I thought this might be a useful source of arguments against "real-world economics". I hope others agree but if not, that's fine that's why we have a thread graveyard.
Most objectors to AE usually default to "real-world" economics as opposed to "theoretical" economics. But although their doctrines are intuitively plausible, they are logically contradictory, so they cannot serve as a true "real-world" understanding of the economy.
For instance, most of these "RW" economists would object to a lower minimum wage by saying that if wages fall, then workers couldn't buy the products of their labor, thereby lowering aggregrate profits and thusly causing the economy to fall into a depression. However they would also say that imposing a minimum wage would not lower aggregate profits enough so that capital couldn't afford to employ people, and so capitalist income -since it falls at a lower rate than worker's income (wages) -doesn't provoke depressions. Now these two scenarios don't really mesh logically. If capitalist income falls slower than a corresponding fall in labor income, then if all labor income fell, then how could capitalist income fall to zero too? Wouldn't it rather be that capitalist income would remain in some small proportion? So it couldn't be true that a fall in wages would provoke a depression and this contradicts one of the central conclusions of real-world economists.
Second, most RW economists hold that if laborers compete with each other over employment, then this will cause wages to drop and further,since owners of the productive factors care about themselves mainly, then why would they want to higher more workers at a lower wage and/or pay higher wages? They would just rule over their workers like feudal lords. This is where marginalism comes in. When everyone is cheaper to employ, jobs that seemed "unnecessary" at the higher wage now seem at least "not ruinously costly". Therefore employers would want to fill these subjectively necessary positions with new workers. Need is subjective. That workers would be paid a higher wage is also a possibility. If workers bargain their wages down to something at or below subsistence, then entrepreneurs -who as we all admit have only their interests at heart -would still bid up their wages, since some businessman would realize, after working with the person, that laborers probably provide more labor when they are paid enough to eliminate the pangs of hunger or weakness or they would realize that it could be less costly to just take care of all labor's needs in one sitting than sabotaging the production period w/feeding breaks or some such thing (Indeed this cuts at the heart of the idea that businessmen are self-centered, indeed that anyone is self-centered, yet another fallacy of empirical experience w/ the economy). Analogous things happen to the normal consumer in everyday life. If the prices of peanuts falls, then I would buy up a lot and planters would experience a rise in income and would probably raise their prices in order to cover the costs of supplying so many more customers. Similarly workers are selling their labor and the output of labor is greater the greater the wage (indifference analysis notwithstanding).
So for all these reasons, real-world economics cannot be accepted as a working model of the economy.
As far as minimum wage goes it's supposedly in place to protect middle-aged workers.