A Rejoinder to Mr. Murphy
Victor Aguilar
Roger Garrison's Innovation: A Maximum Interest Rate
Why is having a maximum rate of interest a problem? Because, clearly, there are people willing to pay very high interest rates and other people, like pawn brokers and payday loan companies, willing to charge such rates. Even if the existence of such transactions does not seem important to Roger Garrison in his ivory tower at Auburn University, the necessity of a having a maximum interest rate, combined with his insistence on using simple rather than compound interest, produces nonsensical results. It was to force him to carry his analysis through to its logical conclusion that I challenged Garrison, "I want to see him derive the maximum interest rate for us" (Aguilar, p. 38).
Murphy defends simple interest, "The absolute most Aguilar could fairly have said, is that using simple interest is so unrealistic as to render Garrison's diagram unsuitable for its intended purpose. Other than that, Garrison's claim is perfectly true" (Murphy, p. 8). This is like saying, except for the fact that someone on the other team caught the ball, the quarterback's pass was a fine throw. Is Garrison an "innumerate boob?" Let's find out!
Garrison insists on using simple interest but will not follow through on this choice to its logical conclusions. If he really wants us to identify the interest rate with the slope of the Hayekian triangle's hypotenuse, then he should do the math and see what interest rates are associated with different marginal propensities to consume. Getting Garrison to actually do the math instead of just vaguely drawing lines on his chalkboard was the point of my challenge to him:
"Garrison writes, ’The choice of a linear construction [for the APS] over an exponential one maintains a simplicity of exposition without significant loss in any other relevant regard' (2001, p. 46). This author disagrees. Math is easier when one does it right" (Aguilar, p. 37-38). I had hoped that Garrison would respond but, after three years, it is clear that I am going to have to do the math for him.
Let us draw the Hayekian triangle with the vertical leg labeled C for consumption, the horizontal leg labeled B and gross national output labeled A, for the area inside the triangle. We will here label the marginal propensity to consume with the letter m, not the more common mpc.4
A = CB/2 and C = mA, so A = mAB/2 and thus B = 2/m. Since Garrison defines r, the interest rate, equal to C/B, we have r = mC/2 and thus r = m2A/2. Q.E.D.
5
As I observed, "Clearly, r = 0 implies that C = 0 and I = A" (Aguilar, p. 38). A marginal propensity to consume of zero is associated with an interest rate of zero. The equation above bears this out as m2A/2 is zero if m is zero. Now let us try it for some more realistic values of m in the neighborhood of 90%, which is what most textbooks estimate the marginal propensity to consume to be:
| Marginal Propensity to Consume |
Real Interest Rate |
| 100% |
0.500 A |
| 95 |
0.451 A |
| 90 |
0.405 A |
| 85 |
0.361 A |
| 80 |
0.320 A |
This does not make any sense at all. The interest rate is a proportion of gross national output??? These two statistics do not even have the same units! Gross national output is a term coined by Skousen to refer to his definition of national income (the statistic that mainstream economists denounced for double counting), which is measured in dollars per year. Skousen's instructions for compiling it (1990, pp. 184-185) require people to save their receipts, which I denounced (Aguilar, p. 6) as being contrary to the subjective theory of value. But, ignoring these controversies for the moment, let us suppose that we have followed Skousen's instructions and found the GNO to be $100 billion dollars a year. Then what, exactly, is the maximum interest rate? What is the interest rate associated with a 90% propensity to consume?
The point of my challenge to Garrison three years ago was to get him to admit that his choice of a linear construction over an exponential one produces nonsensical results, in this case, that the maximum interest rate is half the gross national output. Skousen's conception of the APS as an exponential function is somewhat better (the maximum interest rate is 100%) but, in my opinion, the fact that use of the APS imposes any limit on interest rates is a fatal flaw, regardless of what that limit is.
4 "Without an introduction to the notation, most people who pick up an economics text think MPC (actually C'(Y), the derivative of consumption with respect to national income) means M (money) times P (prices) times C (consumption), all of which appear elsewhere in the same equation. Spelling words with variable names is one of the surest signs of someone without mathematical maturity" (1999, p. 39).
5 Quite Easily Done. Or, as B’hm-Bawerk would say, as plain as a pikestaff.
