No, I think this topic would be more in the realm of political science. That's part of the problem in discussions like this, since a lot of people approach economics as if it's a hard science, while it is actually a social science.
I suppose the perceived value of a person's vocation might be a factor in determining their actual salary, in addition to how rare their abilities might be. For example, a rocket scientist would have to have years of education and training to become qualified for such a position - something that only a few people might be willing or able to do. Thus, a high salary for a rocket scientist would make sense.
This is especially true if there are actual shortages of qualified personnel in various jobs. Where there are shortages in personnel, the principle of supply and demand would dictate that the perceived value of those occupations would increase. There are, indeed, reported shortages in numerous areas, such as healthcare and various skilled occupations. If there aren't enough skilled plumbers to go around, then one might have to pay more to hire a plumber.
On the other hand, those with degrees in business administration and accounting seem rather commonplace in comparison to rocket scientists. There are even people who run businesses even without having an advanced college degree.
And there doesn't appear to be any shortage of people applying to become CEOs. There are lots of people fighting tooth and nail to get up the corporate ladder, so it would seem that the fact that they're easily replaceable should reduce their perceived value.
Of course, no one is arguing that everyone should get the same compensation regardless of occupation or position, but I'd like to see the mathematical model which can logically define what each profession and job category is "worth." If economics was the hard science that so many imply it is, then it should be no problem to do this. Trouble is, capitalists and other conservative economists refuse to admit that economics is a social science, and more in the realm of philosophy, politics, and history - not physics or mathematics.
I don't know what "hard science" is or what that means, but I do know that academically, economics is categorized as a social science. I've taken several economics courses in college (micro, macro, and "money and banking"), as well as a course called "engineering economics" taught as an engineering course, by an engineering professor, for engineering students. From the sound of it, it doesn't seem to me that a "hard science" is mutually exclusive from a social science.
A social science is simply a science that pertains to human behavior involvement, such as psychology, social and cultural geography, (human) history, political science, etc. It's to distinguish it from natural sciences that (can) exist regardless of human existence (physics, chemistry, astronomy, biology, geology, etc.).
Economics is physics and mathematics; it's what distinguishes a practicing engineer from a practicing scientist (an engineer's job is to do the most with the least (that's what optimization & efficiency are about), which is essentially about mainly or predominantly getting the cost as low as possible for that widget (whereas a scientist's job is practically to beg for the billions of dollars it costs to build that fancy new particle collider).
The only mathematical distinction between economics and physics (other than the human involvement stuff) is that economics uses a dollar sign (or whatever denomination) as part of their calculations. If you remove it, you have mass or energy, and if you're talking about something like a pay rate, you're talking about power (pay rate, or something in units of Joules per second in physics).
The word "work" is literally used to describe the action a person does when they're doing a job, and it's a word that has a specific meaning in physics; depending on the system, it's calculated as energy transfer as a product of force x displacement x angle between the force & displacement direction of an object (linear mechanical), torque x angular displacement (rotational mechanical), isobaric: pressure x change in volume of a gas, heat added to a system - change in internal energy aka 1st law of thermodynamics, electrical: charge x potential difference, gravity: mass x g x height, etc. The bulk of manual labor work done by humans is the mechanical type of systems. They all have the same SI units as energy: J (Joules).
You also mentioned political science & I think I can agree that it also plays a role; in a nutshell, political science is about the use of force on society (as in who, what when, where, how, and why to apply it). Force is also a word that has a specific meaning in physics and is Newton's 2nd law of motion: F=ma (force = mass x acceleration). In the political science sense or context, it's about imposing human restrictions on work (e.g. the work involved in breaking into a shop or car to steal things).
I know there's more to work than manual labor, but the same type of principles apply to white collar jobs.
The operation of the economy can be analyzed and designed, just like any other engineering system, for optimization and efficiency, and that's what's happening when an employer is making a decision about who to hire.