(NK)T Note that the last two conditions represent incqualities that hold at the threshold level and do NOT represent conditions that hold for every NK ! Show graphically how the above conditions affect the Solow model! Specifically, draw the investment function, the production function and the depreciation function. Also identify clearly all possible steady states! b. For each of the steady states identify if it is stable or unstable. If the economy starts with a capital stock per worker that is smaller than (NK)T, in which steady state will the economy end up? Consider the simple Solow growth model without techinological progress and without population growth. Assume that the productiou fumetion has the same projerties as we assumed in class. When we look at economic data we usually find that richer individual ave a higher fraction of their income compared to poorer individuals. This problem will ask you to analyze how this will affect Suppose that there is a specific threshold level of the capital stock per worker (Nk)T, belon which individuals save a fraction is and above which individuals save a fraction s2 of their income Mathematically this translates into the following conditions: si(NK)T Note that the last two conditions represent incqualities that hold at the threshold level and do NOT represent conditions that hold for every NK ! Show graphically how the above conditions affect the Solow model! Specifically, draw the investment function, the production function and the depreciation function. Also identify clearly all possible steady states! b. For each of the steady states identify if it is stable or unstable. If the economy starts with a capital stock per worker that is smaller than (NK)T, in which steady state will the economy end up