Eco 3320
1
Lecture Note #8
Expected Inflation is Harmless or Beneficial?
1. Tobin’s Non-Super-neutrality Argument
Tobin argues that if inflation is expected, then people would switch from money holdings
to holding of real goods (substitution effect). This will boost the demand for real goods,
as opposed to money. In response, there may be an increase in the supply of goods, which
will lead to an increase in the national income.
In concrete, this happens when an increase in inflation rate leads to an increase in interest
rates through Fisher’s equation;
i = r + πe
This happens only when the rate of money creation is accelerated, or the percentage of
the increase in money supply rises.
In MV = PY, πe is proportional to dM/M if Yf and V are constant.
And then, an increase in nominal interest rates leads to a decrease in real demand for
money through the Liquidity Preference Function.
md = L(i, Y)
That means that people would like to hold the wealth and income in the forms of other
‘things’ than money. Thus the demand for those ‘things’ rises, and the supply of ‘things’
would rise as well and the production of goods leads to an increase in real national
income.
This is so-call ‘Non Super-neutrality’ of Money.
However, Tobin’s argument misses one point: Income Effect or Waste of Resources due
to Inflation.
Why is Inflation wasteful of resources?
2. Optimal Monetary Policy: Optimal Rate of Inflation
The Policy Invariance Theorem states that no matter what the rate of money creation
might be, say 10% or 1000%, and consequently no matter whatever the rate of inflation
might be, the national income level dose not vary as long as the money supply or the
inflation is fully anticipated.
If so, can we safely afford to be indifferent to the monetary policy as long as it is fully
anticipated? The answer is ‘no’ when the social welfare or social efficiency is taken into
account: Inflation is resource-wasting and welfare-reducing.
Eco 3320
1) Social Welfare Analysis
2
Lecture Note #8
First of all, let us examine the proportion that “Inflation creates a wedge between the
social optimum and the private optimum in terms of money holdings”:
Usually, the social optimum in microeconomics is achieved when the marginal cost is
equal to the marginal benefit or utility.
The marginal utility is given by the demand curve itself.
There are in fact two different marginal costs when it comes to money; the marginal cost
of money for the society, and the marginal cost of money for an individual. The marginal
cost of money for the society is the cost of producing money, which is equal to zero. The
marginal cost of money for an individual is the cost of holding –an individual cannot
create money- money, which is equal to the nominal interest rate.
Thus, the Social Optimum in the use of money is achieved when the Social Marginal
Cost of (producing) money = MB. In fact, SMC = 0. Therefore, money should be held
or used up to the point where MB = 0, which is the saturation point of money holdings.
Illustration
i
md  MU  MB
i0  0
PMC
Private Optimum for i
0
Social Optimum
SMC = 0
PMC = 0
i1  0
Time
Private Optimum for
i1
1) When i0  0 , PMC > SMC = 0
Private Optimum falls short of S.O.
2) When i1  0 , PMC = SMC = 0
Private Optimum = S.O.p
The Private Optimum is achieved when the Private Marginal Cost of (holding) money =
MB. In reality, the PMC = nominal interest rate i. Therefore, any positive nominal
interest rate prevents the public to hold money up to the saturation point.
Only when i = 0, then the Private Marginal Cost of holding money becomes zero (PMC
= 0). Then the general public will be induced to hold money balances up to the point
where the PMC = 0 = MB. Then the private optimum naturally coincides with the social
optimum. This is the saturation point of holding money.
Eco 3320
3
Lecture Note #8
At this point, nobody in the economy foolishly wastes any resources, including his/her
own mental energies, on economizing on the holding of money because the holding of
money incurs no opportunity cost. (Paper) Money is a virtually no-cost means of
transactions, which contrasts with other resource-wasting means of payment such as gold,
silver, and other arrangements.
How can the government make the nominal interest rate equal to zero, and therefore
induce the general public to hold real balances up to the saturation point? The (Irving)
Fisher equation says that i = r +  in the long run () and r is equal to the marginal
product of capital(unaffected by the monetary variables). When the monetary authority
creates money supply in such way to generate  equal to –r (the negative of the given
real interest rate), then i = 0. Thus the socially optimal monetary policy is the one which
leads to the rate of inflation  = -r (and thus to the nominal interest rate i = 0). This is the
first best world.
*Food for thought: The Islamic banking system aspires to eliminate any interest charge
on money lent to ‘brothers’. Under what kind of macro-monetary policy can the Islamic
Banking succeed?
In the second best world, among the positive rates of inflation, the lower rate of inflation
is better than the higher rate of inflation. As for the above question, we can say that 10%
rate of inflation is clearly and far better than 100% rate of inflation from the standpoint of
the social welfare. The loss of social welfare is larger with 10% rate of inflation then
with 1000% rate of inflation.
2) Social welfare comparison between low and high rates of inflation:
The Social Welfare associated with the use of money is the integral or sum of the area
below the demand (marginal benefit) curve over the social marginal cost curve from the
origin to the point of the actual amount of real money balances.
The private sector’s welfare for a given real money demand is the integral or sum of the
marginal benefit over the private marginal cost curve which is given by the horizontal
line at i.
What is the difference between the two, the social and the private welfare? Why is the
social welfare larger than the private welfare? And who gets it? The difference between
the two is taken by the government as its revenue from inflation. It is inflation-tax
revenue, or Seigniorage. It is the rectangular = i  md (and is equal to   md if real
interest r = 0).
* Food for thought: The area of the rectangular changes as the rate of inflation changes.
When is the area of the rectangular maximized for a given MB or money demand curve?
The answer is when the rectangular becomes a square. When inflation rate is at the
point corresponding to the midpoint of the money demand curve, the rectangular has the
largest area being a square. This is called the inflation-tax- maximizing rate of inflation.
Eco 3320
4
Lecture Note #8
i
consumer surplus
i
0
(Social welfare =
consumer surplus + producer surplus )
social dead
weight loss
(seigniorage) producer
surplus
Let us compare zero inflation, 10% inflation, and 1000% inflation. The difference in the
social welfare between zero inflation and 10% inflation is the social deadweight welfare
loss. The difference is larger between zero and 1000% inflations. This means that the
social deadweight loss increases as the rate of inflation increases.
i
i
r  1000  i1
DWL
r 10  r   i0
DWL
The welfare loss represents resources wasted in efforts to economize on real cash
balances. It represents ‘shoe-leather costs’ or ‘menu costs’.
In reality
The optimal rate of inflation is the negative of real interest rate. Then, why do we in
reality observe mostly positive rates of inflation all around the world?
The first answer is found in the political economy surrounding seigniorage. Many
countries rely on seigniorage for financing government expenditures. This forces them to
set the date of money creation above the Friedman’s optimal rate. The second answer is
to be found in the ‘Time Inconsistency’ nature of the optimal inflation policy.