Answer:
Socially Right: Government should interfere with society and social lives of citizens
Socially Left: Gov should NOT interfere in society and social lives of citizens.
Economic Right: Gov should NOT interfere in the economy (tax and spend too much)
Economic Left: Gov SHOULD interfere in the economy (tax and spend much).
Your definitions for Socially Right and Socially Left are reversed. Effectively, the difference between the right and left is:
The right believes in greater personal responsibility with the belief that this freedom will lead to individual success that will open up opportunities for those who are less fortunate. This means that a citizen is responsible for his own life. He must work to earn money. With this money, he can buy food, healthcare, education and consumer items, etc. The government will take a comparatively smaller proportion of this money and with this tax, will use it to pay for key services- law and order, defence, infrastructure etc. The government will interfere as little as possible in the economy, as only the economy can run the economy, and business knows better than politicians.
The left believes in greater state responsibility for the benefit of all citizens, with the goal of a more "equal" society. This means that a citizen will work to earn money, and the government will take a comparatively larger proportion of this. With this tax, the government will pay for more services- law and order, defence, health, education etc. The government takes on a greater responsibility in controlling the economy and in governing people's lives, as the politicians do not allow businesses free reign, and the government sets certain basic standards for all of society.
DOWNSIDES FOR A SOCIETY THAT IS TOO FAR TO THE RIGHT-
-A grass-roots right wing policy is often known as free-market capitalism. This is effectively unhindered capitalism. This has many fatal flaws. The idea of this system is that the rich create jobs and this helps the poor to better themselves. However, this is impractical, as poverty is very hard to break out of, due to all the health provisions that would be required. What you would get is the poor earning money, but in a free market society, they would have to spend all the money on food, healthcare and education. This would mean only the lucky few would break out of poverty.
-With less money to spend, only the government only provides the basic need for society. Things such as health care and education become accessible only to those who have money. Ultimately, this creates a situation in which only the people with adequate financial security can lead healthy lives and meet their full potential.
-Allowing a purely free economy to guide a society means a lot of faith is placed on the people who have the most money, influence and power. With human nature, greed can play a huge role in people's motivations and decisions are often made by the rich that will only benefit themselves at the expense of the poor. This type of greed had, for example, led to the corruption by powerful executives on Wall Street which ultimately played a huge part in the failure of the global economy in late 2008-2009.
-Social equality is diminished in favour of individual rights and freedoms. In a society where everyone is equal with equal power, this would not pose a problem. However, no society has successfully achieved such equality. As a result, survival of the fittest plays a big part and a selfish attitude can begin to thrive.
DOWNSIDES FOR A SOCIETY THAT IS TOO FAR TO THE LEFT-
-Personal responsibility is diminished in favour of social equality. This essentially means taxing the rich and giving to the poor. This can be detrimental as some poorer segments of society may start to feel that society owes them something rather than taking charge of their own lives to improve their situations.
-The left-wing philosophy gives the government more money to spend and, with more money, there's more opportunities to spend irresponsibly. An extreme example currently happening in some European countries is that governments spend larger amounts on social benefits and citizens take advantage or start to develop a sense of entitlement.
-More government control of the private sector means more bureaucracies and more "hoops to jump through", which can increase costs for doing business and thus negatively impact growth.
Ultimately, any system that is pure right or pure left is flawed. The best solution is a mix of the two. An extreme in either direction means too much control by either the government or by the private sector. The trick is how to find the right balance.