Consider a simple Solow model with no population growth and without technology, so the production function under consideration is of type y = k^1/3, by further assuming a = 1/3. Suppose that country 1 is currently in its steady-state with y₁ = y* and k₁ = k*, along with a population L₁= 0.5L. Suppose that country 2, with an identical population size of L₂ = 0.5L, is also in its steady state, albeit at a lower level. Specifically y₂ = 0.5y*

a.What are the growth rates of output for countries 1 and 2, respectively?

b.If now two countries get united into a single country with population L. Find out y, output per capita, in terms of y*, right after the unification.

c.Assuming that it would take the unified nation 10 years to grow its output per capita to its steady-state y*. Calculate the average growth rate during this 10-year period