Question

(Hybrid Harrod-Domar-Solow Model)

An economy has a population of 2 million, the current capital stock of $6 billion, and a current GDP of $3 billion. The savings rate is a constant 8% and depreciation rate is 3%. The population growth rate is 0. Its production function is given by Y_t=A_tK_t, where Y_t denotes GDP, K_t denotes capital stock and A_t denotes productivity of capital in year t. Capital productivity will remain at its current level until the economy achieves a per capita income of $2000. Between per capita income of $2000 and $3000, capital productivity will be at a constant level, which will be 10% lower than what it is currently, owing to some natural resource (energy) constraints. Between per capita income of $3000 and $4000, capital productivity will also be at a constant level, which will be 10% lower what it would be between per capita income of $2000 and $3000. 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) 10% lower what it was for the previous range.

A) Calculate the current and future growth rates of per capita income. how will they differ?

B) What will the growth rate and level of per capita income be in the long-run?

Answer 1