Two Theories of Prices

Last May, John T. Harvey wrote a wonderful post about the quantity theory of money (QTM). This post picks up where John stopped, presenting a different theory of the price level and inflation. It’s a bit technical (so bare with me), but many readers have asked us to elaborate on price theory.
First, a quick recap. The QTM starts with the identity MV ≡ PQ, where M = the money supply, V = the velocity of money, P = the price level, and Q = the quantity of output (Fisher’s version is broader and includes all transactions: T). The identity is a tautology, it just says that the amount of transactions on goods and services (PQ) is equal the to the amount of financial transactions needed to complete those transactions. To get a theory of price (the QTM), one must make some assumptions about each variable. The QTM assumes that:
·         M is constant (or grows at a constant rate) and is controlled by the central bank through a money multiplier
·         V is constant
·         Q is constant at its full employment level (Qfe) or grows at its natural rate (gn)
Given this set of assumptions, we get (note the equality sign to signal causality):
P = MV/Qfe
Or, in terms of the growth rate (V is constant so its growth rate is zero):
gp = gm – gn
This is the QTM, which holds that price changes (inflation and deflation) have monetary origins, i.e. if the money supply grows faster than the natural rate of economic growth, there is some inflation.  For example, if gm = 2% and gn = 1% then gp = 1%.  If the central bank increases the money supply, then inflation rises.

John’s post explains the problems with this theory. M is endogenous, V is not constant, and the economy is rarely at full employment. If you want to know more, you should read John’s post.

Let’s move to an alternative theory of the price level and inflation by starting with another identity based on macroeconomic accounting:
PQ ≡ W + U
This is the income approach to GDP used by the Bureau of Economic Analysis. It says that nominal GDP (PQ) is the sum of all incomes. For simplicity, there are only two incomes: wage bill (W) and gross profit (U). Both are measured before tax.
Let’s divide by Q on each side:
P ≡ W/Q + U/Q
We can go a bit further by noting that W is equal to the product of the average nominal wage rate and the number of hours of labor W = wL (for example, if the wage rate is $5 per hour, and L is equal to 10 hours, then W is equal to $50). Thus:
P ≡ wL/Q + U/Q
Q/L is the quantity of output per labor hour, also called the average productivity of labor (APl) therefore:
P ≡ w/APl + U/Q
w/APl is called the unit cost of labor and data can be found at the BLS. The term U/Q will be interpreted a bit later.
Ok let’s stop a bit here. For the moment all we have done is rearranged terms, we have not proposed a theory (i.e. a causal explanation that provides behavioral assumptions about the variables.)  Here they are:
·         The economy is not at full employment and Q (and economic growth) changes in function of expected aggregate demand (this is Keynes’s theory of effective demand).
·         w is set in a bargaining process that depends on the relative power of workers (the conflict claim theory of distribution underlies this hypothesis)
·         U, the nominal level of aggregate profit, depends on aggregate demand (Kalecki’s theory of profit underlies this hypothesis)
·         APl moves in function of the needs of the economy and the state of the economy.
Thus we have:
P = w/APl + U/Q
Thus the price level changes with changes in the unit cost of labor and the term U/Q. What is this last term? To understand it let’s express the previous equation in terms of growth rate. This is approximately:
gp = (gw – gAPl)sW + (gU – gQ)sU
With sW and sU the shares of wages and profit in national income (sW + sU = 1).
Thus, inflation will move in relation to the growth rate of the unit labor cost of labor, which itself depends on how fast nominal wages grow on average relative to the growth rate of the average productivity of labor. As shown in the following figure, in the United States, a major source of inflation in the late 1960s and 1970s was the rapid growth of the unit cost of labor, with the rate of change between 5 and 10 percent.

Major Sector Productivity and Costs Index (BLS)

Series Id:  PRS85006112
Duration:   % change quarter ago, at annual rate
Measure:    Unit Labor Costs
Sector:     Nonfarm Business
Inflation will also move in relation to the difference between the growth rate of U and the growth rate of the economy (gQ). U follows Kalecki’s equation of profit, which broadly states that that the level of profit in the economy is a function of aggregate demand. Thus the term, (gU – gQ) represents the pressures of aggregate demand on the economy. If gU goes up and gQ is unchanged, then gP rises given everything else. However, to assume that gQ is constant is not acceptable unless the economy is at full employment, so a positive shock on aggregate demand will usually lead to a positive increase in gQ.
Thus, overall, there are two sources of inflation in this approach, a cost-push source (here summarized by the unit labor cost) and a demand-pull source (here summarized by the aggregate demand gap). Note that the money supply is absent from this equation. Money does not directly affect prices. Assuming that a drop of money from the sky leads to inflation, first, does not understand how the money supply is created (it is at least partly created to produce goods and services), second, assumes that people will automatically spend rather than hoard the addition funds obtained (people do hoard for all sorts of reasons and do derive “utility” from hoarding money), third, assumes that the economic output cannot respond to additional demand. If more people suddenly go to the store, producers usually produce more rather than raise prices. Output is not a fixed pie that involves allocation to one group at the expense of another group. The size of the pie increases and decreases with the number of people demanding pie.
A version of this theory has been used in many different models that have endogenous money, liquidity preference, demand-led theory of output and other non-mainstream characteristics. Godley’s and Lavoie’s Monetary Economics as well as Lavoie’s Foundation of Post Keynesian Economics are good books to get more modeling. Of course, modern mainstream monetary economics is rejected in those books; income effect dominates over substitution effect, production is emphasized over allocation, monetary profit affects economic decisions, etc. Be prepared for a change of perspective in which scarcity is not the starting point of economics.

25 responses to “Two Theories of Prices

  1. To me, what seems to be missing in both these theories is the effected of leveraged speculation!TraderAl

  2. Distributed economics posted about this also

  3. Hi Eric, Thanks for a very good exposition of the alternative theory. I can use it!

  4. "John’s post explains the problems with this theory. M is endogenous, V is not constant, and the economy is rarely at full employment. If you want to know more, you should read John’s post.This is the QTM, which (…)John’s post explains the problems with this theory. M is endogenous, V is not constant, and the economy is rarely at full employment. If you want to know more, you should read John’s post."Yes, we got it 😉

  5. So, this isn't actually a quantity theory of prices then?During the Sumner discussion Scott (F) said that MMTers were basically quantity theorists but that they differed in how the money entered the economy. (Not to blame Scott F for this or anything, I think it was a reasonable formulation at the time — and still has some merit).But just to clarify. If we take the above — which is very good by the way, thank you Eric — as the 'MMT standard' are we now firmly saying that MMTers are NOT quantity theorists?

  6. Philip,They're not incompatible. The currency issuer sets (gU-gQ) via its creation of NFA relative to desired leveraging of the non-govt sector, and can also, via, say, the wage it sets for a job guarantee, directly affect (gW-gAPI). It would also affect directly (gU-gQ) via the prices it chooses to spend on purchases of goods and services from private businesses–consider if the govt chose to double prices on all purchases paid to all contractors–this also helps understand how the particular types/choices of spending and tax cuts can have different effects on the price level. Further, consider a payroll tax holiday that reduces employer contributions–this would reduce the price level by reducing (gW-gAPI) in the sense that for the firm gW would include payroll taxes in the cost of labor.It's not a stretch to suggest that that policies that affect (gU-gQ) and (gW-gAPI) also at least indirectly affect the relative sizes of sU and sW (lots of Post Keynesians think so). It also could affect these directly via tax and/or redistributive policy for the two different sectors.So, not only are they not incompatible, Eric's exposition illustrates the channels through which an MMT "fiscal theory of the price level" works.Best,Scott Fullwiler

  7. Scott,I'm not sure that I follow. And I think its because I'm not wholly familiar with Kalecki's theory of profit (I'll bet a few others aren't either, so you might clear this up for us?).You say that the government (currency issuer) sets gU – gQ. Does this mean that the government is setting the rate of economic growth and the level of profit directly?I thought the private sector had discretion over how much they can borrow/lend. Surely this has as much an effect on profits and growth…Also, is Kalecki's theory of profit measuring both the growth of profit AND the growth of aggregate demand?

  8. Philip,As Eric said, gU-gQ is the output gap. Don't worry about trying to understand Kalecki, just remember that simple point. Then it's obvious there's no inconsistency–the currency issuer can directly set the output gap by varying the flow of NFA relative to desired leveraging of the non-govt sector (and thus pvt sector's borrow/lend is already incorporated).

  9. Scott,Thanks. Anything that I might read to get a better understanding of why the output gap is 'profits – economic growth'. Not too clear on this.Phil

  10. Philip, maybe this post by Bill Mitchell helps

  11. Thanks MamMoTh. That also looks like a good lead in to Kalecki's actual work. His 'Theory of Economic Dynamics' has been sitting on my shelf gathering dust for a while. Might be time to break it out…

  12. Yes, thanks MamMoTh. I recalled Bill did a post on that, but didn't know which one it was.

  13. Thanks again for that Bill Mitchell article. Anyone know who the guys are that wrote The Guardian article cited therein: almost read like MMTers… I've never really seen stuff in the media that read like that before.

  14. The David Levy guy is the son of the Jerome Levy mentioned in the article, who, according to their site "and the Levy-Kalecki formula—independently developed by New York physicist-entrepreneur Jerome Levy in 1914 and Polish economist Michal Kalecki in 1935 and then unified by American economist Hyman Minsky in the 1960s—is helping to better elucidate the relationship among debt, savings, and profits."

  15. (or perhaps more distantly related, or perhaps even unrelated; but he shares the last name, in any case, and he works here: )

  16. Apparently Scott read the article and is look for:"Everyone, Again, I’m still looking for the MMT model of different trend rates of inflation; 5%, 10%, 20%, 40%, 80%, etc, in different countries. And I’m not seeing anyone present such a model."

  17. Very interesting. Here's a paper summing it up for anyone interested (and with access to a university library server):

  18. Simplifying, I’d say:a) The quantity theory equation is an almost totally useless identity that expresses NGDP as a sum of transactions, visualized as being consummated according to mutually dependent definitions and quantifications of the stock of money and its velocity – an arbitrary stock medium of exchange times its velocity turnover. Given that required interdependence between the purported stock and its derived turnover, one can construct a valid quantity theory equation using the stock value of dead chickens as the medium of exchange.b) The derivation in this post identifies sources of inflation (i.e. price level changes) based on national accounts logical construction of NGDP and corresponding incomes, and the required equivalence between the two. If there is inflation, it must show up on both sides of this equation. And therefore it must show up in the decomposition of income into labour income and capital income.This doesn’t require much mathematical embellishment of b) to come to the primary conclusion about the relative merits of the two approaches. In no way does the decomposition of b) require an investigation into the stock or money or its velocity. That much is very evident before developing the approach in b) much at all. In fact, the proper decomposition of b), as in this post, will identify the actual distribution of inflation across both products and income. But given the virtually complete freedom to assign arbitrary definitions for money and its related velocity, the quantity theory reveals next to nothing of real truth about the matter.

  19. "As shown in the following figure, in the United States, a major source of inflation in the late 1960s and 1970s was the rapid growth of the unit cost of labor, with the rate of change between 5 and 10 percent."Because labor was winning the conflict over its claims? Falling productivity?

  20. JKH,I agree completely.MMT'ers know that even our version of FTPL is abstract theory, though some information can be gathered from looking at the evolution of the sector balances in real time.But any QTM approach is missing the broader point regarding "going out and looking." Real world inflation is from changes in real-world price indexes, and real-world price indexes often don't match up with theoretical notions of the price level, if they ever do. Eric's post shows how one would go about "going out and looking"; that is, it provides a framework for organizing information as one looks for inflation in real-time or looks at how past price indexes have evolved.As I explained to Philip, what you find once you do that is not inconsistent with the MMT FTPL.Lastly, MMT'ers don't find calls for elucidating a "theory of the price level" all that interesting, for two reasons. First, the tone of the call suggests a belief that somehow MMT's explanations of the monetary system is not valid without a theory of the price level those doing the calling out would find agreeable. Not true at all. Second, it's the height of hypocrisy to judge MMT on its theory of the price level when those doing the calling when their own theory of the price level is actually untenable in the real-world, as they have causation completely backward.

  21. questions for Eric Tymoigne (or STF, or whomever):(1) Does U stand for the gross profits of firms selling only final goods or services, or does it include firms also selling intermediate/investment/factor goods and services? (I'm asking just about the MMT price equation in this blog entry, not about some modified version that makes this distinction explicit.)(2) Gross profit doesn't deduct payroll, right? The equation PQ = W + U double-counts wages unless you use a definition of profit that deducts wages. Am I missing?(3) The QTM equation and the MMT equation for gp are just the derivatives of the two price equations w/r/t time, right?(4) Sorta related to my 1st question and to the comment by "TraderAI" on the "effected [sic] of leveraged speculation": Does PQ = W + U or its derivations in this blog entry take into account the profits made by speculators of real or financial assets? What do Godley, Lavoie, and other MMTers say is the effect (or lack of such) of speculators on the price level?

  22. "Am I missing?" should read "Am I missing something?"

  23. From Eric Tymoigne:@Traderal. This theory is about output-price inflation, not asset-price inflation. Output-price inflation concerns newly produced goods and services and it is the one central bankers and most people tend to be worried about (wrongly if you want my opinion). Asset-price inflation is about outstanding assets (stock, bonds, land, existing houses, commodities, etc.). In the first one the cost of production plays an important role, in the second speculation plays a crucial role. They can affect each other (e.g., speculation in commodities affect costs of production and so the price of output)[email protected] Reithel. Wage growth outpaced productivity growth, both grew on average. The former was in the 5-10% range whereas the latter was mostly in the 0-5% range. My take on the causes of this: 1- in the late 1960s workers were able to outpace productivity growth because of their strength in wage bargaining due to low unemployment 2- in the 1970s the oil shocks boosted inflation and workers tried to maintain their real wage (they failed) by demanding an increase in nominal wages. This further reinforced [email protected] U is the gross profit from final demand (profits of on intermediaries cancel out between firms) and indeed it does not include payroll. All gross employees compensations are included in W (wage and salarary, employer’s and employee’s contribution to SS and pension fund, benefits, etc.).Yes gp is the derivative relative to time, growth ratesInflation in this post is about output-price inflation, not asset-price inflation.

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