Question: consider the basic solow model where for simplicity a0 1...
Consider the basic Solow model where, for simplicity, A(0) =1. Suppose the economy is initially on a BGP where the growth rate of the effectiveness of labour is zero, denoted g0 = 0. At time t1 > 0 there is a permanent rise in the growth rate of the effectiveness of labour, i.e. g1 > g0 = 0.
(a) (2 marks) Illustrate how this change affects the break-even investment and actual investment lines and steady states
(b) (3.5 marks) Find the equation for the path of ln[Y(t)/L(t)] for t < t1. Find the equation for the new BGP after the change at t1; i.e. ln[Y(t)/L(t)]* 1 for t ≥ t1. What is the difference between these two paths at t1? Find the general expression for the proportionate rate of growth of per capita output for t ≥ t1. Is this rate of growth always positive at t1 assuming that the elasticity of output with respect to capital is one-third, i.e αK(k(t1)) = 1/3