Does a leader need power or authority? How do you influence people?

In social science and politics, power is the ability to influence the behavior of people. The term authority is often used for power perceived as legitimate by the social structure. Power can be seen as evil or unjust, but the exercise of power is accepted as endemic to humans as social beings. In the corporate environment, power is often expressed as upward or downward. With downward power, a company's superior influences subordinates. When a company exerts upward power, it is the subordinates who influence the decisions of the leader.

People use power more than rewards, threats, and information to influence people.In everyday situations people use a variety of power tactics to push or prompt people into particular action. There are plenty of examples of power tactics that are quite common and employed every day. Some of these tactics include bullying, collaboration, complaining, criticizing, demanding, disengaging, evading, humor, inspiring, manipulating, negotiating, socializing, and supplicating. These power tactics can be classified along three different dimensions: softness, rationality, and laterality.

The word authority is derived from the Latin word auctoritas, meaning invention, advice, opinion, influence, or command. In English, the word authority can be used to mean power given by the state (in the form of Members of Parliament, judges, police officers, etc.) or by academic knowledge of an area (someone can be an authority on a subject). The word Authority with capital A refers to the governing body upon which such authority.

In government, the term authority is often used interchangeably with power. However, their meanings differ: while power is defined as "the ability to influence somebody to do something that he/she would not have done", authority refers to a claim of legitimacy, the justification and right to exercise that power. For example, while a mob has the power to punish a criminal, for example bylynching, people who believe in the rule of law consider that only a court of law has the authority to punish a criminal.

Overall in my view authority is the capacity, innate or acquired for exercising ascendancy over a group so, a leader needs more authority. 

A leader earns his/her power for their followers but leaders are not authororitative.

Leaders influence thier followers by being savvay. Influencing takes a soft touch, time to understand your audience, and ability to bring them to your side of the table.

Good question , people to tend misunderstand the meaning and the role of these two .... power  & authority ... according to my experience a good leader needs no extra power to lead people, his or her , the experinced leader will know how to encourange people , by being part of the solution , being part of the team , to show whats right , and knowing ones facts , automaticaly wins the attention of the staff under him and no need half special athurority . or power,  good leadership come in hand in hand with power of ther positon held and the granted authroity to do so .

which in both cases should be used wisely and moderatly and within limits.