Please answer each part of the question on paper and show all work.

Question 2 (Firm optimization problem in a two period model with investment) Suppose the production function is given as: Y = ln(z) + aln(K) + (1 a)1n (N). Assume that there is an investment tax on the firm given as T. This means that for every unit of investment the firm has to pay tax T (It's a proportional output). The law of motion is given as: K' = (1 d)K + I Answer the following questions: 1. Write down the profit function of the firm 2. Solve for the optimal value of N\