In my previous post, I had touched upon the basic concepts value, utility, marginal utility and total utility. In particular, I had emphasized the nature of these important economic concepts – their subjective and ordinal nature. This time, I shall take the process of reasoning a few steps further and demonstrate the mechanisms that drive exchange and price discovery on the free market.
Ends, Means, Value Scales and Human Action
Consider a man who has a variety of ends that he seeks to attain through the employment of cows and horses. Let’s further say that the first cow satisfies the most valued end, the first three horses satisfy the next three most valued ends, the next cow satisfies the next lower valued end and so on as per the table below.
|Ranking of End||Satisfied by|
Let us try to understand how the man would act if he had a certain number of cows and horses and faced choices. Let us start with the scenario that he has 3 cows and 4 horses. Let us also suppose that he has to give up 1 animal – a horse or a cow. Which would he forego? Clearly, the 3rd cow satisfies an end ranked higher than then end satisfied by the 4th horse. Hence, he would give up a horse and be left with 3 cows and 3 horses. If instead of 3 cows and 4 horses, he started off with 2 cows and 3 horses and faced the same choice of giving up 1 animal, we see that the 2nd cow satisfies an end ranked lower than the end that the 3rd horse satisfies. Hence, he would give up a cow rather than a horse.
If on the other hand, the man starts off with 4 cows and 4 horses and has the option of adding one animal to his stock, which one would he add? Clearly, the 5th horse satisfies an end ranked higher than the end satisfied by the 5th cow. Hence, he would have to add a horse to his stock. To take another example, let us assume that he starts off with 3 cows and 3 horses and faced the same option of adding an animal to his stock. From the table above, we see that the 4th horse satisfies a higher ranked end than that satisfied by the 4th cow. Hence, he would choose a horse rather than a cow.
Many men and the phenomenon of trade and price
Let’s say there are 2 men – Smith and Johnson. Smith has barrels of fish and wishes to trade some barrels for a horse while Johnson has a horse and seeks to trade it for some barrels of fish. Let’s say their value scales are as below. Items in brackets are what a person does not have but has ranked on his value scale.
|103 barrels of fish||(103) barrels of fish|
|(A horse)||(101) barrels of fish|
|100 barrels of fish||(100)|
In this case, 100 barrels of fish is Smith’s maximum buying price for a horse while 102 barrels of fish is Johnson’s minimum selling price for a horse. Clearly, Johnson would not trade his horse in for anything less than 102 barrels of fish because doing otherwise would require him to act to lower his own utility. Smith, on the other hand, would not trade anything more than 100 barrels of fish to acquire a horse because offering more than that would require him to act to lower his own utility. Thus, we see that no trade is possible between Smith and Johnson.
If on the other hand, Johnson’s value scale were as below,
|(84) barrels of fish|
|(80) barrels of fish|
Smith’s maximum buying price of a horse would be 100 barrels of fish while Johnson’s minimum selling price of a horse would be 81 barrels of fish. Thus, we see that there is scope for Smith and Johnson to exchange a horse for anything from 81 to 100 barrels of fish and with both attaining positions higher on their value scales as a result of the exchange. We thus note an important point about trade – for trade to happen, the maximum buying price of the buyer has to be higher than or equal to the minimum selling price of the seller. Thus, we see in this case that the price of a horse can be any number from 81 to 100 barrels of fish. The exact figure would depend on the circumstances and the negotiating skills of Smith and Johnson.
This mechanism of price discovery becomes more complicated with the addition of more buyers and sellers in the market. Let’s for instance include another buyer of horses, Brown and let’s assume that their value scales are arranged as below.
|103 barrels of fish||93 barrels of fish||(84) barrels of fish|
|(A horse)||(A horse)||(81)|
|100 barrels of fish||90||A horse|
|99||89||(80) barrels of fish|
In this case, Smith’s maximum buying price is 100 barrels of fish while Brown’s maximum buying price is 90. Johnson, on the other hand has a minimum selling price of 81 barrels. Clearly, Johnson could trade with either Smith or Brown and be better off. For any price Brown offers, Smith is in a position to “outbid” him by offering a higher price that is still lower than his maximum buying price. If and when Smith offers 91 barrels of fish for the horse, Brown drops out of the race as any higher price would leave him giving up a higher ranked end to satisfy a lower ranked end. In such a circumstance, we call Smith the more capable buyer and Brown the less capable buyer. The actual price in such a circumstance would be high enough to exclude the less capable buyer though the exact price would be somewhere above the maximum buying price of the less capable buyer and up to the maximum buying price of the more capable buyer. Specifically, the price in this case could be anything from 91 to 100 barrels of fish and the exact price would depend on the circumstances and on Smith’s and Johnson’s negotiating skills.
On similar lines, when there are two sellers, the more capable seller would be the one with the lower minimum selling price while the less capable seller would be the one with a higher minimum selling price.
Let us now extend this case to a situation where there are multiple buyers and sellers. Let their maximum buying prices and minimum selling prices be as below.
|Buyer||Maximum Buying Price||Seller||Minimum Selling Price|
Let us assume that each seller has exactly 1 horse to sell. Let us draw out a table of the number of horses that would be offered by sellers (supply) and asked for by buyers (demand) at various prices from 81 to 100 barrels.
We see from the above table that at a price of 89 barrels of fish, the supply of horses is equal to the demand for horses and the market is said to be cleared at this price. There is no surplus or shortage of horses. At any price higher than this, it is possible for more capable sellers to outbid less capable sellers by bringing the price down. At any price lower than this, it is possible for more capable buyers to outbid less capable buyers by pushing the price up. Thus, we see that the market clearing price is also an equilibrium price towards which the market price of horses tends.
The table of the quantity supplied at each price level may be called the supply schedule for horses and the table of the quantity demanded at each price level may be called the demand schedule for horses. A graphical representation of the 2 tables (using the example described above) plotting the price at each quantity demanded and supplied will give us a very clear illustration of the principle of price discovery and equilibrium price and will show how the commonly used demand curves and supply curves of any good actually evolve from the process of reasoning explained above.
From the data in the table above, we can see that the Demand “curve” would be downward sloping and that the Supply “curve” would be upward sloping. This principle, demonstrated with horses priced in terms of barrels of fish, is applicable to any good priced in terms of any other good.
We also note that the demand and supply schedules, the identification of the equilibrium price and our understanding of the equilibriating process stems from our ability to draw up a hierarchy of values for each actor for each set of goods involved. This in turn is made possible by our understanding of the concepts value, utility, marginal utility and total utility as applied to ends and means, which in turn is a straightforward logical corollary of the action axiom.
The action axiom and its logical corollaries – value, utility, marginal utility and total utility – and their subjective and ordinal nature are powerful concepts that help us understand the processes of exchange and price discovery in a free market. Proper application of these concepts enables us to draw up the demand and supply schedules of any good in terms of any other good and thus understand the processes of price discovery and equilibriation of price on the free market.
p.s. : My entire analysis above is based on the far more elaborate analysis done by Murray N. Rothbard in his book Man, Economy and State with Power and Markets.