Q7. (40 pts) Consider the Solow model with population growth for country X and Z. Ax and Az represent fixed level of hum

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Q7 40 Pts Consider The Solow Model With Population Growth For Country X And Z Ax And Az Represent Fixed Level Of Hum 1 (127.1 KiB) Viewed 20 times

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, d, sx, sz, nx, and nz are exogenous variables. Country X Country Z Production function: Yxt = AxKN | Production function: Yz,t = Az K2 Nº Saving Rate: 8x 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 yx, capital per worker ky, 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 6. (Superscript indicates variables at steady state) (b) For country X, if the population growth rate nx increases, what happens to output per worker yxt, capital per worker kxt, and consumption per worker cx,t 3 at steady-state? Use a diagram to illustrate your result. [Hint: think about the diagram with capital per worker kx, as the horizontal axis and investment per worker ix, 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 kxt, output per worker yx,t, and the consumption per worker cx, should respond [Hint: using time as the horizontal axis]. (d) For country X, derive the golden rule saving rates. (e) Suppose these two countries have not reached their steady states. Given that nx = nz, Ax = Az and sx = sz. At year t, the capital per worker in country X is smaller than country Z (ie. Kx. <Kzt or kx,t < kz,t < k*). At year t, 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. Kx,t Nx,t