6. Determination of Prices

How are prices formed in a barter economy?  Let us start with the case of an isolated exchange, and then later bring in additional buyers and sellers.

Suppose Johnson and Smith are considering making an exchange: Johnson’s horse for some of Smith’s barrels of fish.  Whether the exchange is made will depend on the value scales of Johnson and Smith.

Smith’s Value Scale

• …
• 103 barrels of fish
• 102 barrels of fish
• 101 barrels of fish
• (A horse)
• 100 barrels of fish
• 99 barrels of fish
• …
•   ...

Smith will only make the exchange if he can give up 100 barrels of fish or less (100 is his maximum buying price).

Johnson’s Value Scale

• …
• (103 barrels of fish)
• (102 barrels of fish)
• A horse
• (101 barrels of fish)
• (100 barrels of fish)
• (99 barrels of fish)
• …
•  ...

Johnson will only make the exchange if he can obtain 102 barrels of fish or more (102 is his minimum selling price).  It is clear that in this case, the exchange will not be made.

Suppose however that Johnson’s value scale was as follows:

Johnson’s Value Scale

• …
• (83 barrels of fish)
• (82 barrels of fish)
• (81 barrels of fish)
• A horse
• (80 barrels of fish)
• (79 barrels of fish)
• …
•  ...

Johnson’s minimum selling price is now 81, so he will now make the exchange if he can obtain 81 barrels of fish or more.  What price will they agree on?  All we can say is that it will lie somewhere between 81 and 100 barrels of fish for the horse.  Exactly what it will be depends on the bargaining skill of the parties.

Now let us add another individual, Brown, who also has fish to offer Johnson in exchange for a horse.  Smith and Brown are competing against each other, both trying to buy a horse by selling as few fish as possible.

Suppose Brown’s value scale is as follows:

Brown’s Value Scale

• …
• 93 barrels of fish
• 92 barrels of fish
• 91 barrels of fish
• (A horse)
• 90 barrels of fish
• 89 barrels of fish
• …
•  ...

Since Johnson is looking for the highest price possible, now Smith will not be able to acquire the horse in exchange for 81-90 barrels of fish, because Brown will outbid him, until the price is above 90 barrels.  At this point, Brown will stop bidding (90 is his maximum buying price) and the exchange will be made with Smith and the price will lie somewhere between 91 and 100 barrels of fish.

We see that as more individuals are added, the band of possible prices – the bargaining zone – gets narrower.  With a few more individuals competing with Smith to make the exchange, there may be one willing to pay 99 barrels, so Smith would may be forced to pay exactly 100 barrels of fish, because any less and this competitor would still be interested.  Unless a competitor emerges who is willing to bid 101 barrels, thus outbidding Smith, Smith will be the most capable buyer and the sale will be made to him.

So, the price will be between the maximum buying price of the most capable and that of the next most capable competitor, including the former and excluding the latter.

The case of many sellers to one buyer is the direct converse of this.  Thus, the price of barrels of fish in terms of horses could be considered.  Johnson seeks out sellers of fish, and begins by bidding 1/120 of a horse per barrels, say.  That is, he offering one horse to buy 120 barrels of fish.  Since none of the sellers will accept this, he will need to bid lower.  When he bids 1/100 horse per barrel, Smith will accept the offer, since this is his minimum selling price.  It is clear than Johnson will not buy 99 fish from someone else when he can get 100 fish from Smith.  In this case, Smith is considered the most capable seller. 

So, the price will be between the minimum selling price of the second most capable and that of the most capable competitor, excluding the former and including the latter.

Now that we have looked at one-sided competition, either from the buyers’ side or the sellers’ side, let us now consider competing sellers and competing buyers together.

The following lists the maximum buying prices of each of the individuals looking to buy horses in exchange for fish.

Buyers of Horses      Maximum Buying Price

X1                               100 barrels of fish

X2                               98

X3                               95

X4                               91

X5                               89

X6                               88

X7                               86

X8                               85

X9                               83

The following lists the minimum selling prices of each of the individuals looking to sell horses in exchange for fish.

Sellers of Horses      Minimum Selling Price

Z1                                81 barrels of fish

Z2                                83

Z3                                85

Z4                                88

Z5                                89

Z6                                90

Z7                                92

Z8                                96

Naturally, buyers will tend to start by bidding a low price, while sellers will start by asking for a high price.  Suppose the buyers bid 82.  At this price, only one seller will sell, Z1.  He would be foolish to accept this offer however, as the buyers are willing to pay more. 

At a price of 84, two sellers, Z1 and Z2, will be in the market, and one buyer, X9, will have dropped out, leaving 8 buyers.  That is, there is now a supply of 2, and a demand of 8.  As the price increases, the supply increases and the demand decreases.  It can be seen that at price of 89, the supply will exactly equal the demand.  5 exchanges will be made, and they will all be made at a price of 89.  Z6, Z7 and Z8 will not be able to obtain the prices they were looking for to sell, and X6, X7, X8 and X9 will not be able to buy at the prices they were willing to pay.  This price, established by a market of competing buyers and competing sellers, is known as the equilibrium price.

Note that for Z6 (and Z7 and Z8), at a price of 89, they valued holding their stock rather than selling it.  This may be because they feel the horse in direct-use value is more than 89 barrels of fish in direct use value.  Alternatively, it may be because he expects to sell the horse later for more than 89.  This is called speculation.  A seller may refuse to sell a good at a certain price because he speculates that the price will rise in the near future.  Conversely, a buyer may refrain from purchasing at a certain price because he speculates that the price will soon fall.  Speculation (if correct) tends to smooth out price fluctuations and speeds the movement of the price towards the equilibrium price.  Speculation provides a great service to consumers, by providing goods at times when they are needed most.

Hence, in addition to the demand from X1-X9 to obtain horses, there is also the reservation demand from Z1-Z8 – their demand to hold on to their stock.  The total demand to hold therefore includes both the demand from non-owners for exchanges and the demand from owners for refraining from selling.  With a high degree of specialization, the reservation demand in usually for speculative reasons; specialized sellers do not tend to value their product very highly for direct use-value.

If (for some reason) the price was held down at 84, there would be “unsatisfied demand” or excess demand, or shortages.  Conversely, if the price was 95, there would be “unsatisfied supply” or excess supply, or surpluses.  On a free market, where the equilibrium price is attained, there are neither shortages nor surpluses; the market is said to have “cleared”.  If shortages or surpluses appear, it is a sign to the buyers and sellers that the price needs to be changed.

Note that this analysis is unchanged by removing the assumption that each of X1 to X9 are separate buyers and Z1 to Z8 are separate sellers.  They could be the same seller, with multiple horses, who will value each of his marginal units of horses separately.  He may have a minimum selling price of 81 for one of his horses, and then 83 for a second horse, then 85 for a third horse, etc.  As his stock decreases, the marginal utility will increase; each additional horse that he may sell will be worth more to him than the one before it.  If Z1 to Z8 are all the same individual, he will sell 5 horses on this day.

It is clear that one price must rule over the entire market.  Otherwise, arbitrage opportunities would exist; middlemen could buy low and sell high and the price discrepancy would disappear.  Prices will always tend towards the equilibrium price.  Because value scales are constantly changing however, the equilibrium price itself is constantly changing.  If there are (non-temporary) variations between prices in different locations or businesses, then the goods in the different locations must be being evaluated separately (i.e. they must be two different goods, not merely two separate supplies of the same good). 

Durable goods (whether producer or consumer) yield a flow of services over time.  The price of a service is the hire or rental price of the good; it is how much someone would pay to use the durable good for a given period of time.  The rental price is determined by the marginal productivity (if a producer good) or marginal utility (if a consumer good) of the service.

The outright purchase of a durable good is its capitalized value, and tends to equal the “discounted” present value of its total expected flow of future services.  It is discounted because of time preferences; an actor will not evaluate a given unit of service in the distant future the same as a unit of service available today or tomorrow.  For example, a machine that will produce 100 units of a good over the next year might be valued less than 90 units of that same good now.  This applies to all capital, land and labor.  In the case of labor, the rental price is called the wage of the worker.  Note that unlike land and capital, labor cannot be bought outright, due to the inalienable will of individuals.  Such a purchase would imply slavery.

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