# Daily Archives: July 27, 2011

## 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:  PRS85006112Duration:   % change quarter ago, at annual rateMeasure:    Unit Labor CostsSector:     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.

## RESPONSE TO BLOG 8: MORE ON TAXES DRIVE MONEY

Thanks again for well-focused questions and comments. Here we are concerned with why government “fiat”currency is accepted. The short answer was that “taxes drive money”: since you have a tax liability that must be cleared by delivering the government’s own currency back to government, you want to obtain government currency. So in that sense, it is the tax liability that drives the desire to obtain government currency.
I did leave a couple of teasers, which some touched on in their comments. First, does it have to be a tax? Clearly the answer is “no”: if government imposes a fine on you in the form of five Dollars, you need five Dollars in the form government is willing to accept to pay your fine—sovereign currency. Until the 20th century, taxes were relatively less important; what mattered more were fines and tithes and fees.
To go further, let us say government monopolizes the water supply (or energy supply, or access to the gods, etc); it can then name what you need to deliver to obtain water (energy, religious dispensation, etc). In that case, if it says you must obtain a government IOU, then you want government IOUs—currency—to obtain water in order to avoid death by dehydration. In early 19th century England, almost all activities necessary to keep your family alive were illegal by dictate of the crown. You had to pay a fine after you killed game to feed your family. You needed the crown’s currency to pay the fine—hence “fees drove money”. You get the picture.
All you need to drive a currency is a more or less involuntary obligation to deliver the currency—and that can be a tax, fee, fine, or even religious tithe. Or a payment to obtain water or any other necessity. We can go into this later, but at UMKC students need buckaroos to pay a “tax” to pass their courses—that drives the buckaroo currency—it creates a demand for buckaroos (the sovereign currency at UMKC).
That answers the question: yes it is not enough to impose the obligation (fee, fine, tax); the obligation must also be enforced. A tax liability that is never enforced will not drive a currency. A tax that is only loosely enforced can create some demand for the currency, but it will be somewhat less than the tax liability for the simple reason that many will expect they can evade the tax.
We can next move on to the second teaser: why would those who do not have tax liabilities also be willing to accept currency?
That leads us to the Tobin, “snowball” point: if some segment of society owes the tax (or fee or fine) denominated in the currency, others will accept it. Note this is not an infinite regress argument. It is the tax standing behind the currency. But it is not necessary for every individual to owe the tax.
Let us say that Bill Gates owes \$1.5 trillion in taxes. I’d be happy to accept Dollars since I know Gates will accept them when I purchase Microsoft software. And that explains why foreigners want dollars—not because they owe taxes, but because a sufficient number of Bill Gates do.
From inception we know that if the total tax liability in dollars is, say, \$100 billion, the taxpayers will want a minimum of \$100 billion. (How much more? \$120 billion? \$180 billion? We will investigate that later.) Government can spend into the economy at least that amount.
How much will the Dollar be worth? Well, that depends on what must be done to obtain it. We will have much more to say about that in coming weeks.
A commentator did hit on this point: what if the tax liability is too low? Let us say the tax liability is \$100 billion but government tries to spend \$1000 billion. This is ten times what the taxpayers need to cover their liabilities. It is possible—even probable—that government will not be able to find takers for the \$1000 billion. It can bid the price it is willing to pay (for labor, finished output, or resource inputs) up, but still find no takers. We could register “inflation” and still find government cannot spend as much as it wants.
A better solution—obviously—is to raise the tax liability toward \$1000 billion, rather than to increase the price government is willing to pay. Again, that is something we will come back to, but it also sheds some light on what determines the value of the currency. As I said last week, we need to separate the willingness to accept currency from the value of the currency. Raising the tax liability will increase the desire to obtain currency although that does not tell us exactly how much the value of currency (in terms of labor or other resources) will rise.
Valuing something like a bridge is very difficult—especially if we are talking about a bridge already in place. Fortunately, it is also a question that is not very important, so long as the bridge is public—not owned by some profit seeking entity. There really is very little reason to value public infrastructure once it is in place, except perhaps in terms of all the pleasure it provides to the population. That is probably something that cannot be and should not be measured in money terms.
But, yes, raising the tax liability while holding government issue of the currency constant is likely to lead to what we might call unemployment: those willing to work to get the currency in order to pay taxes, but who cannot find work or demand for output to obtain the currency.
We will later go through the accounting to answer the question raised by a commentator: what about the reserve effects of tax payments? But, briefly, yes, paying taxes will all else equal reduce outstanding bank reserves. In practice, if the central bank targets overnight interest rates, it will replace lost reserves if they were desired or required—by lending at the discount window or through open market purchases of treasuries.
There were several questions/comments that were not comprehensible to me: what about interest, which requires one to repay more than what is owed. I do not see the relevance to this week’s topic. What about issuing money with no offsetting debt? Well, all money “things” are IOUs hence are debts, hence there is no possibility of issuing money that is not a debt. What about socio/political ramifications of who pays the tax? Yes very important, but I do not see the relevance to the topic at hand.

OK I hope I have covered the main comments and questions. More next week.