**What is Interest?**

When an
agent owns wealth, whether in the form of a commodity or currency, he or she may
decide to temporarily relinquish control of his or her asset in exchange
for a return whose value is dependent upon the length of time for which the asset is
relinquished. The value of the return divided by the original investment – the
value of that which was lent – represents the

*rate of return*. The rate of return implies a time period over which investment occurs. Typically this period is one year. If the rate of return is 10%, an agent who invests $100 or an asset worth $100 in year one receives a value of $110 in year two. The rate of return in this sense is a rate of return for an individual investment. We might weight the returns from an agent’s investments to calculate an average rate of return for an individual agent or we might attempt to calculate the rate of return for the market as a whole. The latter of these is known as the*market rate of return*.
When
working with the rate of return, either for analysis of the past or estimations
of the future, we use the equation for present-value. In its simplest form, we
compound over one year (period):

PV = FV/(1 + r)

Where:

PV = Present Value

FV = Future Value

r = Interest Rate

We can use this
equation to estimate the rate of return for any investment, monetary or
otherwise. Alchian and Allen (1983, 108) show us that we might calculate the rate of return
using physical assets. This is known as an own rate of interest. (For a
discussion of own rates see this
post from David Glasner). Imagine that we have 3 pound of grapes. That one
pound of grapes might be sold immediately or they might be processed for a year
and sold as a bottle of wine.

**Let us assume that, aside from time, this process is costless.**In this case, the*present value*of the grapes is equal to the price they would sell for on the market. The*future value*is equal to the price that a bottle of wine is expected to fetch one year from the present. If the bottle of wine is expected to sell for $1.10 and the three pounds of grapes is expected to sell for $1.00, then we again have a case where the expected rate of return is 10%:
1 + r

_{e}= $1.10/$1.00
1 + r

_{e}= 1.1
r

_{e}= .1
This calculation can also
be performed

*ex post*in order to compare the actual return to the return on another investment.
Recall that agents
achieve profit by transforming the present state of the world into one that
they prefer more greatly. Interest helps to expand this definition of profit.
We can now imagine not only a transformation of the present state, but so also
the exchange of expected states in the future. If an agent comes to realize a
return that is less the market rate of return, she may choose to invest in assets whose returns she expects to at least match the market rate of
return. This exercise in arbitrage is what drives the market toward an

*equilibrium*state so long as expectations are convergent; that is, so long as agents’ expectations about the present state of reality and its future unfolding tend to cohere with one another. This is not an unreasonable assumption as those who fail to predict the future state of the market will tend to be out-competed by those who do. In the short run, extreme, even systematically destabilizing outcomes may occur. We should beware against ignoring context and process by turning belief in market efficiency into a tautology. (For more on expectations, see Koppl 2002; Koppl and Butos 1993)
The rate of interest
emerges as a result of agents’ time-preferences. Given one’s context, an agent
reflects time preference in his or her decisions to refrain from consumption or
not. If an agent refrains from consumption

*and*invests his or her wealth for a period of time, that agent increases the availability of loanable funds. Assuming*normal*conditions – i.e., the future is expected to look mostly like today – a typical agent demonstrates positive time preference. He prefers having goods in the present to having the same goods in the future. Absent other influences, this results in a positive rate of interest. It is possible that markets might arrive at a negative rate of interest, but this categorically cannot be the result of an inversion of time-preference where agents prefer a state in the future to an otherwise identical state in the present. This positive time preference leads agents to invest so long as they receive a positive rate of interest.
The other, secondary
determinate of the interest rate is the productive sector. If agents are
lending their wealth to other agents with expectation of a certain rate of
return, then agents who are borrowing expect either to earn higher rate of
return. If this expectation is incorrect, the borrower will incur a loss, and in the worst case,
default. For now we deal with the first case. Time preference is reflected by
the supply of loanable funds, investment opportunities determine the demand for
loanable funds. If an increasing number of agents expect that rate of return in
the market will be greater than the interest rate, the demand for loanable
funds will increase (See Figure 1). The rate will tend to rise until agents, in
aggregate, no longer expect a rate of return higher than the interest rate.
Likewise, the interest rate will fall if agents, in aggregate, expect that the
rate of return will be less than the market rate of interest. (This analysis
may be further complicated by differing expectations for a variety of time
horizons. For simplicity, I leave this case out.)

**Figure 1**

**Natural Rate of Interest**

The interest rate plays
a significant role in coordinating investment across time. Of particular
concern in the

*natural rate*. Wicksell explains,
There is a certain rate of interest on loans which is
neutral in respect to commodity prices, and tends neither to raise nor to lower
them. This is necessarily the same as the rate of interest which would be
determined by supply and demand if no use were made of money and all lending
were effected in the form of real capital goods. It comes to much the same thing
to describe it as the current value of the

*natural rate of interest on capital*. ([1898] 1936, 102)
The natural rate of
interest is the rate of interest that would exist absent nominal factor such as
fluctuations in the money stock or fluctuations in demand for money. The
nominal rate of interest is thought to fluctuate within proximity of the
natural rate and is ultimately bounded by the natural rate. In the long
run, the natural rate constrains the viability of particular investments,
although in the short-run profits might be made from investments that are
unsustainable. If a tendency arises for unsustainable investment projects to
receive funds, this will eventually be checked by liquidity constraints. A rising interest rate thus reveals this problem and forces funds to be
allocated away from those projects.

**Real and Nominal Rates**

Interest rates are
observed in

*nominal*form. This means that the observed rate of interest can, and typically does, deviate from the natural rate, defined in terms of a real rate. In equilibrium, meaning all exchanges have been made and under conditions where perception and expectations cohere with objective reality, the observed rate is equal to the sum of the real rate and the inflation rate. This is known as the Fisher Equation
i = r
+ π

Where:

i = Nominal (Observed) Interest Rate

r = Real Interest Rate

π = Inflation Rate

Through a process of
trial and error, agent action factors the average rate of inflation into the
money rate of interest. Within this construct, the money rate of interest converges
with the natural rate of interest.

To sum, the interest rate is emerges as the result of positive time preference. Individuals value present goods over future goods. The interest rate tells us by how much agents, on average, these agents prefer the future to the present. A secondary factor of influence over the interest rate is the rate of return on investments in the market. If opportunities for profitable investment, in terms of dollar value, are expected to exceed the rate of return, this pushes the rate of interest upward. Likewise, if there is a general expectation that the value of investment opportunities are shrinking, this will push down the rate of interest. In the long run, the interest rate will tend to reflect the real return on capital. Nominal factors such as changes in demand for money and changes in the available money stock tend to produce short-run deviations away from the natural rate. These fluctuations tend to be limited by liquidity restraints and are mitigated by a short-run rise in the interest rate. In the long run, inflation will be factored into the observed rate such that observed rate of interest is equal to the sum real rate and the nominal rate of interest. Finally, the reader should be aware that this analysis occurs within a static framework and ignores complications that arise due to destabilizing events such as herding, distortions from Big Players, political, economic, and/or natural disasters, etc... These additional sorts of details require a careful study of history and the use of simulation to further our understanding.

In the graph provided, is the "rate" the market rate or the interest rate?

ReplyDeleteIn equilibrium, the market rate of return and the rate of interest match one another as all profit opportunities have been exhausted.

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