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Question 4 : Solow Model combined with the Malthusian Model [20 marks] Consider a Solow economy with the following production function F(K, N) = zKl/3N2/3 and parameters d = 0.05, s = 0.2, N0 = 100 and z = 1.0. Suppose K = 300 in period 0 and the unit period is one year. In contrast to the standard Solow model, we assume that the population growth rate n is no longer exogenous but rather endogenous and determined by (1 + n) = N'/N = 9(C/N) = (C/N)3 as it is the case in the Malthusian model. 1. Determine the dynamics for the per worker capital (k). [05 marks] 2. Determine the per capita quantities k,y,c and the aggregate quantities K, C and Y of the capital stock, consumption and output for years 1, 2 ,3, 4 and 5. Summarize your results using a table. [05 marks] 3. Find k* the steady state per-capita. capital stock, consumption per capita (c*) and output per capita (y*). [07 marks] Note: You can use an online solver if you face an equation that is too difcult to be solved manually. You can nd some free online solvers here https: / / www.wolframalpha.com / calculators / equation-solver-calculator https: / / www.symbolab.com / solver / precalculus-solveforequation calculator. 4. Show that in the steady state, the pOpulation grows at a constant rate. What is this rate? [03 marks]