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Savings Relation

Eric Voskuil edited this page Nov 26, 2019 · 50 revisions

Time preference is the catallactic assumption of human preference for present goods over future goods. It is well established that time preference is reflected as the interest rate. It is shown here that the capital ratio has the same meaning and value.

The level of the pure rate of interest is determined by the market for the exchange of present goods against future goods, a market which we shall see permeates many parts of the economic system. [...] Thus, if, on the time market, 100 ounces of gold exchange for the prospect of obtaining 105 ounces of gold one year from now, then the rate of interest is approximately 5 percent per annum. This is the time-discount rate of future to present money. [...] The pure rate of interest will then be the going rate of time discount, the ratio of the price of present goods to that of future goods.

Rothbard: Man Economy and State

A hoard (consumption) is the opportunity to invest, and an investment is the opportunity to consume. One is traded for the other until no further increase in utility is obtained from doing so.

By investing, one values the amount of future interest more than the present amount not invested. By not investing, one values the present amount not invested more than the future interest. If this was not the case there would be a lower or higher level of investment respectively. The fact of the trade makes this time preference objective. The interest rate is used to relate the present hoard to the future interest.

hoarded-value = invested-value * interest-rate

As shown in Depreciation Principle, no actual consumption occurs in the trade of a product from producer to consumer. A product is only consumed to the extent that it depreciates. This is evident in that a product can be resold at present price, recovering the monetary value of the unconsumed portion. Similarly, any unconsumed portion can be consumed in the future, offsetting the present price of purchasing more of the same. Hoarding is the act of consumption, and the depreciated fraction of the original hoard has been consumed.

Goods that remain unconsumed are future goods relative to the original hoard of goods. A depreciation ratio is used to obtain the future reduced value of the hoard.

unconsumed-value = hoarded-value * depreciation-ratio

Rearranging and substituting unconsumed value for hoarded value obtains the relation between depreciating hoarded goods and non-depreciating invested goods. Future goods do not exist until they are present goods, so do not depreciate.

interest-rate = (hoarded-value * depreciation-ratio) / invested-value

The capital ratio is the ratio of hoarded (reserved) to invested capital. The interest rate is the capital ratio. Each is the same reflection of time preference. The interest rate is the ratio of consumption capital to investment capital.

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