Why is Marginal Cost = Price better than Marginal Cost > Price for maximizing profit? [closed]

Isn't MC>P a better aim? Given the revenue you earn from each unit is more than cost in producing each unit?

• I think you mean MC < P, don't you? i.e. marginal cost less than price? (not greater than) – EnergyNumbers Apr 24 '19 at 5:31
• Also, aim in terms of what...? My aim is to have MC = \$0, P = \$10 billion and Q = 1, but perhaps that is not possible given the model? – Giskard Apr 24 '19 at 5:45
• The MC is not the cost of producing each unit. Rather, it is the change in total cost when you produce one more unit. – David Apr 24 '19 at 8:28

If $$MC, then the producer would want to produce one more unit of the good.

If $$MC>P$$, then she would want to produce one less unit of the good.

If $$MC=P$$, then she is maximizing her profits.

Your intuition is correct (assuming that you mean $$MC < P$$ rather than $$MC > P$$ as you wrote). For a given level of production, profits are indeed higher when $$MC < P$$ than when $$MC = P$$, as you'd expect from an increase in the price holding everything else constant.

So why do we say that a firm in a competitive market maximizes profit by setting $$P = MC$$? Because we're not looking at an increase in the price holding everything else constant, we're looking at a change in the quantity, holding price constant.

It may help to think first about the traditional model of monopoly, where a monopolist will maximize profit by choosing a quantity $$Q$$ that sets $$MC = MR$$, i.e. marginal cost = marginal revenue. Then, because they're a monopolist, they can sell that quantity $$Q$$ at a price $$P > MR$$ (and so we get $$P > MR = MC$$ or $$P > MC$$). This is because the monopolist has some control over their price: they can choose to go high price/low quantity or low price/high quantity. In the process of selling an additional unit, their revenue goes up ($$MR$$) by less than the price ($$MR < P$$), since they're moving towards the "low price/high quantity" end of the scale - they get paid the price $$P$$ by selling an additional unit, but they had to lower their price too and so make less on the other units they sell, making $$MR < P$$.

That takes us back to the competitive market. In the competitive market, each firm has no control over the price and so there's no price/quantity tradeoff - whatever quantity they pick, the price stays the same. So, in a competitive market, $$P = MR$$ by definition. So when they maximize their profit by choosing a quantity that sets $$MR = MC$$, since $$P = MR$$ we get $$P = MR = MC$$ or $$P = MC$$.

Intuitively, the reason the firm in the competitive market doesn't shoot for $$P > MC$$ is that the price is real darn stubborn. You can't coax it to go higher by picking a lower quantity (like you could if you were a monopoly). So it's not "I'd like to pick a price higher than my $$MC$$" because you can't pick a price. Instead, it's "I may as well continue producing more and more until my $$MC$$ meets the price". So, for a firm in a competitive market, profit is maximized at $$P = MC$$.