One can delegate authority but not responsibility. Discuss.
This means that a manager (or other person) can decide to relegate tasks to a person (or people) who is subordinate in the organization. In fact, delegation is one of a manager's most important responsibilities. As a manager, one has to handle big-picture issues and cannot carry out all the tasks involved in a department. However, while the manager gives the authority to others to carry out certain tasks, the manager is still ultimately responsible for the results and for the employees' completion of those tasks. While the subordinates are carrying out a task, the manager must continually check to see that their work is being completed efficiently, accurately, and in a timely way. If the subordinates do not do their work well, it is ultimately the manager who will be responsible and who will have to face the consequences both within the organization, with administration, and with other stakeholders such as customers or clients.
Because authority comes in the form of titles, ranks, and positions, authority can be delegated to one who is appointed. Responsibility, however, is a personal choice: One can choose to be responsible or not. It is an individual quality rather than a concrete "name." If one is assigned an authoritative post, that choice is essentially eliminated.
Hence, a supervisor can bestow titles and authority, but it remains up to the named person to live up to the responsibility inferred by positions of trust. Both words can be used as nouns, but they each have related but different implications. One can be responsible without being an authority, just as one can be an authority without being responsible.
I think the opposite happens most often. There are plenty of times when a person, such as the head of a department, has responsibility but not authority. He or she might be held responsible for making something happen with coworkers or subordiates, but not the actual authority to enforce any directives or incentives. This is one of the major stressors that middle managers face.
In a business (or any organization, really), you have certain responsibilities that are part of your job. You can give a staff person the authority to do something or make a decision that is part of your job, but you remain responsible for the outcome.
In an organizational set up delegation of authority from superior to his subordinate is not only possible but essential. Once the authority to take a decision is delegated to the subordinate, the boss free from performing those tasks himself, and can devote his or her time and energies to tasks that subordinate cannot perform successfull for one reason or other. This way work of the organization gets done more effectively and efficiently.
However when it comes to delegating responsibility things are somewhat different. When authority is delegated to the subordinate for performing some specific work, the subordinate must also assume responsibility for successful execution of the work done. But does this mean that subordinate in no longer responsible for the results of the subordinates. The answer is an emphatic "No".
If the responsibility is also delegated then the boss can wash off his hand from all that his subordinates, and as managers get most of their results through the efforts of their subordinates, it would amount to them having no or limited responsibility. There will be no one to take responsibility for the organization as a whole and steer it in the right direction.