Trying to explain inequality to my students

I have been working in trying to explain better to my Master's degree students recent developments in academic research on inequality, including contributions by Milanovic and Piketty among others. Here are some notes of what I have been preparing:
Milanovic: global inequality among all citizens in the world is today more explained by between-country than within-country differences compared to 150 years ago, although more recently the tendency is being reversed.
  ∙  Global inequality is higher than the inequality levels of the most unequal countries.
  ∙  There are discrepancies about the sign of the changes in global inequality in the recent past.
  ∙  Globalization (increase in trade and economic integration) has increased mean income of some developing countries and affected within income inequality.
The economic surges of China, India and other nations have been among the most egalitarian developments in history, so national growth may play a big role in reducing global inequality: but not clear that they compensate for increasing within inequality in the USA and other countries and for the decline of other nations.
  ∙  Should we care about global inequality or we should care only about poverty?
 1. Bhagwati: even the calculation of global inequality is a "lunacy:" there is no "global polity," no "addressee."
 2. Krueger: "poor people are desperate to improve their material conditions... rather than to march up the income distribution ladder."
But there are ethical (universalism or cosmopolitan Social Welfare Functions -SWFs) and practical (globalization of media and information creates a sense of injustice or at least a desire to migrate) reasons to care about global inequality.
  ∙An idea: an international agency with taxation power to tax from the rich in rich countries to the poor in poor countries without government involvement that takes away national sovereignty from both rich and poor countries.
  ∙Problem: "no taxation without representation," hence difficult to implement without global democratic federalism (according to Milanovic himself, soccer has been better than politics at this, with FIFA and rules for national teams redistributing welfare gains to poor countries).
How much of our individual welfare is determined by the country where we are born? Around 1/2 (Milanovic). Given that personal circumstances (gender, race) also affect, the probability of effort greatly affecting income in the global scale is low: migration is rational for citizens of the poorest countries.
  ∙Rodrik: if a small efficiency improvement implies large redistribution of income, we should use criteria of justice (who are the parties affected? do they deserve the redistribution? should we compensate the losers?), "we should need some assurance that the process conforms with our conceptions of distributive justice."
  ∙The distributional impacts of economic restructuring (structural reforms) are big: no pain, no gain.
Stern: we do not need social welfare and individual utility functions to theorize about the need to reduce inequality:
 1.sometimes the difficulties of interpersonal utility comparisons with a utilitarian SWF make it difficult to use them to redistribute: it would be efficiency-improving to transfer income from depressed to non-depressed people because the latter are deemed more efficient in converting income into individual utility;
 2.with a rawlsian SWF, it may allow for a very wide and rising inequality, where additional gains are disproportionately received by the rich, so long as tere is some, albeit very modest, increase in the income of the poor.
  ∙  Capabilities or empowerment approach by A. Sen: individuals should have right to basic goods, abilities and services to develop a free life -eg learning to read, access to basic health.
Bowles and Gintis: inheritance of inequality higher than expected, and not necessarily related to genetic inheritance of Intelligence Quotient (IQ) or other traditional inputs to wealth, but related to inherited traits (such as race, population group).
  ∙  Krugman: inequality may be reflected in biased political power.
  ∙  From Kuznets to Piketty: from the prevalence of the view that development and inequality followed an inverted U-shaped relationship, to the believe that capital income is increasingly concentrated internationally.
Inequality of income reflects a continuous measure. There are also important discrete categories that add information on social power: social classes, groups. These categories occupy different contractual roles in hierarchical relations.
  ∙  How to redistribute: pre-distribution? international taxation? highest jurisdictions should raise the taxes with the more mobile bases. Is inequality good for growth? Essential dilemma: social monopoly versus incentives.
  ∙  Should we care about equality of opportunity or also about equality of outcomes?