Guest Blog: The Two Fundamental Welfare Principles of Monetary Economics (By David Eagle)

I am extremely happy that David Eagle is continuing his series of guest blogs on my blog.

I strongly believe that David’s ideas are truly revolutionary and anybody who takes monetary policy and monetary theory serious should study  these ideas carefully. In this blog David presents what he has termed the “Two Fundamental Welfare Principles of Monetary Economics” as an clear alternative to the ad hoc loss functions being used in most of the New Keynesian monetary literature.

To me David Eagle here provides the clear microeconomic and welfare economic foundation for Market Monetarism. David’s thinking and ideas have a lot in common with George Selgin’s view of monetary theory – particularly in “Less than zero” (despite their clear methodological differences – David embraces math while George use verbal logic). Anybody that reads and understands David’s and George’s research will forever abandon the idea of a “Taylor function” and New Keynesian loss functions.

Enjoy this long, but very, very important blog post.

Lars Christensen


Guest Blog: The Two Fundamental Welfare Principles of Monetary Economics

by David Eagle

Good Inflation vs. Bad Inflation

At one time, doctors considered all cholesterol as bad.  Now they talk about good cholesterol and bad cholesterol.  Today, most economists considered all inflation uncertainty as bad, at least all core inflation uncertainty.  However, some economists including George Selgin (2002), Evan Koenig (2011), Dale Domian, and myself (and probably most of the market monetarists) believe that while aggregate-demand-caused inflation uncertainty is bad, aggregate-supply-caused inflation or deflation actually improves the efficiency of our economies.  Through inflation or deflation, nominal contracts under Nominal GDP (NGDP) targeting naturally provide the appropriate real-GDP risk sharing between borrowers and lenders, between workers and employers, and more generally between the payers and receivers of any prearranged nominal payment.  Inflation targeting (IT), price-level targeting (PLT), and conventional inflation indexing actually interfere with the natural risk sharing inherent in nominal contracts.

I am not the first economist to think this way as George Selgin (2002, p. 42) reports that “Samuel Bailey (1837, pp. 115-18) made much the same point.”  Also, the wage indexation literature that originated in the 1970s, makes the distinction between demand-induced inflation shocks and supply-induced inflation shocks, although that literature did not address the issue of risk sharing.

The Macroeconomic Ad Hoc Loss Function vs. Parerto Efficiency

The predominant view of most macroeconomists and monetary economists is that all inflation uncertainty is bad regardless the cause.  This view is reflected in the ad hoc loss function that forms the central foundation for conventional macroeconomic and monetary theory.  This loss function is often expressed as a weighted sum of the variances of (i) deviations of inflation from its target and (ii) output gap.  Macro/monetary economists using this loss function give the impression that their analyses are “scientific” because they often use control theory to minimize this function.  Nevertheless, as Sargent and Wallace (1975) noted, the form of this loss function is ad hoc; it is just assumed by the economist making the analysis.

I do not agree with this loss function and hence I am at odds with the vast majority of the macro/monetary economists.  However, I have neoclassical microfoundations on my side – our side when we include Selgin, Bailey, Koenig, Domian, and many of the market monetarists.  This ad hoc social loss function used as the basis for much of macroeconomic and monetary theory is basically the negative of an ad hoc social utility function.  The microeconomic profession has long viewed the Pareto criterion as vastly superior to and more “scientific” than ad hoc social utility functions that are based on the biased preconceptions of economists.  By applying the Pareto criterion instead of a loss function, Dale Domian and I found what I now call, “The Two Fundamental Welfare Principles of Monetary Economics.”  My hope is that these Fundamental Principles will in time supplant the standard ad hoc loss function approach to macro/monetary economics.

These Pareto-theoretic principles support what George Selgin (p. 42) stated in 2002 and what Samuel Bailey (pp. 115-18) stated in 1837.  Some economists have dismissed Selgin’s and Bailey’s arguments as “unscientific.”  No longer can they legitimately do so.  The rigorous application of neoclassical microeconomics and the Pareto criterion give the “scientific” support for Selgin’s and Bailey’s positions.  The standard ad-hoc-loss-function approach in macro- and monetary economics, on the other hand, is based on pulling this ad hoc loss function out of thin air without any “scientific” microfoundations basis.

Macroeconomists and monetary economists have applied the Pareto criterion to models involving representative consumers.  However, representative consumers miss the important ramifications of monetary policy on diverse consumers.  In particular, models of representative consumers miss (i) the well-known distributional effect that borrowers and lenders are affected differently when the price level differs from their expectations, and (ii) the Pareto implications about how different individuals should share in changes in RGDP.

The Two Direct Determinants of the Price Level

Remember the equation of exchange (also called the “quantity equation), which says that MV=N=PY where M is the money supply, V is income velocity, N is nominal aggregate spending as measured by nominal GDP, P is the price level, and Y is aggregate supply as measured by real GDP.  Focusing on the N=PY part of this equation and solving for P, we get:

(1) P=N/Y

This shows there are two and only two direct determinants of the price level:

(i)             nominal aggregate spending as measured by nominal GDP, and

(ii)           aggregate supply as measured by real GDP.

This also means that these are the two and only two direct determinants of inflation.

The Two Fundamental Welfare Principles of Monetary Economics

When computing partial derivatives in calculus, we treat one variable as constant while we vary the other variable.  Doing just that with respect to the direct determinants of the price level leads us to The Two Fundamental Welfare Principles of Monetary Economics:

Principle #1:    When all individuals are risk averse and RGDP remains the same, Pareto efficiency requires that each individual’s consumption be unaffected by the level of NGDP.

Principle #2:    For an individual with average relative risk aversion, Pareto efficiency requires that individual’s consumption be proportional to RGDP.[1]

Dale Domian and I (2005) proved these two principles for a simple, pure-exchange economy without storage, although we believe the essence of these Principles go well beyond pure-exchange economies and apply to our actual economies.

My intention in this blog is not to present rigorous mathematical proofs for these principles.  These proofs are in Eagle and Domian (2005).  Instead, this blog presents these principles, discusses the intuition behind the principles, and gives examples applying the principles.

Applying the First Principle to Nominal Loans:

I begin by applying the First Principle to borrowers and lenders; this application will give the sense of the logic behind the First Principle.  Assume the typical nominal loan arrangement where the borrower has previously agreed to pay a nominal loan payment to the lender at some future date.  If NGDP at this future date exceeds its expected value whereas RGDP is as expected, then the price level must exceed its expected level because P=N/Y.  Since the price level exceeds its expected level, the real value of the loan payment will be lower than expected, which will make the borrower better off and the lender worse off.  On the other hand, if NGDP at this future date is less than its expected value when RGDP remains as expected, then the price level will be less than expected, and the real value of the loan payment will be higher than expected, making the borrower worse off and the lender better off.  A priori both the borrower and the lender would be better off without this price-level risk.  Hence, a Pareto improvement can be made by eliminating this price-level risk.

One way to eliminate this price-level risk is for the central bank to target the price level, which if successful will eliminate the price-level risk; however, doing so will interfere will the Second Principle as we will explain later.  A second way to eliminate this price-level risk when RGDP stays the same (which is when the First Principle applies), is for the central bank to target NGDP; as long as both NGDP and RGDP are as expected, the price level will also be as expected, i.e., no price-level risk..

Inflation indexing is still another way to eliminate this price-level risk.  However, conventional inflation indexing will also interfere with the Second Principle as we will soon learn.

That borrowers gain (lose) and lenders lose (gain) when the price level exceeds (fall short of) its expectations is well known.  However, economists usually refer to this as “inflation risk.” Technically, it is not inflation risk; it is price-level risk, which is especially relevant when we are comparing inflation targeting (IT) with price-level targeting (PLT).

An additional clarification that the First Principle makes clear concerning this price-level risk faced by borrowers and lenders is that risk only applies as long as RGDP stays the same.  When RGDP changes, the Second Principle applies.

Applying the Second Principle to Nominal Loans under IT, PLT, and NT:

The Second Principle is really what differentiates Dale Domian’s and my position and the positions of Bailey, Selgin, and Koenig from the conventional macroeconomic and monetary views.  Nevertheless, the second principle is really fairly easy to understand.  Aggregate consumption equals RGDP in a pure exchange economy without storage, capital, or government.  Hence, when RGDP falls by 1%, aggregate consumption must also fall by 1%.  If the total population has not changed, then average consumption must fall by 1% as well.  If there is a consumer A whose consumption falls by less than 1%, there must be another consumer B whose consumption falls by more than 1%.  While that could be Pareto justified if A has more relative risk aversion than does B, when both A and B have the same level of relative risk aversion, their Pareto-efficient consumption must fall by the same percent.  In particular, when RGDP falls by 1%, then the consumption level of anyone with average relative risk aversion should fall by 1%.  (See Eagle and Domian, 2005, and Eagle and Christensen, 2012, for the basis of these last two statements.)

My presentation of the Second Principle is such that it focuses on the average consumer, a consumer with average relative risk aversion.  My belief is that monetary policy should do what is optimal for consumers with average relative risk aversions rather than for the central bank to second guess how the relative-risk-aversion coefficients of different groups (such as borrowers and lenders) compare to the average relative risk aversion.

Let us now apply the Second Principle to borrowers and lenders where we assume that both the borrowers and the lenders have average relative risk aversion.  (By the way “relative risk aversion” is a technical economic term invented Kenneth Arrow, 1957, and John Pratt, 1964.)  Let us also assume that the real net incomes of both the borrower and the lender other than the loan payment are proportional to RGDP.  Please note that this assumption really must hold on average since RGDP is real income.  Hence, average real income = RGDP/m where m is the number of households, which means average real income is proportional to RGDP by definition (the proportion is 1/m).

The Second Principle says that since both the borrower and lender have average relative risk aversion, Pareto efficiency requires that both of their consumption levels must be proportional to RGDP.  When their other real net incomes are proportional to RGDP, their consumption levels can be proportional to RGDP only if the real value of their nominal loan payment is also proportional to RGDP.

However, assume the central bank successfully targets either inflation or the price level so that the price level at the time of this loan payment is as expected no matter what happens to RGDP.  Then the real value of this loan payment will be constant no matter what happens to RGDP.  That would mean the lenders will be guaranteed this real value of the loan payment no matter what happens to RGDP, and the borrowers will have to pay that constant real value even though their other net real incomes have declined when RGDP declined.  Under successful IT or PLT, borrowers absorb the RGDP risk so that the lenders don’t have to absorb any RGDP risk.  This unbalanced exposure to RGDP risk is Pareto inefficient when both borrowers and lenders have average relative risk aversion as the Second Principle states.

Since IT and PLT violate the Second Principle, we need to search for an alternative targeting regime that will automatically and proportionately adjust the real value of a nominal loan payment when RGDP changes?  Remember that the real value of the nominal loan payment is xt=Xt/P.  Replace P with N/Y to get xt=(Xt/Nt)Yt, which means the proportion of xt to Yt equals Xt/Nt.  When Xt is a fixed nominal payment, the only one way for the proportion Xt/Nt to equal a constant is for Nt to be a known in advance.  That will only happen under successful NGDP targeting.

What this has shown is that the proportionality of the real value of the loan payment, which is needed for the Pareto-efficient sharing of RGDP risk for people with average relative risk aversion, happens naturally with nominal fixed-payment loans under successful NGDP targeting.  When RGDP decreases (increases) while NGDP remains as expected by successful NGDP targeting, the price level increases (decreases), which decreases (increases) the real value of the nominal payment by the same percentage by which RGDP decreases (increases).

The natural ability of nominal contracts (under successful NGDP targeting) to appropriately distribute the RGDP risk for people with average relative risk aversion pertains not just to nominal loan contracts, but to any prearranged nominal contract including nominal wage contracts.  However, inflation targeting and price-level targeting will circumvent the nominal contract’s ability to appropriate distribute this RGDP risk by making the real value constant rather than varying proportionately with RGDP.

Inflation Indexing and the Two Principles:

Earlier in this blog I discussed how conventional inflation indexing could eliminate that price-level risk when RGDP remains as expected, but NGDP drifts away from its expected value.  While that is true, conventional inflation indexing leads to violations in the Second Principle.  Consider an inflation indexed loan when the principal and hence the payment are adjusted for changes in the price level.  Basically, the payment of an inflation-indexed loan would have a constant real value no matter what, no matter what the value of NGDP and no matter what the value of RGDP.  While the “no matter what the value of NGDP” is good for the First Principle, the “no matter what the value of RGDP” is in violation of the Second Principle.

What is needed is a type of inflation indexing that complies with both Principles.  That is what Dale Domian’s and my “quasi-real indexing” does.  It adjusts for the aggregate-demand-caused inflation, but not to the aggregate-supply-caused inflation that is necessary for the Pareto-efficient distribution of RGDP among people with average relative risk aversion.

Previous Literature:

Up until now, I have just mentioned Bailey (1837) and Selgin (2002) without quoting them.  Now I will quote them.  Selgin (2002, p. 42) states, ““ …the absence of unexpected price-level changes” is “a requirement … for avoiding ‘windfall’ transfers of wealth from creditors to debtors or vice-versa.”  This “argument … is perfectly valid so long as aggregate productivity is unchanging. But if productivity is subject to random changes, the argument no longer applies.”  When RGDP increases causing the price level to fall, “Creditors will automatically enjoy a share of the improvements, while debtors will have no reason to complain: although the real value of the debtors’ obligations does rise, so does their real income.”

Also, Selgin (2002, p. 41) reports that “Samuel Bailey (1837, pp. 115-18) made much the same point.  Suppose … A lends £100 to B for one year, and that prices in the meantime unexpectedly fall 50 per cent. If the fall in prices is due to a decline in spending, A obtains a real advantage, while B suffers an equivalent loss. But if the fall in prices is due to a general improvement in productivity, … the enhanced real value of B’s repayment corresponds with the enhanced ease with which B and other members of the community are able to produce a given amount of real wealth. …Likewise, if the price level were … to rise unexpectedly because of a halving of productivity, ‘both A and B would lose nearly half the efficiency of their incomes’, but ‘this loss would arise from the diminution of productive power, and not from the transfer of any advantage from one to the other’.”

The wage indexation literature as founded by Grey and Fischer recognized the difference between unexpected inflation caused by aggregate-demand shocks and aggregate-supply shocks; the main conclusion of this literature is that when aggregate-supply shocks exist, partial rather than full inflation indexing should take place.  Fischer (1984) concluded that the ideal form of inflation indexing would be a scheme that would filter out the aggregate-demand-caused inflation but leave the aggregate-supply-caused inflation intact.  However, he stated that no such inflation indexing scheme had yet been derived, and it would probably be too complicated to be of any practical use.  Dale Domian and I published our quasi-real indexing (QRI) in 1995 and QRI is not that much more complicated than conventional inflation indexing.  Despite the wage indexation literature leading to these conclusions, the distinction between aggregate-demand-caused inflation and aggregate-supply-caused inflation has not been integrated into mainstream macroeconomic theory.  I hope this blog will help change that.


As the wage indexation literature has realized, there are two types of inflation:  (i) aggregate-demand-caused inflation and (ii) aggregate-supply-caused inflation.  The aggregate-demand-caused inflation is bad inflation because it unnecessary imposes price-level risk on the parties of a prearranged nominal contract.  However, aggregate-supply-caused inflation is good in that that inflation is necessary for nominal contracts to naturally spread the RGDP risk between the parties of the contract.  Nominal GDP targeting tries to keep the bad aggregate-demand-caused unexpected inflation or deflation to a minimum, while letting the good aggregate-supply-caused inflation or deflation take place so that both parties in the nominal contract proportionately share in RGDP risk.  Inflation targeting (IT), price-level targeting (PLT), and conventional inflation indexing interfere with the natural ability of nominal contracts to Pareto efficiently distribute RGDP risk.  Quasi-real indexing, on the other hand, gets rid of the bad inflation while keeping the good inflation.

Note that successful price-level targeting and conventional inflation indexing basically have the same effect on the real value of loan payments.   As such, we can look at conventional inflation indexing as insurance against the central bank not meeting its price-level target.

Note that successfully NGDP targeting and quasi-real indexing have the same effect on the real value of loan payments.  As such quasi-real indexing should be looked at as being insurance against the central bank not meeting its NGDP target.

A couple of exercises some readers could do to get more familiar with the Two Fundamental Welfare Principles of Welfare Economics is to apply them to the mortgage borrowers in the U.S. and to the Greek government since the negative NGDP base drift that occurred in the U.S. and the Euro zone after 2007.  In a future blog I very likely present my own view on how these Principles apply in these cases.


Arrow, K.J. (1965) “The theory of risk aversion” in Aspects of the Theory of Risk Bearing, by Yrjo Jahnssonin Saatio, Helsinki.

Bailey, Samuel (1837) “Money and Its Vicissitudes in Value” (London: Effingham Wilson).

Debreu, Gerard, (1959) “Theory of Value” (New York:  John Wiley & Sons, Inc.), Chapter 7.

Eagle, David & Dale Domian, (2005). “Quasi-Real Indexing– The Pareto-Efficient Solution to Inflation Indexing” Finance 0509017, EconWPA,

Eagle, David & Lars Christensen (2012). “Two Equations on the Pareto-Efficient Sharing of Real GDP Risk,” future URL:

Sargent, Thomas and Neil Wallace (1975). “’Rational’ Expectations, the Optimal Monetary Instrument, and the Optimal Money Supply Rule”. Journal of Political Economy 83 (2): 241–254.

Selgin, George (2002), Less than Zero: The Case for a Falling Price Level in a Growing Economy. (London: Institute of Economic Affairs).

Koenig, Evan (2011). “Monetary Policy, Financial Stability, and the Distribution of Risk,” Federal Reserve Bank of Dallas Research Department Working Paper 1111.

Pratt, J. W., “Risk aversion in the small and in the large,” Econometrica 32, January–April 1964, 122–136.

© Copyright (2012) by David Eagle


[1] Technically, the Second Principle should replace “average relative risk aversion” with “average relative risk tolerance,” which is from a generalization and reinterpretation by Eagle and Christensen (2012) of the formula Koenig (2011) derived.

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  1. Benjamin Cole

     /  January 22, 2012

    Nice blogging. The advantages of Market Monetarism are many. I just don’t understand the encrusted, shibboleth-ridden economics profession, an the inability of many economists to grasp the obvious.

  2. Integral

     /  January 22, 2012


    This is a big post and it’s going to take some time for me to digest all of its implications. Nevertheless, thank you for posting it.

    Your comments on the social welfare function are important. I was under the impression that one could derive the NK loss function through linearization around the steady-state; but I don’t have the relevant textbooks in front of me and will not press the issue, because it becomes moot once one allows for heterogeneity. And indeed one cannot analyze debt dynamics without heterogeneity, and it’s well known that there is no general way to generate a social welfare function when agents are heterogeneous. I look forward to reading your paper in full to see how you apply the Pareto criterion, since it tends to be able to say very little but be quite stark in the few things it can say.

    I have a variety of minor quibbles (in particular that I don’t think you can “summarize” aggregate supply with RGDP except in the long run, and we are concerned with the short-run here) but they can wait until a later comment.

  3. Sebastian Bermudes

     /  April 27, 2012

    Yes you are very right.
    The Central Bank may also buy and sell securities to and from the public and banks in what is known as Open market operations. If it buys securities, its money is entered into the economy, hence allowing for more transactions to be made. If it sells securities, it takes money out of the economy, slowing it down.

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