I was reading this article on power laws in economics.
If you look at figure.5 on page 11, you come across an interesting note.
Notes: Left panel: The CEO compensation is the ex ante one, including Black–Scholes value of options granted. The slope is about 1/3, a reflection of Roberts’s law: $Pay $~$Size^b$ with b ≃ 1/3. Right panel: The pay–performance sensitivity (PPS) is the Jensen–Murphy measure: by how many dollars does the CEO wealth change, for a given dollar change in firm value. The slope is about −2/3, so that PPS ~ Sizeb−1 with b ≃ 1/3. The congruence between the scalings is predicted by the Edmans, Gabaix, Landier (2009) model.
I found the source of such a law on the works cited page:
Roberts, David R. 1956. “A General Theory of Executive Compensation Based on Statistically Tested Propositions.” Quarterly Journal of Economics 70(2): 270–94.
However I am yet to find an open source document which explains the derivation of such a law.
If anyone knows of a source Id appreciate it.