Nicely put. In my parable the rich can now buy much more gruel than they could before (even though they choose not to) and the poor can buy less beef wellington (even though they choose not to) so , while own-consumption adjusted incomes may not have diverged, this still amounts to an increase in inequality. As you have it, changes in feasible consumption sets may be the kind of ‘inequality that matters’.

Nicely put. In my parable the rich can now buy much more gruel than they could before (even though they choose not to) and the poor can buy less beef wellington (even though they choose not to) so , while own-consumption adjusted incomes may not have diverged, this still amounts to an increase in inequality. As you have it, changes in feasible consumption sets may be the kind of ‘inequality that matters’.

Suppose there are rich people and poor people. Suppose poor people have flat income growth and flat price growth– no change. Suppose rich people have high income growth and high price growth — suppose at the exact same rate — so that their bundle-adjusted income growth is also flat.

So, for rich and poor alike, flat growth in bundle-adjusted incomes. Is inequality growing? Maybe!

The rising cost of rich goods shrinks poor people’s consumption possibility frontier (CPF). This is true even if poor people aren’t buying rich goods!

Since in this example, poor people’s CPF is weakly shrinking, while rich people’s CPF is weakly expanding, poor people are becoming worse off relative to rich people.

Now, OK. If I have a 25K/year job, and the price of yachts goes up, I probably don’t care. But if the price of IPod’s goes up, I might care! You can’t tell me that I didn’t care just because ex post facto, I didn’t buy an IPod! That’s bad reasoning. Maybe I would have bought one if there was less inflation in the price.

We cannot examine the counterfactual world where rich people have flat nominal income growth and flat bundle price inflation.

But I think we have to assume that shrinking someone’s CPF is utility-decreasing.

Suppose there are rich people and poor people. Suppose poor people have flat income growth and flat price growth– no change. Suppose rich people have high income growth and high price growth — suppose at the exact same rate — so that their bundle-adjusted income growth is also flat.

So, for rich and poor alike, flat growth in bundle-adjusted incomes. Is inequality growing? Maybe!

The rising cost of rich goods shrinks poor people’s consumption possibility frontier (CPF). This is true even if poor people aren’t buying rich goods!

Since in this example, poor people’s CPF is weakly shrinking, while rich people’s CPF is weakly expanding, poor people are becoming worse off relative to rich people.

Now, OK. If I have a 25K/year job, and the price of yachts goes up, I probably don’t care. But if the price of IPod’s goes up, I might care! You can’t tell me that I didn’t care just because ex post facto, I didn’t buy an IPod! That’s bad reasoning. Maybe I would have bought one if there was less inflation in the price.

We cannot examine the counterfactual world where rich people have flat nominal income growth and flat bundle price inflation.

But I think we have to assume that shrinking someone’s CPF is utility-decreasing.