An economy has a population of 2 million, current capital stock of $10 billion, and a current GDP of $8 billion. The savings rate is a constant 10% and the depreciation rate is 5%. The population growth rate is 0. Its production function is given by Yt = AtKt, where Yt denotes GDP, Kt denotes capital stock and At denotes productivity of capital in year t. Capital productivity will remain at its current level until the economy achieves a per capita income of $5000. Between per capita income of 5000 and $6000, capital productivity will be at a constant level, which will be 20% lower than what it is currently, owing to some natural resource (energy) constraints. Between per capita income of $6000 and $7000, capital productivity will also be at a constant level, which will be 20% lower what it would be between per capita income of $5000 and $6000. And so on: for every successive range of per capita income of a thousand dollars, capital productivity will be constant at a level which is) 20% lower what it was for the previous range. Calculate: (You must show all the calculations) 1. At 2. Current growth rates of p.c.i (p.c.i is between $4000 to $5000) 3. Growth rates of p.c.i. (p.c.i is between $5000 to $6000) 4. Growth rates of p.c.i. (p.c.i is between $6000 to $7000) 5. Growth rates of p.c.i. (p.c.i is between $7000 to $8000)