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1) What is the role of government?
In the modern world, we can see that society is government itself and the society governs itself. The first accepted form of leadership and governance was the early  tribal leaders, followed by monarchy and democracy. The question 'what is the role of government in society?' is not possible to describe the role of government in society. Why do people need government?' and 'what is the role of government in society? .   

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  • Military Duties: The original function of military was to protect people from foreign aggression. The military duties have have increased such as external affairs, alliances, treaties and development of arms and related manpower have also come into being. The military duties insure the integrity of a nation. This help civilization, economic activity and social components within, thrive.
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  • Civic Amenities: Another important thing that government helps is civic amenities. These include facilities provided by government such as water supply, electricity, roads, bridges etc.
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  • Education: The government helps bring about education in the broadest range possible. From kindergarten to university, the government tries to ensure education for everyone as much as possible. Long ago, education was kept to the noble but now, government has pushed education to be attained by everyone.
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  • Justice and Mechanism: Justice and mechanism must be included in society because it keeps society from entering chaos. The government needs to enforce laws and restrictions in order that society doesn’t enter chaos. People can’t just do whatever they want. Such restrictions include having lines for bus lines.

(http://www.buzzle.com/articles/what-is-the-role-of-government-in-society.html) 

2) The invisible hand leads the government to be more efficient. But the invisible hand is very limited. Although the invisible hand might push for effeciency, there is still favoritism towards the more appealing thing but the government is able to easen that favoritism and be able to distribute equally. (Essentials of Economics; Mankiw) 

3) The people itself are limited and the government needs to intervene so that the people can have equal share. In the economy, there is no organization or institution that is bigger than or as impactful as the government. The government should try to implement equality through social benefits such as healthcare and free education. The government has the power to distribute the pie equally to as many people as possible. (http://www.buzzle.com/articles/what-is-the-role-of-government-in-society.html)

4) In economics, there is usually some sort of market failure. A market failure refers to when the market fails to allocate resources effeciently. In this case, government intervention can help immensely because the government can check whether markets are being effecient or whether they are being wise in their decisions. 

(http://tutor2u.net/economics/content/topics/marketfail/market_failure.htm)  

 
5) In general, people are selfish and when left alone without some sort of sovereign authority governing them, the whole market would be even more corrupt. The market is a set of behaviors that is structured by rules, in which most of the rules have been enforced by the government. The government also allows for a stable money supply. Instead of relying on private banks, which was unreliable, people can rely on the government which ensures stable amount of money and that is really good for the people to get the equal opportunity. (http://www.governmentisgood.com/articles.php?aid=13)

6) Equality is a big part of a stable economy. The government comes hand in hand with the economy and the government plays a big role in pushing for equality for people as much as possible. The government supplies things like free education and welfare systems for the people. Also the people can rely on government for things like stable money supply, law and order, bankruptcy protection, property rights and limited liability laws. Through things like this, the government helps provide opportunities for people.