Rethinking Economics 2 : Perfect Competition, Maths & Crap

This is originally posted on Thursday, 14 January 2010 at 00:24

This is not my own work or discovery, but it comes from George Stigler, "Perfect Competition, Historically Considered" in The Journal of Political Economy, 1957. I merely put this online to propogate the reality of neoclassical economics. However, I will add that this alone does not justify the notion that neoclassical economics is entirely flawed- other flaws will be explored in the future.

As we are taught in schools, perfect competition consist of a few features:

P - Price which varies according to the quantity. In perfect competition, prices for individual firms and the market in which they belong are the same since no firm has substantial market power to influence prices.

X - Total quantity/output of demand in the market.

Q - Quantity/output of demand of an individual firm. Mathematically,

X = Q1 + Q2 + Q3 + Q4 + Q5 + ..........+ Qn,

where n is the number of firms in the market.

dP/dX is the gradient of the Market Demand curve - a downward sloping curve that reflects the total quantity of output of all the individual firms in the market

dP/dQ is the gradient of the Individual Firm Demand curve - in perfect competition, the firm has a perfectly horizontal demand curve. This suggests that as the individual firm's output approaches infinity, price remains constant and unaffected. It is also calculated as dP/dQ = dP/infinity = zero.

Here's the beef (slang):

dX/dQ = 1

What?! It basically means a change in the individual firm's output only cause a same change in output in the market.

To illustrate:

X = Q1 + Q2 + Q3 + Q4 + Q5 + ..........+ Qn

X - Q1 = Q1 + Q2 + Q3 + Q4 + Q5 + ..........+ Qn - Q1

A reduction in firm output of Q1 (we can intepret as Firm 1 collapsing entirely) will cause a reduction of Market output by Q1.

Hence, dX/dQ = -Q1/-Q1 = 1

Ok, so under neoclassical economics theory of perfect competition, we define

dP/dQ = Horizontal curve of value zero.

dP/dX = Downward sloping curve

dX/dQ = 1

THAT'S A LIE. THE MATHEMATICS IMPLIED IN THE CURVES ARE FLAWED. WHAT STUDENTS HAD BEEN LEARNING ALL ALONG (AND ACTUALLY DRAWING THE PERFECT COMPETITION FIRM DEMAND CURVE ALONGSIDE ITS MARKET DEMAND CURVE) IS NOT EVEN CONSTRUCTED ON SOUND AND "SCIENTIFIC" MATHEMATICS.

Check it out:

dP/dQ

= (dP/dQ) (dX/dX)

= (dP/dX) (dX/dQ)

= (dP/ dX) (1), since we established dX/dQ = 1

= dP/dX

Now we have done it! Look what we got here:

dP/dQ = dP/dX (what the hell?!)

Recall what was mentioned: "obviously dP/dQ does not equate to dP/dX in value since their slopes are different in the first place"

So why do we observe this contradiction? I'm not manipulating figures since they are all variables worked out through simple calculus and differentiation. It makes me wonder why nobody notice this fatal flaw since 1957. Or were they just blindly assuming it?

Ironically, the ideal state of Perfect Competition is fundamentally flawed in the mathematics used to construct it.

Sad. Really sad. But in the meantime, I'll stick to this theory for the sake of my exam results. And anyway, perfect competition will never exist.