Purchasing power

The price system makes possible to communicate the combined knowledge (in terms of supply and demand) from people each of whom possessed only a portion of it. Based on that equally divided knowledge people plan, interact and coordinate the utilization of resources, producing a solution. — Summary from The Use of Knowledge in Society. F.A. Hayek. 

An economic good is any product or service that is desired.

Economic goods may be subjectively classified as consumer goods and capital goods. 

Consumer goods are final goods, those which function is to be enjoyed. Capital goods are tools, intermediary goods which main function is to achieve another good, usually by helping to its creation. But if the capital good is intended to be used to obtain another good by exchange, that is, to store purchasing power to allow the acquiring of products and services in the future, then we are referring to a special kind of capital good called money.

Examples:

-Gold, a good that is generally considered money, could also be considered a consumer good if the intention is to work as a relic.

-Houses, a consumer good that today usually works as money because it may be able to store value better than fiat currencies.

The exchange rate between a money and another good is called price or purchasing power depending on which side is chosen as the unit of measure. It is determined by individuals' preferences (supply and demand). 

Purchasing power: amount of goods (demand for a money) exchanged per a specific amount of monetary units (supply of a money).

Purchasing power = 1 / price. 

Price: amount of monetary units (demand of a good) exchanged per a specific amount of a certain good (supply of a good).

The monetary equation of exchange (M*V = P*Q) have been used to justify different theories about prices.

M = # monetary units

V = # times a monetary unit is exchanged for goods per time "t"  =  1 / average "t" holding a monetary unit.

P = price per product

Q = # goods exchanged per time "t"

substituting:

purchasing power = Q * average "t" holding an unit / M

average "t" holding an unit is the average time those savings last when maintaining an average rate of spending. 

The quantitative theory of money states that the increasing in the quantity of monetary units (M) should proportionally increase total goods' prices (P*Q). It assumes V will tend stay constant which constitutes a fallacy.

V is a consequence of the aggregate demand for a money versus the aggregate demand for other capital and consumer goods. This relation varies over time due to new individual preferences.

Examples of conditions that could cause rapid changes:

-Economic restructuring like an economic depression due to excess debt.

-Relative change in the monetary properties of money with respect to other goods (such as the deterioration of the quality of a money when its quantity of monetary units (M) increases significantly).

-Redistribution of (M): different entities tend to demand different goods (including money) to different degrees.

Basic example on how P and V may change even if we assume M and Q stay constant:

Society consisting of two members. M and Q are constant.

M = 4 gold coins

in terms of price, 1 apple = 1 fish

Alice produces 8 fishes per day and Bob 8 apples per day, so Q = 16

Alice only consumes what Bob produces and vice versa.

t = 1 day

if preference for savings = 1 day of average consumption:

Purchasing power of 1 gold coin = 16 * 1 / 4 = 4 (4 fishes or 4 apples)

if preference for savings = 2 days of average consumption:

Purchasing power of 1 gold coin = 16 * 2 / 4 = 8 ( 8 fishes or 8 apples)

A higher preference for that money forces prices to go down. Now Alice and Bob have a greater quantity of savings, while their production and consumption level is maintained.

In this case, P and V depend exclusively on the appreciation for that money. P and V decrease until the exchange is desired by both parties.

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Summary:

The purchasing power of money is not only about its quantity, it is also about its relative demand as savings.

​Presumably, higher quality money will be more demanded.