Culture has a very significant role sir.

Murray sir, kindly elaborate what are those roles and what are the channel through which they work.

I agree it has a significant role. I expect the inequalities will be easier accepted in the countries, that are less individualistic, having higher power distance (you can check what those mean on geert hofstede home page - you will find there some culture indexes, you can run a correlation or regression).

From a historical perspective - some religions stronger then others will push people to accept inequalities - like i.e. hinduism or buddhism, where the inequalities are a part of a karma, and they are having their meaning. On other hand, when you look at the european values, built on French Revolution ideas: freedom, equality, brotherhood- there is distinctively less 'space' for inequality in that vision of the world. 

This is just a VERY short answer, if you would like to discuss it more, I'am open.

Well I need to ask more from @Malgorzata about the link between inequality and its acceptance in different cultures. Are you not essentializing ?

Of course, it is just a short answer. I wouldn't dare call it  a 'social law' (or any other social phenomenon...). I think it is a good hypothese, thou. If you look at the Gini's Coefficient map - you will see, there is a relation with the civilisations, with the political system, attitude to democracy, understanding a concept of freedom, kind of colonisators etc. It is surely very fixed phenomenon, but talking about acceptance of the inequalities is really talking about the values and values are crucial element building a culture. I don't think, regarding values, you can entirely explain a problem of inequalities (you need to involve political, historical, natural aspects, and probably many more), but I am convinced it is an important factor. 

Maybe really the easiest way, to build some empirical base for this hypotese is to run a few regressions between the values connected with inequality problem (rights of individuals, individualism, understanding of freedom, model of democracy, model of social fairness etc.) 

Another perspective - if we would assume the attitude towards inequalities is up to culture, another words - it is a manifestation of a culture - we can expect, that this term will be understood differently in different cultures. But then it will be more antropological disertation. 

Culture, genetics and social attitudes are minor factors of human inequality to be counted with; the major facor of human inequality in any given socio-economic system is the landlord' s game of monopolies, privileges and inherited wealth. The more economic rent flows to land value monopolies (i.e. privatized nature), the higher is the social inequality. The economic behavior to capture vital natural resources of human life is  rooted in the animal kingdom; the only ethical pathway to remedy this animal instincts is to tax economic rent and to make it public revenue. This is the practical teaching of almost all 'holy scriptures' of the human fraternity, i.e. ethical human action is decisive, not official or theoretical belief systems which are a produce of coincidencies.

What is the role of culture in cross country economic and social inequalities?

Culture tends to identify a particular country's value system so that when people from different countries get together, everyone can compare, contrast & comment how different issues / tasks / situations can be handled differently.  This can prompt how different countries can complement & collaborate in various aspects including economical, political, social, technological etc.  At the same time, cultural differences (sometimes also motivated by political & economical gains) can cause alienation or hostility among certain countries.  As researchers, we can conduct research from many angles but cultural values are something we can't ignore as this can be one of the independent variables, mediators or moderators influencing our conceptual framework / research model.

culture in all of the world is the base of forming property on the economic and social .for example Prodigality is one of important problem that is augment of increase the economic growth .

On the contrary, I think the economy has an influence on culture