Romer Model Consider an endogenous growth model with the following equations.
Yt = AtLyt (1)
At+1 = At + zAtLat (2)
(1 - l)N = Lyt (3)
lN = Lat (4)
A0 > 0 (5)
1. Use equation (2) to solve for the growth rate of technology ga Your answer should only include l, z, N
2. Use your answer in part (a) and A0 to write an equation that determines what At would be for any time t.
3. Sub in equation (3) into equation (1) and use your answer to part (b) and write down Yt in terms of A0, z, l, and N.
4. Notice that Y grows at a constant rate through time if all parameters in the model remain constant. Suppose that at time t1 the government encourages workers to switch from non research jobs to research jobs. (Increasing l). Graph the time path of ln(Y ) if such a policy was put into effect.