Do you think that personal/individual responsibility and social responsibility are in competition with one another?
In the U.S they certainly are, but that is because there is an extremist focus on the individual and there is a poor sense of proper boundaries.
Do you profess a belief in one but not the other?
I strongly value both in their proper spheres.
Can they or should they be harmonious ideas which compliment one another?
I think they can, but not when dysfunctional dynamics are the norm. In dysfunction, the sense of Self and Other is distorter so that there is an absence of negotiation and one will dominates the other. In the same manner these notions can be harmonious in the family unit, they can by extension be harmonious at the society level. The family is the microcosm of society. I hold a belief that the most healthy political systems for a given society can be found in the dynamics of its healthy family structures. In this way cultures that value and operate with extended family values will have more success with socialistic programs. Cultures that have more individual focus where family members are more distant but also allowed more variation in choices and values, will operate more successfully with Libertarian programs.
How do you determine the limits or proper sphere of either idea?
As I just mentioned there is a cultural element that establishes healthy, functional dynamics of Self and Other at the family unit. In addition there is a notion of public vs. private. We operate in these two spheres and I see modern society having low sense of healthy boundaries between the two. Spirituality and religion are within the private sphere, so when these ideas are imposed onto others sociologically, there is a dysfunctional boundary violation happening. The same is true of individual identity. When society attempts to impose a sense of self communally onto the individual, requiring or not allowing them to define self, a boundary has been crossed revealing dysfunction. The same is true of sexuality which is not shared with society as a whole, but is part of individual intimacy and privacy, and so that falls inside the personal boundary. Any sociological imposition on this choice is grossly dysfunctional.
Public issues involve the sharing of resources. National parks, roadways, education, medicine, utilities, etc. all involve society based cooperation. Policies need to accommodate larger diverse groups of people, so that maximum freedom can be insured for the most people. If there is shared space, shared usage, shared benefit, then we have a social responsibility to protect, regulate, and distribute at the social level.