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3 Productivity Increases in the Malthus Model (short-term dynamics) Suppose output is given by Y = z L" N' . where 21 = 1, L = 1 and a = 0.5. Let population growth be equal to N' = Ng (). Suppose g = ()" . Find Ni, Yr, C; and ci = No,li = N in steady state. Suppose there is a productivity shock so that z2 = 2. Under this new technology level, find a new steady state of N2, Y2 , Cz and (2 = ME,12 = N; 1. Calculate the initial and new steady states. You need to find N*, Y', C*, c* and l' before and after the productivity changes. 2. What changes did you find by comparing the aggregate and per-capita level variables? 3. Draw a diagram showing the transition dynamics of e and I from the initial steady state to the new steady state