Again on supply and demand - a critique of Marshall

why am i doing a new video on the topic of supply and demand well it's become clear to me from comments people are putting on the previous videos that my account of why demand Theory has more free variables than unknowns was a bit too cryptic and technical so I'm gonna try and explain this in more detail so the first thing is to say what was the attitude of Marx to supply and demand he says it's supply and demand regulate nothing but the temporary fluctuations of market prices they'll explain to you why the market prices of a commodity rises above or sinks below its value but there never account for the value itself at the moment when supply and demand equilibrate each other and ceased to act the market price of a commodity coincides with its real value with the standard price around which its market prices oscillate in inquiring into the nature of value we have therefore nothing at all to do with the temporary effects of market for on market prices of supply and demand now in saying that Marx was sticking to the line of his predecessors so Ricardo had said it is the cost of production which must ultimately regulate the price of commodities and not us has often been said the proportion between supply and demand the proportion between supply and demand may indeed for a time affect the market value of a commodity until it is supplied in greater or less abundance according as the demand may have increased to diminished but the effect will only be of temperature Asian and Adam Smith before that said when the quantity of any quantity which is brought to market falls short of the effectual demand all those who are willing to pay the whole value of the rent wages and profit which must be paid in order to bring it thither cannot be supplied with a quantity they want rather than want it all together some of them will be willing to give more he's using the word want in a slightly in archaic 18th century used there now you have to realize that in Smith the term natural price corresponds to what Ricardo and Marx called value and Smith held that supply and demand could only bring temporary fluctuations around the natural price all the classical's to a greater or lesser extent of clarity agree that the labor required for production is the source of value supply and demand only produced temporary fluctuations and this had political consequences if you accept that labor as a source of value the Ricardian socialists could argue that labor had the right to the full value of product now this was obviously an ideological problem for capitalist economics and it was resolved by Marshall who aimed to overcome the Disick illiberal view of the classical's in which market price was given by with one in which the market price was given by the intersection of supply and demand curves previously the classical economists had said the equilibrium price is the labor value and supply and demand are disequilibrium phenomena instead Marshall says no supply and demand interact to produce an equilibrium which is the market price and this has been the standard treatment by neoclassical economists ever since and the diagram to the right is Marshalls original supply and demand curve hand-drawn in his book economics this had certain ideological advantages if supply and demand explain equilibrium price then you can dispense the classical theory that supply and demand was just disturbing factors and if supply and demand determine value then the Labour theory of value can be discarded it was no longer necessary to explain the center of gravity of prices because that was now given by the intersection of these two curves now I'm going to examine the curves Marshall gave in some detail now at one level these curves are just something he sketched on graph paper with actual values for them and I'm going to examine them in detail because once you examine them algebraically you see what nonsense this whole theory is let's look at his demand curve this curve here the buyers demand curve now because it's turning down sloping down but curved because it's not a straight line it must be at least a second-order polynomial so the function D of Q were curious their quantity can be expressed as a polynomial a constant a plus a constant B times Q plus a constant C times Q squared you need at least a second order polynomial to do that since Marshall gives actual points we can solve this polynomial he shows that when demand is zero demand is zero price is 15 so we know a must be 15 in his equation when demand is 10 price is 9 when demand is 13 price is 8 so we can fill these in and get to other points of his polynomial now with two unknowns two other points we can solve the polynomial you first we simplify into 10 B plus 100 C equals minus 6 13 B plus 169 C equals minus 7 if we eliminate B by multiplying the top row by 1.3 and subtracting it from the bottom row we get the equation 39 this is standard Gaussian elimination we get the equation 39 C equals 0.8 so C equals zero point two zero five and filling this into the equation 10 B 400 C equals minus six we can solve that B must be 0.85 so we actually can deduce from the curve he's drawn what the equation for demand is the demand as expressed as a quantity is 15 minus 0.85 Q plus 0.205 Q squared that's actually the equation for the curve he's drawn now let's look at this it's a really odd formula and it's got three constants 15 zero point eight zero five zero point 205 and where does he get these constants for well he just made them up he plays let's suppose that this is the function but he doesn't write it down explicitly as a polynomial because once you write it down as a explicitly is a polynomial it's clear this totally arbitrary senseless equation but behind the scenes that's the equation he's got now if we look his supply curve it seemed more complicated we see it curves one way then it curves the other way so it must be at least a third degree polynomial so it must be an equation of this form our peril means squared and cubed sorry I should have formulated it properly I'm not going to drive the actual graph actual values for the constants e FG and H from his graph that's just tedious to go through the steps but the full set of equations that Marshall has for the determination of price is a demand function a plus B - 4 C Q squared and a supply function s Q equals E Plus F Q plus G Q squared plus h q to the power of three and he then says the equilibrium is given by DQ cos s Q and he claims this math enables him to simultaneously obtain in the price that will obtain and the quantity that will be solved well just as a piece of deduction that's fair enough but note that he's got seven free variables a b c e f g and h now where do these come from as i said he just makes them up but in general if you want to formulate a mathematical rule explaining a phenomena a rule that you want to say is a law that governs that phenomena according to the mathematician and philosopher like nets it should have as few free variables as possible now we can illustrate that with Leibniz is contemporary Newton who formulates his law of universal gravitation his law of universal gravitation says that force is a function of the mass of planet 1 the mass of body 2 and the distance between them and it takes the form G m1 m2 d squared sorry over d squared I've missed outer term put that back in three explicit parameters the masses of the two bodies and their distance in addition to that one free variable the universal gravitational constant G now that's a free variable and that has to be filled in it has to be given a value before you can use Newton's equations to work out the force between the Earth and the moon or the force between the Sun and the earth you need to know the masses the distances and you need to know G so how do you determine what G is well it can be done experimentally cavendish in 1897 used a technique called torsion balance to measure what the gravitational forces and the torsion balance involved two large lead weights here and two iron weights here and a thin wire which could take rotation and act as a slight spring and by adjusting the distance between the bar and the the balls moving the balls together he could measure the force by the degree of deflection of the lower bar and he measured the degree of deflection by a mirror which he shall now beam through and used saw by how much the beam was deflected to give a measurement of the force acting there so in principle the G could be measured experimentally now let's take another theory from the same from the 18th century the Smith Ricardo Labour theory of value says that the price of kamon TX is by the labor content of X divided by the labor content of a pound of silver that's the price in terms of silver it has only two variables both of which are in principle measurable and it's got zero free variables Smith actually examines the price of corn in terms of silver and the influence of more productive silver mines coming in into production to see that now he has a testable theory here Smith has because word the case that the productivity of Agriculture were rising let's say more bushels of corn were produced by labor and the productivity of silver were falling and that is to say the silver mines were getting depleted and requiring more labor Smith's prediction where is that the formula predicts that silver price of corn will fall that is to say a given pound of silver will buy more corn if we found historically that in fact the silver price of corn rose then Smith's theory of price would have been falsified Smith actually went back looking at price records of corn on the witch's tur market to 1280 he's writing in the mid 1700s so he looked 500 years back at the corn prices to test his theory now let's go back to Marshall Marshalls got his seven free variables but he has no practical way of measuring any of these constants they're just virtual constants that he's imagined what can you observe in practice all you can observe is that at the Winchester market so many tons of corn were sold and that it was sold for say three shillings and sixpence a bushel this allows you to fix at most two of seven free variables if you've got two observables an equation with seven variables you've only got two constraints and that leaves sorry that should say Li five as a fudge factor now could you get over this with a time series could you take a time series of prices and quantities which Smith did with corn prices no you can't because according to Marshalls theory any change in price involves a change in either the supply or demand function let's assume only demand is changing at time one we have demand function one which has got constants a1 b1 and c1 demand at time two we have demand function two with a2 b2 and c2 now we now have observations in the year let's say 1200 and the year 1300 we have 10 free variables instead of the original 7 the original 7 plus the three new ones for the year 1300 so we've got four observations - prices in two quantities but whereas feet previously we had five extra free variables now we've got six extra free variables the longer the time series you use the more underdetermined becomes Marshalls theory now mathematically you say a set of equations are under determined when there aren't enough equations to constrain the free variables and another way of saying that is it if you've got an underdetermined theory it's essentially random an underdetermined theory is compatible with any observation you can play around with the free variables to make it fit anything and has no scientific predictive powers this is the point that libelous makes that you can put down any random series of dots and fit a function through it but if unless your function contains a lot less free variables and observations it can't be treated as a law so how did Marshall pull off this confidence trick this mathematical absurdity how do you get it accepted well I think it's through the trick of using visual reasoning broaden algebraic reasoning it's partly what I call the power of icons this was I can't remember which classical philosopher observed that if you stare daily at the statue of Diana you of any of the gods you come to believe that God really exists and Catholics are going and adore the icon of the Virgin Mary come to believe that the Blessed Virgin is real because they look at this icon so often it forms a concept in their mind that there really is a thing corresponding to the icon if you show students an icon in this case the icon of these supply-and-demand curves and they look at it repeatedly through their studies they will come to believe that these curves represent something real run just something that marshals scribbled on a sheet of graph paper pictures are powerful because they enter the brain by the visual cortex in an immediate an uncritical way sometimes this is useful in maths this is white Venn diagrams are easier to work with when teaching set theory than using formal set theory it's much easier to understand because it enters directly into the highly parallel part of our brain the visual cortex which is the most powerful information processing section of our brain but it is an intuitive information processing system it's not a deductive and critical system if you want to go into this in more detail I can advise you to read like of an honest book on the underlying neural basis of maths there it's it's called where mathematics comes from now marshals supply curves have an intuitive appeal but as soon as we translated them into algebra we saw the war problems the point is don't trust optical illusions your brain your visual cortex is very susceptible to optical illusions instead of relying on visual images like that which are okay for pedagogy but if you want to see whether something is true don't trust optical illusions actually look

Channel: Paul Cockshott

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Length: 20min 58sec (1258 seconds)

Published: Sun Apr 05 2020