Purchasing power: # of products exchanged per monetary unit.
It is determined by the demand of money (# of products exchanged) and the supply of money (# of monetary units exchanged).
Price: # of monetary units exchanged per product.
Purchasing power = 1 / price.
A higher preference for saving causes a purchasing power increase and makes the society wealthier.
Monetary equation of exchange: M*V = P*Q
M = # monetary units
V = # times a monetary unit is exchanged for products per time "t"= 1 / average "t" holding a monetary unit.
P = price per product
Q = # products exchanged per time "t"
purchasing power = Q * avg "t" holding an unit / M
Purchasing power is directly related to avg "t" holding an unit, that is, how much time savings last when maintaining an average consumption.
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 saving forces prices to go down. Now Alice and Bob have a greater quantity of savings, while their production and consumption level is maintained.