The correct answer is: B. ensure that costs become the responsibility of a specific manager.
Responsibility accounting is a system of accounting that assigns costs to specific managers so that they can be held accountable for their performance. This system helps to improve efficiency and effectiveness by ensuring that managers are aware of the costs that they are responsible for and that they take steps to control those costs.
Option A is incorrect because responsibility accounting does not aim to punish managers. Instead, it aims to hold them accountable for 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 managers.
Option D is incorrect because responsibility accounting does not aim to reduce the costs that a department incurs. Instead, it aims to improve efficiency and effectiveness by ensuring that managers are aware of the costs that they are responsible for and that they take steps to control those costs.