The correct answer is: B. Ensure costs become the responsibility of a specific manager.
Responsibility accounting is a system of accounting that assigns costs and revenues to specific individuals or departments within an organization. This allows managers to track their performance and identify areas where costs can be reduced or revenues increased.
Option A is incorrect because responsibility accounting does not aim to punish managers. Instead, it aims to hold managers accountable for their actions and to help them improve their performance.
Option C is incorrect because responsibility accounting does not allocate costs to all areas of a business. Instead, it assigns costs to specific individuals or departments.
Option D is incorrect because responsibility accounting does not aim to reduce the costs a department incurs. Instead, it aims to help managers track their performance and identify areas where costs can be reduced.
In conclusion, responsibility accounting aims to ensure costs become the responsibility of a specific manager. This allows managers to track their performance and identify areas where costs can be reduced or revenues increased.