Consider chief executives. Without doubt, they are paid handsomely, and their pay has grown over time relative to that of the average worker. In 2012, the median pay of C.E.O.’s for companies in the Standard & Poor’s 500-stock index was nearly $10 million. Did they deserve it?

Critics sometimes suggest that this high pay reflects the failure of corporate boards to do their job. Rather than representing shareholders, this argument goes, those boards are too cozy with the chief executives and pay them more than they are really worth.

Yet this argument fails to explain the behavior of closely held corporations. A private equity group with a controlling interest in a firm does not face this supposed principal-agent problem between shareholders and boards, and yet these closely held firms also pay their chief executives similarly high compensation. In light of this, the most natural explanation of high C.E.O. pay is that the value of a good C.E.O. is extraordinarily high.

That is hardly a surprise. A typical chief executive is overseeing billions of dollars of shareholder wealth as well as thousands of employees. The value of making the right decisions is tremendous. Just consider the role of Steve Jobs in the rise of Apple and its path-breaking products.

Image Steve Jobs demonstrated the high value of making tough decisions in his years at Apple. Credit... Jim Wilson/The New York Times

A similar case is the finance industry, where many hefty compensation packages can be found. There is no doubt that this sector plays a crucial economic role. Those who work in banking, venture capital and other financial firms are in charge of allocating the economy’s investment resources. They decide, in a decentralized and competitive way, which companies and industries will shrink and which will grow. It makes sense that a nation would allocate many of its most talented and thus highly compensated individuals to the task.

In addition, recent research establishes that those working in finance face particularly risky incomes. Greater risk requires greater reward.