Write down the production function in per worker units at time t. (5 points) Show that the total consumption (private plus government) is a fraction of the aggregate incomefoutput. (5 points} Write down the goods' market equilibrium condition at time t. (5 points) Using your answer to c), show that in equilibrium the aggregate investment is a fraction of the aggregate incomeg'output. (5 points) Show that the change in the physical capital per worker from time {to time {+1 is a function of the physical capital per worker at time t. (5 points) Derive the steady-state formula for the physical capital per worker. (1'22I points) How does the tax rate T affect the steady-state incomefoutput per worker? (5 points) Derive the steady-state formula for the total consumption per worker. (5 points} Using your answer to h). derive the tax rate I'\" that maximizes the steady-state consumption per worker. (5 points}