Consider the Solow growth model developed in class. The production function is Y = K(AL)-, where...

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Consider the Solow growth model developed in class. The production function is Y = K(AL)-, where 0 < a < 1. Population grows at the exogenous rate n, Lt+1 = (1 + n)Lt. The capital stock accumulates acording to Kt+1 = (1 8)K + SY, where s is the investment rate in capital and 0 < s < 1. (a) [5 points] Define capital per capita in period t as k = K/Lt. Derive the accumulation equation for capital per capita. (b) [10 points] Derive an expression for the growth rate of capital per capita gk,t = (kt+1 kt) /kt. (c) [5 points] Solve for the steady state level of capital per capita, denoted ks. (d) [10 points] Solve for the growth rate of capital per capita and total capital in steady state. (e) [10 points] Show that gk,t > 0 when k ks. (f) [10 points] Assume that the economy is on its balanced growth path (steady state). Assume that there is a one time permanent increase in the level of A (from Ao to A1, A > A0). In a graph with time in the horizontal axis, plot the behavior over time of the following variables after the increase in A (that is, plot the variable's initial value and the transition to the new long run value): 1) capital per capita, and 2) growth rate of capital per capita. Consider the Solow growth model developed in class. The production function is Y = K(AL)-, where 0 < a < 1. Population grows at the exogenous rate n, Lt+1 = (1 + n)Lt. The capital stock accumulates acording to Kt+1 = (1 8)K + SY, where s is the investment rate in capital and 0 < s < 1. (a) [5 points] Define capital per capita in period t as k = K/Lt. Derive the accumulation equation for capital per capita. (b) [10 points] Derive an expression for the growth rate of capital per capita gk,t = (kt+1 kt) /kt. (c) [5 points] Solve for the steady state level of capital per capita, denoted ks. (d) [10 points] Solve for the growth rate of capital per capita and total capital in steady state. (e) [10 points] Show that gk,t > 0 when k ks. (f) [10 points] Assume that the economy is on its balanced growth path (steady state). Assume that there is a one time permanent increase in the level of A (from Ao to A1, A > A0). In a graph with time in the horizontal axis, plot the behavior over time of the following variables after the increase in A (that is, plot the variable's initial value and the transition to the new long run value): 1) capital per capita, and 2) growth rate of capital per capita.