Especially, now, since I have been living in China where people are desperate to get ahead in the modern capitalistic Chinese world I have seen many people who believe that, if they charge a high price, they will be able to get rich quick and retire early.  As a former member of the Wall Street proprietary trading community, in arbitrage, I have always been taught that greed is not good.  The Wall Street expression goes: bulls make money, bears make money, and pigs end up broke or in jail.

A basic law of economics, based on psychology and logic, is that the demand curve is downward sloping: people are more willing to buy a [product, if the price decreases; less willing, if the price increases.  Then, equilibrium will occur at the intersection of the upward sloping supply curve and the downward sloping demand.  To fill in a few more details, total revenue can be found as the rectangle on such a supply-demand graph touching the intersection and going to the origin of the graph: it is simply Revenue = PxQ where P is the sales price per unit and Q is the quantity sold.

Profit is defined as revenue - cost, which can be put into equation form as: I = R - C = PxQ - ATCxQ, where ATC is the average unit cost and I stands for income or profit.  From calculus, we know that a maximum (technically, an extremum, which could be a max, min, or turning point) is found by taking the first derivative of something and setting it equal to zero.  Thus, in the case of profits, we have the condition for maximum ΔI/ΔQ = QxΔP/ΔQ + P - QxΔATC/ΔQ - ATC = 0.  Other standard concepts, in economics are marginal variables, which are just first derivatives of quantities.  Specifically, marginal revenue = MR = ΔR/ΔQ = P + QxΔP/ΔQ, which is always less than P with downward sloping demand, and marginal cost = MC = QxΔATC/ΔQ + ATC.  In the latter case, we also, note that since cost curves are U-shaped, MC will be under ATC for sometime, and it will cross over at minimum ATC, then, move above it. 

Looking back at our profit maximization condition, we see that we can rewrite it as ΔI/ΔQ = 0 = MR - MC.  Thus, without going into the proper secondary condition for actual maximization, which requires that the second derivative is less than 0, we arrive at the profit maximization condition MR = MC, which simply says that we should sell units up to the point where marginal revenue is just equal to marginal cost.

That condition, in turn, gives us a price and quantity for sales.  If we sell less than that maximal quantity at higher prices, our profits will be less than maximal; if we sell more than that quantity at a lower price, the same is true.  That this theorem is valid, even in the case of a pure monopoly, tells us that we should abide by it because even a pure monopolist, much less a lowly competitor in any other business, cannot get away with charging any price they desire.

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Craig L. Mattoli, CEO
Red Hill Capital Corporation, Delaware, USA
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