3. The textbook Solow-Swan model gives you the following framework setup: Aggregate production function: Y_t = AK_t^αL_t^1 - α, where Y_t, K_t, and L_t are aggregate output, aggregate physical capital, and total labor force at time t, respectively. Total factor productivity A and the capital share α are assumed constant. Physical capital accumulation: K_t + 1 = I_t + (1 - d)K_t , where I_t is the gross investment at time t and the capital depreciates at a constant rate of d > Labor force growth: L_t+1 = (1 + n)L_t, where n is a constant labor growth rate. > Aggregate output is distributed to aggregate consumption, C_t = (1 - s)Y_t, and aggregate saving, S_t = sY_t, where the saving rate s is constant. There is no government in this closed economy. Goods market is in equilibrium for all time. (1) Let k_t = K_t / L_t and y_t = Y_t / L_t be capital-labor ratio and output per worker, respectively, find the first-order difference equation for k_t, that is k_t + 1 = g(k_t). (5 分)