Do bosses increase profits? The justification for the mega-million salaries is that they do. But at an aggregate level, this is not obvious.

To see what I mean, start from the basic national accounts identity that GDP equals consumer spending (C), investment (I), government spending (G), plus net trade (X-M), and also equals wages (W), profits (P) and taxes (T). Rearranging gives us:

P = (C - W) + I + (G - T) + (X - M).

Aggregate profits, then, can only rise if one of the right hand side variables rises.

This tells us something important. Bosses cannot increase aggregate profits merely by cutting their wage bill. If workers respond to the lower wages or job cuts by spending less, C - W doesn't change. One firms' higher profits are another's lower demand. It is only if consumer spending holds up as wages fall that profits will rise. But this depends to a large extent upon factors outside of CEOs' ordinary powers - such as consumer confidence and credit availability.

Yes, bosses can increase aggregate profits by going on an investment boom or export drive. But these are two things that have not happened in the US or UK economy in recent years.

Now, you might reply here that bosses' organizational skills raise firms' efficiency and productivity. Let us suppose this is true (which it isn't really, as most productivity growth comes from entry and exit (pdf) rather than internal restructuring). Higher productivity means only one of two things. One is the same output from fewer workers. But we've already seen that this doesn't raise aggregate profits. The other is higher output from existing workers. But how will this output be sold? It is only if macroeconomic conditions permit. But these conditions depend upon factors exogenous to the firm such as policy and external demand.

Take an example. Say the economy is pootling along as normal and then a great CEO comes along with a new product he's invested, such as Steve Jobs with the iPad. Clearly, this increases Apple's sales and profits. But it doesn't necessarily increase aggregate profits. If people cut their spending on other goods in order to buy the iPad, Apple's profits only rise at the expense of other firms. It is only if macro conditions permit increased aggregate spending that aggregate profits will rise.

This means that even if bosses are not exploiters, shysters and rent-seekers but do genuinely add value, they do not necessarily do so at the aggregate level. Instead, they raise their own firms' profits at others' expense.

This in turn means that bosses' high pay might well be due to an arms race. Each individual firm bids to get the best CEO, with the result that aggregate spending on them is sub-optimally high; if CEO pay were cut across the board, there'd be no overall loss - just a transfer from CEOs to shareholders.
In other words, you don't need to believe my rants against managerialism in order to suspect that bosses are overpaid. They might be even if they really do add value.

Now, you might object here that I'm ignoring the possibility that although bosses don't raise profits they do raise welfare; if the iPad displaces other consumer spending, consumer surplus rises.

True. But this is not the only form of innovation. Not only is there Jobsian innovation, which raises consumer surplus. There's also O'Learyan innovation which aims at capturing it for the firm. It's not clear which type is dominant.