Roger Garrison, Correct to Mistaken

Roger Garrison knows that one concerned with the theory of interest better not be confused about units of measurement:

"The price of any factor is measured in terms of dollars per unit of the factor. Land rent is measured in $/(acre-year); the wage rate in $/(worker-hour); the service price of a capital good, say a machine, in $/(machine-hour). The interest rate is measured in frequency units, in inverse time. That is, the dimensions of the interest rate are 1/year - e.g. 10% per year. Any attempt to recast the interest rate as the price of a factor must be squared with this dimensional characteristic.

It can be seen immediately that the interest rate cannot be the price - or even the service price - of capital goods. The dimensions of $/machine - or of $/(machine-hour) - are not the same as the units of the interest rate." - Roger Garrison (1988, p. 50)

And he knows the textbooks to be misleading to wrong:

"The Fisherian analytics are simple enough, but the basic construction is conceptually flawed. Again, the issue of dimensions comes into play. The slope of the indifference curves has the dimensions of the interest rate (1/year). The slope of the opportunity curve must be dimensionally the same if the point of tangency is to have any intelligible meaning at all. If the slope is a marginal value product, then it must be the marginal value product of waitings not of capital. But as demonstrated in the previous section, the quantity of waiting is itself dependent upon factor prices, which in turn are dependent upon the interest rate. It cannot legitimately be argued, then, that the rate of interest has two independent co-determinants; one of those co-determinants is dependent upon the magnitude it supposedly helps to determine.

Modern textbook writers have attempted to skirt this problem by using a one-good model. In all such models, questions of value, which may be affected by changes in the rate of interest, simply do not arise. Value productivity and physical productivity are indistinct; productivity is modelled as the rate of increase in the quantity of the good. The phenomenon of interest is being analogized once again to sheep that reproduce or to plants that grow. But, as Professor Rothbard often reminds us, the rate of interest is a ratio of values, not of quantities. This modelling technique unavoidably conflates growth rates with interest rates and fails thereby to shed any light on the phenomenon of interest." - Roger Garrison (1988, p. 52-53)

Garrison knows that dimensional analysis has implications about the theory of capital:

"Suppose the current rate of interest (the price of waiting) is 5 per-cent and that the equilibrium quantity of waiting supplied and demanded is 1000 $-years, which consists of owning durable machines, whose current value is $1000, for one year. Now suppose that the demand for waiting increases. Simple supply-and-demand analysis would allow us to predict that the interest rate will rise, say from 5 to 10 percent, and that the quantity of waiting supplied and demanded will increase.

If the value of the machines could be assumed not to change, this prediction would be valid. But a rise in the interest rate will cause the value of the machines, which is simply the discounted value of the machines' future output, to fall. More specifically, the doubling of the rate of interest, which serves as the basis for the discounting, will cause the value of the machines to decrease from $1000 to $500. Owning those same machines for a year now constitutes only half the waiting. It is possible, then, that in the subsequent equilibrium, more machines will be owned for a longer period of time yet the amount of waiting, which is now based on a lower machine price, may be less than in the initial equilibrium." - Roger Garrison (1988, p. 51)

Here Garrison is just wrong:

"There is no ambiguity, however, about the direction of change in the rate of interest given a particular shift in supply or in demand. An increase in the demand for waiting, which is the same thing as a rise in time preferences, will cause the rate of interest to rise." - Roger Garrison (1988, p. 51)

• Garrison, Roger W. (1988). "Professor Rothbard and the Theory of Interest", in Man, Economy, and Liberty: Essays in Honor of Murray N. Rothbard (edited by Walter Block and Llewellyn H. Rockwell, Jr.), Ludwig von Mises Institute