The link between the size of the company and the pay of the CEO is one that is nearly impossible to make go away. One measure of the company-size-to-CEO-pay relationship is called elasticity by economists. It turns out that we can estimate the CEO compensation elasticity with respect to firm revenue, and this number is around 0.3. That is, for a 1% increase in company size, CEO pay goes up by about one-third of 1%, or for a 10% increase in company size, CEO pay goes up by about 3%. The relationship between organization size and top executive pay in nonprofits is near the same size as it is for for-profit organizations.
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Hallock, Kevin F. 2011. "The Relationship between Company Size and CEO Pay." Workspan 54 (2) (02): 10-11.