1. Consider the two-period firm optimization problem. For simplicity, suppose that the only factor of production is capital (no labor is used in production). The production function is Y = zk in the current period and Y' = z'K'a in the future period, where z, z' and K are given exogenously. Profits are n = Y - I in the current period and r' = Y' + (1 - d)K' in the future period. The firm aims to maximize the present value of lifetime discounted profits, which is V = + where r is the real interest rate, given exogenously. The evolution of capital is given by K' = (1 - d)K +1. a) Solve for the optimal level of investment in terms of the parameters (a, d) and the exogenous variables. b) Show how the optimal level of investment changes with i. current capital K ii. current total factor productivity z the real interest rater. iii. 1. Consider the two-period firm optimization problem. For simplicity, suppose that the only factor of production is capital (no labor is used in production). The production function is Y = zk in the current period and Y' = z'K'a in the future period, where z, z' and K are given exogenously. Profits are n = Y - I in the current period and r' = Y' + (1 - d)K' in the future period. The firm aims to maximize the present value of lifetime discounted profits, which is V = + where r is the real interest rate, given exogenously. The evolution of capital is given by K' = (1 - d)K +1. a) Solve for the optimal level of investment in terms of the parameters (a, d) and the exogenous variables. b) Show how the optimal level of investment changes with i. current capital K ii. current total factor productivity z the real interest rater