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Homework answers / question archive / Consider a Solow economy with the following production function F(K, N) = 2K1/3N2/3 and parameters 0! = 0
Consider a Solow economy with the following production function F(K, N) = 2K1/3N2/3 and parameters 0! = 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 71 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). 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. 3. Find 13* the steady state per-capita capital stock, consumption per capita (c*) and output per capita (y*). 4. Show that in the steady state, the pOpulation grows at a constant rate. What is this rate?
