Consider an active battery with the physics of where:
P is then solved as
When the energy power is constant, it is then
Classify the energy powers as
So, it follows:
Let be the consuming time length and be the charging time length. The shorter time length, the more efficient the battery. Some facts about the battery:
When people have some unexpected energy consumption which is not saved off other economic activity, they get the energy from the standby battery provided by those battery owners who are willing to help and charged back later by the borrower who is obliged to save off his economic activity. Denote the following:
Assuming the repay never default, it is the compound interest and time preference concept, for examples:
The activity of lending someone A energy then getting the repayment B energy after t can be done by the physical consuming/charging activity as well as the change of the ownership of the battery. Therefore, the same additional risk-free lending interest rate shall apply to the change of ownership of energy to be arbitrage-free as well. Energy storage is the only medium to move energy across time. Money is the only medium to move capability of purchasing power across time. Currently the major method to storage energy is pumped-storage hydroelectricity which claims A/B can be hopefully 87%. The repayment B can be partially sponsored by others, particularly Mother Nature, who provides part of the energy necessary for the repayment in . Let N be the part sponsored by Mother Nature and L be the part responsible by the borrower saved from his steak in , then B = N + L in the above formula. It is possible A/B is 0.87 and the genuine risk-free lending rate is 13% while A/L is 0.995 and the post-sponsored risk-free lending rate is only 0.5% because N is 14% of L. More precisely, . It all comes down to how much energy people contribute in the . If Mother Nature provides all the , then the post-sponsored risk-free lending rate can be zero. Many parts of life are cheaper simply because Mother Nature sponsors and the real price will appear when Mother Nature is doomed or people grow up and pay the fee/interest to Mother Nature as well as if she is a real person in the economics.
That purchase of goods by money needs some fee is basically short of energy and to borrow the energy at the time of purchase. This also explains the fee rate is the same as the post-sponsored risk-free lending rate. However, this battery is competing with our body battery, meaning that a borrower might appeal to the body battery of his friends rather than appeal to the money battery if the lending interest rate of the money battery is higher than that of the body battery. Therefore, people may adjust the contribution in the energy for money battery so that the post-sponsored risk-free lending rate is the same as the body's risk-free lending rate aka time preference. After all of the above, the three rates: fee rate, risk-free lending rate and time preference are then the same. The change of the battery ownership is the transaction ledger for energy accounting. The active batteries, consuming and charging, serve as medium to move energy across time. The inactive batteries, off the grid and consuming no energy, serve as saving which the owner can command anytime. Saving is never lending or investment said by Keynes.