Question 3. Consider a Malthusian economy with the following aggregate production function Y = z[05N0.5 with z = 1. Let the population dynamics be N'=N()5. 1. Find the initial steady-state c*, N*, C*. 2. When z rises from 1 to 2, find a new steady-state c*,N*, C*. Interpret the results. 3. Draw a transition dynamics over time from the old steady-state in (1) to the new steady-state in (2) for consumption/output per worker, land per worker and population. Explain the short run and long run effects of a productivity increase on welfare