1. Consider an economy that operates under competitive markets and meets the assumptions of the Solow model. The production function is given as follows: Y(t) = K (t) 0.3 (A(t)L(t)) ⁰.7 Assume a saving rate of 15%, labor force growth rate of 2% and depreciation rate of 5% and effectiveness of labor growth rate of 8%. a. Show that the production function exhibit constant return to scale? b. Derive the production function for output per capita. c. Derive the production function for output per effective unit of labor. d. Find equilibrium real wage as a function of capital per unit of effective labor and effectiveness of labor. e. Find equilibrium real rental price of capital as a function of capital per unit of effective labor and effectiveness of labor. f. Solve for steady state level of capital per unit of effective labor. g. Find steady state level of output per unit of effective labor. h. Find growth rate of output and output per worker on the balanced growth path. i. Which one would increase consumption per unit of effective labor: an increase in saving rate or a decrease in saving rate. Explain. Find the golden-rule level of capital per unit of effective labor and optimal saving rate. Describe how a decrease in saving rate affects the break-even line and actual investment line and use graphs to show the impact on k, k, growth rate of Ln() and cover time. j. k. 1. Describe how an increase in growth rate of effectiveness of labor affects the break-even line and actual investment line and use graphs to show the impact on k, k, growth rate of and Ln() and c over time. m. Describe how a decrease in growth rate of labor affects the break-even line and actual investment line and use graphs to show the impact on k, k, growth rate of Ln () and c over time. 2. Find the elasticity of output per unit of effective labor on the balanced growth path y with respect of rate of population growth, n if production function is given as Y(t) = K (t) 0.3 (A(t)L(t)) ⁰.7 Assume that the growth rate of effectiveness of labor, g, is equal to 8% and depreciation rate of 4%. By about how much does a fall in n from 2% to 1% raise y*