Consider a firm that chooses investment to maximize the sum of discounted profits. Each period it starts with a capital stock of ke which is used to produce output through a strictly concave production function, f(k) (f'(k) > 0, f"(k) 0) and "() > 0. Notice that the adjustment cost is a function of the size of the period investment relative to the size of the firm's beginning of the period capital stock kt. For simplicity we will assume that (1) = f (). The firm discounts the future at a rate r. Thus the firm solves the following problem max {it,kt+1}.0 :(1+)'{s(n) [1+ } 1-0 subject to the flow constraint k4+1 = 14 + (1 5)kt 1. What is the control variable and what is the state variable? 2. Using dynamic programming, set up the Bellman equation and then find the firm's optimal intertemporal trade-off condition (between investing in the cur- rent period versus investing in the following period) and interpret it in words