So, the demand for real money balances (Money Demand/Price Level) is a function of interest rates, and the level of income (or real GDP) in the economy.This is a real departure from Fisher because of the emphasis on the importance of interest rates and their impact on money demand. If households’ real money balances are larger than they desire, the interest rate (opportunity cost of holding money balances) is higher than its equilibrium rate. Households will use their undesired excess cash to buy securities, bidding up securities prices and reducing the interest rate toward equilibrium.

The Opportunity Cost Of Holding Real Money Balances Is The Amount
The Opportunity Cost Of Holding Real Money Balances Is The Cost

Reading: AB, chapter 7, sections 2 and 3.

The demand for money

The Opportunity Cost Of Holding Real Money Balances Is The

Consumption and saving decisions indirectly involve a decision about how much money to hold

Individuals need money for transactions involving consumption goods and services. This is the transactions demand for money.
Given income, what is not consumed is saved. Individuals must then decide how divide their savings into various kinds of assets: cash, savings accounts, government bonds, stocks etc. This is the asset allocation or portfolio problem. Since money pays very little interest (has a low return) the higher the interest rate on non-money assets the higher the opportunity cost of holding money.

Simplifying assumptions

Since the general asset allocation problem involves many different kinds of assets with different risk and return characteristics we simplify this decision by assuming that there are only two kinds of financial assets in the economy.

Money assets - low return, high liquidity and low risk. i_m = nominal interest rate on money assets.
Non-money assets (bonds) - higher return than on money assets and less liquidity. We assume that the risk associated with investing in bonds is not too high (think of government bonds as the generic non-money asset). Let i denote the nominal interest rate on non-money assets. Note that, by assumption, i > i_m. Also, recall that i = r + ^e, where r denotes the real return on non-money assets and ^e denotes expected inflation.

Model for money demand

Our model for the demand for nominal money balances takes the following form:

where

M^d = demand for nominal money balances (demand for M1)

L^d = demand for liquidity function

P = aggregate price level (CPI or GDP deflator)

Y = real income (real GDP)

I = nominal interest rate on non-money assets

r = real interest rate on non-money assets

^e = expected inflation

Remarks

Nominal money demand is proportional to the price level. For example, if prices go up by 10% then individuals need 10% more money for transactions.
As Y increases, desired consumption increases and so individuals need more money for the increased number of desired transactions.
As the nominal interest rate on non-money assets, i, increases the opportunity cost of holding money increases and so the demand for nominal money balances decreases.
Since i = r + ^e, we can decompose the effects on an increase in i into real interest rate increases (holding expected inflation fixed) and expected inflation increases (holding the real interest rate fixed).

The demand for real balances

Since the demand for nominal balances is proportional to the aggregate price level, we can divide both sides of the nominal money demand equation by P. This gives the liquidity demand function or the demand for real balances function:

The left-hand-side of the above equation is the demand for nominal balances divided by the aggregate price level or the demand for real balances (the real purchasing power of money). The right-hand side is the liquidity demand function. The demand for real balances is decomposed into a transactions demand for money (captured by Y) and a portfolio demand for money (captured by i).

The real money demand function is graphed below:

The demand for real balances is graphed as a function of the real interest rate holding income and expected inflation fixed. When the real interest rate is high the opportunity cost of holding money - keeping income and expected inflation fixed - is high so that real money demand is low. Conversely, when the real interest rate is low the opportunity cost of holding money is low so that money demand is high (due to the liquidity convenience of money over bonds). Whenever income or expected inflation change the real money demand curves shifts. For example, if Y increases the real money demand function shifts up and right; if expected inflation increases the real money demand function shifts down and left.

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Last updated on July 15, 1996 by Eric Zivot.

I suppose I should not have been shocked. Economics is full of obvious truths that sound odd when expressed in an unfamiliar way. Everyone knows that the real demand for money slopes downward, as a function of the nominal interest rates. It’s in all the textbooks. If you raise the opportunity cost of holding base money (the interest rate) people will hold less base money. It’s basic supply and demand.

But people seem shocked by the implications. Higher interest rates raise velocity. In a moment I’ll show you some evidence. And there is a mountain of academic studies that show this to be true (Cagan, etc.) But what it implies is that holding the money supply constant, higher interest rates will raise not just V, but also NGDP and inflation. And that’s what shocks people.

The Opportunity Cost Of Holding Real Money Balances Is The Amount

They are not always shocked by this relationship. They understand that fiscal stimulus can raise interest rates and raise inflation, holding M constant. Ditto for greater animal spirits leading to more investment. It’s the tight money that throws people off. How can tight money raise inflation? It doesn’t, but the higher short term interest rates caused by tight money do raise inflation. We don’t notice it because the overall effect is for lower inflation. The reduction in M reduces NGDP and inflation by more than the higher interest rates from tight money raises V and inflation. There is nothing at all controversial in what I am saying here. Indeed this is an argument that Keynesians frequently make to criticize monetarism. The gains from more M will be offset by less V.

I could not find a time series of base velocity, but I did find it’s inverse, the base/GDP ratio. And I found short term interest rates since 1934. Note that between 1929 and 1934 (not shown on graph) the short term rate plunged from about 6% to little more than zero. That explains the huge surge in the base/GDP ratio during 1929-34, and the resulting plunge in base velocity. There is a drop in the base/GDP ratio in 1937 as rates rose slightly above zero in a premature exit from the zero rate trap (coming soon to theatres near you.) Then rates go right back to zero, and the base/GDP ratio shoots up again peaking in 1940, when T-bill yields hit bottom. After the war, interest rates trended upward all the way to 1981, and the base/GDP ratio falls, bottoming out in 1981 (i.e. velocity peaks). Then interest rates fall gradually, and velocity falls as well, as the base/GDP ratio rises. Recent years are a repeat of the 1930s. I would add that after 2008 you don’t want to look at the nominal interest rate alone, rather the velocity of bank reserves depends on the short term interest rate minus IOR, which is actually negative. The last 4 years are the least costly time in all of world history to hold reserves.

The Opportunity Cost Of Holding Real Money Balances Is The Cost

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