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.

Thanks for the reply. Yes I used an example with changing proportions of rich & poor in an attempt to get at what I thought the issue was in a simple way; this does not mean I think the proportions of the population in each income declines changes!

When I wrote in terms of neutralising ‘concerns’ (which may have been a mistake) I was trying to get at whether the ‘kind of inequality that matters’ (i.e. concerns us) has increased. In my example, I meant to suggest that while increased gruel buying power for the poor may decrease the kind of inequality that matters to some extent, the inequality that matters has more to do with who is eating beef wellington and who is eating gruel.

I’ll try to get closer to reality. Say the top decile eats beef wellington and the bottom eats gruel. Now say the real wage as measured against an economy-wide average price index is unchanged for the poor, but trebles for the rich. At the same time gruel prices fall and beef wellington prices rise by exactly the right amounts so that, when adjusted by their own consumption baskets, the ratio of income between the top and bottom deciles “has risen only 2 percent in this period”. The real income of the rich, measured against the economy average price index, has increased by much more. Perhaps we also need to assume that beef wellington is sufficiently expensive so that the gruel price decline income effect is not large enough for the poor to now choose to purchase a little beef wellington. I’m not sure how well this new story now fits the Broma paper – I haven’t read it closely enough to figure out how they calculate their adjusted change in income ratios – but would you say that in my little revised parable, the sort of inequality that matters has increased?

Thanks for the reply. Yes I used an example with changing proportions of rich & poor in an attempt to get at what I thought the issue was in a simple way; this does not mean I think the proportions of the population in each income declines changes!

When I wrote in terms of neutralising ‘concerns’ (which may have been a mistake) I was trying to get at whether the ‘kind of inequality that matters’ (i.e. concerns us) has increased. In my example, I meant to suggest that while increased gruel buying power for the poor may decrease the kind of inequality that matters to some extent, the inequality that matters has more to do with who is eating beef wellington and who is eating gruel.

I’ll try to get closer to reality. Say the top decile eats beef wellington and the bottom eats gruel. Now say the real wage as measured against an economy-wide average price index is unchanged for the poor, but trebles for the rich. At the same time gruel prices fall and beef wellington prices rise by exactly the right amounts so that, when adjusted by their own consumption baskets, the ratio of income between the top and bottom deciles “has risen only 2 percent in this period”. The real income of the rich, measured against the economy average price index, has increased by much more. Perhaps we also need to assume that beef wellington is sufficiently expensive so that the gruel price decline income effect is not large enough for the poor to now choose to purchase a little beef wellington. I’m not sure how well this new story now fits the Broma paper – I haven’t read it closely enough to figure out how they calculate their adjusted change in income ratios – but would you say that in my little revised parable, the sort of inequality that matters has increased?

So, the best variation on this analysis might include more gradations, or or a continuous function, of bundles, rather than 2. But I think this is a quibble.

A possible non-quibble is that what the authors are doing seems really, really hard. Are they sure they’re holding “bundle goodness” constant over the years? That seems to involve a lot of subjectivity. I’d like to understand more about the methodology.

It’s a problem with any price index, though. I trust they followed good standard methodology, and so this is the best guess we have.

So, the best variation on this analysis might include more gradations, or or a continuous function, of bundles, rather than 2. But I think this is a quibble.

A possible non-quibble is that what the authors are doing seems really, really hard. Are they sure they’re holding “bundle goodness” constant over the years? That seems to involve a lot of subjectivity. I’d like to understand more about the methodology.

It’s a problem with any price index, though. I trust they followed good standard methodology, and so this is the best guess we have.