What would a perfect meritocracy look like?
Suppose we could all agree on a definition of "merit" as "ability to contribute to the common good".
Suppose that each individual was born with a certain quantity of "merit", and that we could observe and measure each individual's "merit" perfectly. It's indelibly stamped on their foreheads.
Suppose that we had an economic system where each individual's income was strictly and perfectly proportional to that individual's "merit".
That perfect meritocracy is not a good economic system. Not in my eyes, anyway. Because, for example, it would mean that an individual who was unlucky enough to be born with zero "merit" would get zero income.
Standard Optimal Tax Theory says that if we lived in such a world we should put a tax on "merit", and only on "merit". And we should put the tax rate high enough to ensure that all individuals earn exactly the same after-tax income, regardless of "merit". Because doing so would maximise total utility of the population (assuming diminishing marginal utility of income).
The only difference between the imaginary world I have described above and the world described in (the simplest) models in standard optimal tax theory (Mirlees?) is that the latter assume that "merit" is not observable by the tax authorities. The tax authorities can only observe income, which equals "merit" times hours worked. So they can't tax "merit" and can only tax income. So unlike my imaginary world, the standard optimal tax theory model says that the marginal tax rate should be less than 100%. It balances the gains from equalising individuals' incomes through high marginal tax rates against the losses of the disincentive effects and lower total incomes. So differences in after-tax income would still exist. (Did I get that roughly right, Frances?)
How much mobility would there be in such a world, from one generation to the next? That would depend on the extent to which "merit" is inherited (either through nature or nurture) from one's parents. If parents' and their children's "merit" were perfectly correlated, there would be zero mobility in a perfect meritocracy. If the correlation were zero, there would be perfect mobility.
But I'm not sure why mobility matters.
Now let me change my imaginary world slightly. Suppose individuals differ both by "merit" and by "rent extraction skill", where "rent extraction skill" means "ability to transfer income from others to themselves". So an individual's income depends on his "total ability", which is the sum of "merit" plus "rent extraction skill".
If the tax authorities could observe each individual's "total ability", it wouldn't change the results in any way. Total utility of the population would still be maximised by taxing "total ability" to eliminate all differences in after-tax income.
If the tax authorities could not observe ability, and could only observe income, it would change the results. High marginal tax rates would discourage socially productive effort, which is bad, but would also discourage rent-seeking effort, which is good. So marginal tax rates should be higher than in a pure meritocracy where income depended only on merit.
Would intergenerational mobility be higher or lower than in a pure meritocracy where income depended only on merit? That depends. If the degree of heritability were exactly the same for "merit" as for "rent extraction skills", the amount of intergenerational mobility would be exactly the same as in a world of pure meritocracy. There is no obvious relationship between mobility and meritocracy.
But I'm still not sure why mobility matters.