Using the physical capital resource constraint: K; = M, + R; and your answer to b., show that output per capita can be written as a function of kt and rt. (5 points) Write-down in per capita units the equilibrium law of motion for the aggregate physical capital. (5 points) In the situation in which automation does not exist: (2 = 0), derive the steady-state physical capital per capita and the steady-state output per capita. (10 point) Derive an expression for the level of robot per capita maximizing the output per capita. Display in a two-dimensional diagram the output per capita maximizing level of robot per capita as a function of the physical capital per capita. For which levels of physical capital per capita the use of robot becomes Optimal? (15 points) Using your answer to f. show that the resulting expression for the maximized output per capita is linear with respect to the physical capital per capita. (10 point) If it is optimal to use robots, does the economy grow forever or converge to a steady-state solution? Please justify your answer(s). (10 points)