Given the production function in Y = A*K.666666*.33333333 Recal the growth rate of capital per worker = s*y/k-s8-n. and the growth rate of output per worker is Ay/y = a k/k For this country Technology is 2. Savings rate = 10%, depreciation rate = 20% and population growth rate = 3%. Also initial capital is 400 and initial labor is 100. 1. Derive the equation for the steady state of capital. 2. Given the info above what is the steady state of capital k*? 3. What is output per worker y*? 4. If we are in the steady state and Thanos snaps his fingers and kills half the population. What is the new k & y immediately after the snap? 5. What is the growth rate of k and y immediately after the snap? 6. What is the new y*? 7. If instead he snapped his fingers and made it such that a baby is born only when a person dies. What is the new k* & y* a. How much does per capita GDP rise by? (percent)