7.3. A firm operates in an uncertain profit environment. The firm takes an operating loss of one unit in a bad year, it makes a operating profit of two units in an average year, and it makes an operating profit of four units in a good year. At the beginning of a bad year, the firm may elect to shut down, avoiding the operating loss. Although the firm faces no fixed costs or shut-down costs, it incurs a start-up cost 0.2 units if it reopens after one or more periods of inactivity. The profit environment follows a stationary first-order Markov process with transition probabilities: tobadavggood CHAPTER 7. DISCRETE STATE MODELS 213 (a) Suppose the firm adopts the policy of staying open regardless of the profit environment in any given year. Given that this is a bad year, how much profit can the firm expect to make one year from now, two years from now, three years from now, ten years from now? (b) Suppose the firm adopts the following policy: (i) in a bad year, do not operate; (ii) in a good year, operate; and (iii) in an average year, do what you did the preceding year. Given that this is a bad year, how much profit can the firm expect to make one year from now, two years from now, three years from now? Graph the expected profits for both parts on the same figure. 7.3. A firm operates in an uncertain profit environment. The firm takes an operating loss of one unit in a bad year, it makes a operating profit of two units in an average year, and it makes an operating profit of four units in a good year. At the beginning of a bad year, the firm may elect to shut down, avoiding the operating loss. Although the firm faces no fixed costs or shut-down costs, it incurs a start-up cost 0.2 units if it reopens after one or more periods of inactivity. The profit environment follows a stationary first-order Markov process with transition probabilities: tobadavggood CHAPTER 7. DISCRETE STATE MODELS 213 (a) Suppose the firm adopts the policy of staying open regardless of the profit environment in any given year. Given that this is a bad year, how much profit can the firm expect to make one year from now, two years from now, three years from now, ten years from now? (b) Suppose the firm adopts the following policy: (i) in a bad year, do not operate; (ii) in a good year, operate; and (iii) in an average year, do what you did the preceding year. Given that this is a bad year, how much profit can the firm expect to make one year from now, two years from now, three years from now? Graph the expected profits for both parts on the same figure