Answer Happy

Q7. (40 pts) Consider the Solow model with population growth for country X and Z. Ax and Az represent fixed level of human capital for country X and Z. Ax, Az, 8, sx, sz, nx, and nz are exogenous variables. Country X Country Z Production function: Yx,t = AxKxN Production function: Yz,t = AzKN/₂ Z,t Saving Rate: sx Saving Rate: sz Depreciation rate: 8 Depreciation rate: 8 Population growth rate: nx Population growth rate: nz (a) For country X, derive the steady-state levels of output per worker y, capital per worker k, and consumption per worker cx in terms of the level of human capital Ax, the saving rate sx, population growth rate nx and the depreciation rate d. (Superscript * indicates variables at steady state) (b) For country X, if the population growth rate nx increases, what happens to output per worker yx,t, capital per worker kx,t, and consumption per worker cx,t
at steady-state? Use a diagram to illustrate your result. [Hint: think about the diagram with capital per worker kx,t as the horizontal axis and investment per worker ixt as the vertical axis]. (c) Country X reaches the steady state. Suppose there is a permanent increase in the level of human capital Ax, draw diagrams to show how capital per worker kx,t, output per worker yx,t, and the consumption per worker cx,t should respond [Hint: using time as the horizontal axis]. (d) For country X, derive the golden rule saving rate s. gr (e) Suppose these two countries have not reached their steady states. Given that At year t, the capital per worker in country Kx,t Kz,t or kx,t < kz,t < k*). At year t, Nx,t Nz,t nx nz, Ax < Az and sx = sz. X is smaller than country Z (i.e. which country's output per worker should be higher? Which country's output per worker growth rate should be higher? Use a diagram to illustrate your results. = =