Value & Capital, Note to Chapter VIII -- CONVENTIONAL OR RIGID PRICES

Chapter VIII concludes with a note that examines what happens when some price is fixed.  Figure 22 shows supply and demand curves (S and D) for a single commodity, with the prices of all other commodities assumed to be fixed.  If the price of this particular commodity were not fixed, then it would move to the level represented by the intersection of the supply and demand curves.

If the price were fixed at a higher level (say at the level OL), then the demand curve implies that only a quantity ON would be sold, even though the supply curve implies that sellers would be willing to sell a quantity LT.  (Note that, by construction, the quantities ON, LP, and MQ are all equal.)  The note then argues that

The situation is therefore identical with that which would have arisen if a price OL had been fixed for buyers only, a price OM for sellers only, the difference between those prices being handed over as a bonus to those sellers who actually do make sales.  (Alternatively, we may suppose that a tax equal to LM per unit is laid upon the commodity, and the proceeds of that tax handed over to the sellers.  A process made familiar to us by the [UK] Ministry of Agriculture!)

The text points out that this construction retains an equilibrium in which supply equals demand, but "we have to sacrifice the rule that there is only one price in the market."  The real price is the assumed fixed price, and the text introduces the term "shadow price" to represent the price determined by equilibrium conditions.  In this context, the shadow price is OM.  The text notes that this shadow price is not the price that the sellers actually receive, so there is no income effect associated with it, but it does govern substitution effects on the supply side.

The text then assumes that demand for the commodity increases (represented by a change in the demand curve from D to D').  If the price remains fixed at OL, the amount bought will increase from LP to LP', and the shadow price will increase from OM to OM'.  The text points out the significance of the fact that the "supply will increase in just the same way (apart from the income effect) as if the actual price had increased from OM to OM'.  That is why the shadow price is important."  Any reactions in the markets for other commodities that are caused by changes in the supply of this commodity "will proceed as if there had been a real change in price; it is only is only reactions on the demand side which are cut off by the price-fixation."

Finally, the text considers an example in which there is "a minimum price for wheat, combined with jut sufficient restriction of supply to make the minimum price effective."  If there is an increase in demand, our model above shows that even though the fixed price doesn't change, there should be an increase in supply (as described by the supply curve).  Because this expansion in supply may come at the expense of some other crops (i.e. lower quantities of these other crops may be supplied), the prices of these other crops may rise, just as if the price of wheat had risen.

The note concludes that "The significance of this proposition (which is equally valid for maximum prices, when all term are reversed) is self-evident.  Price control can damp down a general rise in prices; but, unless it is absolutely complete, it cannot prevent it altogether."