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V) Consider two economies, economy X and economy Z, which share exactly the same attributes (i.e., characteristics), apart from the saving rate; in particular, economy X has a higher saving rate. In the steady state, which economy is going to have the higher output per worker, the higher growth rate of output per worker, and higher welfare for their citizens? Consider now, that they also differ in their initial stock of capital; in particular, the economy Z has a higher initial stock of capital. Does your answer now change, and why? Consider now, instead, that economy Z invests more in education than economy X. Does your answer now change, and why? Consider the Solow model in discrete time. The following system of equations fully describe the economy: n=q+n Yr = AtF(Kt:Nt) = AtKExNga I, = 3, Kt+1 = (1 5)Kt + It 5, = 31', Y defines income, C defines consumption, I investment, 5 saving, K the capital stock, N employment (or labour) and A the state of technology; 6 6 (0,1) is the rate of capital depreciation, s 6 (0,1) the saving rate and a: E (0,1) is the capital elasticity of output. The previous equations describe a closed economy with no government. We further assume no technological progress, normalising for A, = 1, and no population growth. We assume that both the participation rate (labour force over population) and the unemployment rate are constant, which means that the labour force is constant; so, N, = N