Suppose that the production function is Y = AKIN and that 8% of capital wears out every year, which means d = 0.08. Assume that the rate of growth of the population is 2% and the saving rate is 20%, which means n = 0.02, s = 0.2. Total factor productivity A = 2. (a) (5 points) What is the steady-state capital per worker, k.,, the steady-state output per worker, y.s, the steady-state consumption per worker, c.,, and the steady-state investment per worker, i..? (b) (5 points) What is the steady-state growth rate of the capital per worker, k,,, and the steady-state growth rate of the output per worker, y.s? And what is the steady-state growth rate of the capital stock, K.s, and the steady-state growth rate of the aggregate output, Y.,? Show your process. (c) (5 points) What is the golden rule savings rate s*? Can the country increase the consumption per-capita by changing the saving rate? Discuss both the steady-state and transitional dynamics. (d) (5 points) We call the level of capital per capita &* given the golden rule saving rate s* the golden rule level of capital. Based on part (c), what is the the golden rule level of capital k*? Now assume that there is no population growth, i.e. n = 0. What is the the golden rule level of capital k*? (Hint: note k,, is a function of saving rate s)