Procrustean Art of Backtracking: “Growth-Inflation Tradeoff”

 

We already know that the Phillips curve of tradeoff between the inflation rate (T^-1, or per period) and the unemployment ratio (T⁰, as at a certain moment) makes little sense. Other than the curve, we never plainly compare the driving speed to the driving distance: the two are different in the time dimension.

                Somehow, we have the Baumolite equation in hands: The wanted stock of money for expected transactions of all purposes M^w= (b∙T/ 2i)^1/2. (We avoid the denotation M^d because “money demand” is a fatal misnomer.) Now, we do purposefully move from transactions in general to the nominal gross expenditures (P∙Y) in particular, together with the convenient assumption T= k∙(P∙Y), where k is constant of course.  

                Then we can derive this equation: g= 2m+ Δi/ i – π– Δb/ b, where g for the GDP gross rate per annum, m for monetary growth rate PA and π for inflation rate PA.

                Let us discuss the effects on the economy of an “expansionary monetary policy,” or ΔM. What will happen afterwards? 

                To begin, we might well neglect the effect on the economy-wide level of interest rate (Δi/ i) because the incremental money, as a part of ΔM, headed to all the assert markets in the nation would be negligible in comparison to the annual aggregate turnover therein. Then on, we push the effect on the financial costs aside (Δb/ b) in that “monetary policy” alone would not have a notable impact thereon.

                As a result, we have this tradeoff equation g+ π= 2m. First of all, there is no such thing as mismatch in dimensions; all “variables” are in the percentage per annum (% PA). This is it!

                The genuine trade-off predicts that over the coming year we shall have inflation if the economy fails to grow twice as fast as the monetary growth. To paraphrase, the money affects the economy in two channels. The one is the necessity to get rid of ΔM, or the “useless money” (cf. Irving Fisher, and Paul Samuelson and William Nordhaus). The other is ΔV, or an enhancement of the velocity of money due to “fallacy of composition” (cf. Paul Samuelson and William Nordhaus). More specifically, the velocity must go up because all cannot do away with the “useless money” even as each tries.

                Probably, one of the reasons why Cambridge macroeconomics is so otherworldly is because the velocity is assumed to be constant (V*) or equal to the unity (the so-popular “normalization for the sake of convenience”). Alas, convenience gets macroeconomists to hit the dead end.

                One of the two keys in monetary policy is, after all, a change in the velocity of money (ΔV).