Consider the following special case of the Malthusian model. Let N_t be population at the beginning of period t. Aggregate output in period t is given by Y_t = zN_t^0.5, where z = 1. Total population at the beginning of period 0 is 1: N₀ = 1. Population at the beginning of period t + 1 is given by N_t+1 = 1.5N_t if t < 3. However, for the other values of t, N_t+1 = 1.1N_t

1. Plot the time path of population for t= {0,1,2,3,4} (show your work and label the graph) [10 pts]

2. Plot the per-capita consumption levels for periods t= {0,1,2,3,4}. (Show your work and label the graph) [10 pts]

3. Suppose now that total factor productivity increases. How will it aect the per-capita consumption levels for the above periods? Illustrate graphically. [10 pts]