Money demand should be inversely related to the nominal interest rate – the sum of the real interest rate and the current inflation rate.
◦ The cash in your purse or wallet does not earn interest. Your checking account balances earn little or no interest as well.
◦ Their purchasing power over real goods and services erodes at the rate of inflation.
◦ The expected real return on keeping your money in readily spendable (liquid) form is the negative of the expected inflation rate.

Were you to take a dollar out of your checking account and invest it, its real return would be the real interest rate r.
◦ The difference between the rate of return on money balances and the rate of return on other assets is the opportunity cost of holding money.
◦ This opportunity cost is the sum of the inflation rate and the real interest rate: that is, the nominal interest rate.
◦ The higher is the opportunity cost of holding money, the lower is the demand for money balances.

Economic theory thus tells us that the velocity of money will be a function like
V

V
L


V
0

V i

 r
  e
 
◦ V
L is the financial technology-driven trend in the velocity of money.
◦ The second term captures the dependence of the demand for money on the nominal interest rate.
The higher is the nominal interest rate, the higher is the velocity function V, and the lower is the demand for money.

Keynes considered three motives for holding money:
1. Transactions Demand: Money is a medium of exchange, and individuals hold money for use in transactions. The amount of money held for transactions would vary positively with the volume of transactions in which the individual is engaged which, in turn, depends on income.
◦ Interest rate and transactions demand (negatively related); economies of scale in wealth management

2. Precautionary Demand: Beyond money for planned transactions, additional money balances were held in case of unexpected expenditures such as medical or repair bills.
◦ The amount held for this purpose depends positively on income, and negatively on interest rates.

3. Speculative Demand: Given uncertainty about future interest rates and the relationship between changes in the interest rate and the price of bonds, investors may hold money in lieu of bonds. Money is held by those speculating on future changes in the interest rate.

We can write the money demand equation as either
M d 
P

L
  or
M d

L

Y , r
  e

P

The higher the price level, the more money you need for transactions.
Prices are 10+ times as high today as in 1935, so it takes 10+ times as much money for equivalent transactions.
Nominal money demand is thus proportional to the price level.

The more transactions you conduct, the more money you need. Real income is a prime determinant of the number of transactions you conduct, so money demand rises as real income rises.
◦ But money demand isn’t proportional to real income
◦ higher-income individuals use money more efficiently
◦ a country’s financial sophistication grows as its income rises (use of credit and more sophisticated assets).
◦ Therefore, money demand rises less than 1-to-1 with a rise in real income.

An increase in the interest rate or return on nonmonetary assets decreases the demand for money.
◦ Though there are many nonmonetary assets with many different interest rates, because they often move together we assume that for nonmonetary assets there’s just one nominal interest rate, i.

An increase in the interest rate on money increases money demand; this occurs as people trade off liquidity for return. For the most part, the nominal interest rate on money is zero, and so we ignore it.
The real interest rate, which affects saving and investment decisions, is r
 i
  e

Wealth: A rise in wealth may increase money demand, but not by much
Risk
◦ Increased riskiness in the economy may increase money demand.
◦ Times of erratic inflation bring increased risk to money, so money demand declines.
Liquidity of alternative assets: Deregulation, competition, and innovation have given other assets more liquidity, reducing the demand for money.
Payment technologies: Credit cards, ATMs, and other financial innovations reduce money demand.

We need to put together the money supply and money demand to get an equilibrium condition.
To do this, assume that total wealth is either held as money or as bonds (i.e., nonmonetary assets). Then M d + B d = nominal wealth. Because there are only two types of assets, M s + B s = nominal wealth as well.
In equilibrium, M d = M s and B d = B s . Note that the equilibrium conditions can be written

M d 
M s
 
B d 
B s


0 .
This is an example of Walras’ Law.

Example of asset market in action: Suppose M s > M d . Then it must be that B d > B s . To restore equilibrium, B d must decline and M d increase.
This occurs via the bond market – excess demand for bonds causes the price of bonds to be bid up, causing nominal interest rates to fall. As i declines, L(Y,i) increases.
Thus, the nominal interest rate works to equilibrate the asset market in the short run.

We are assuming that Y is at Y fe and that r is unaffected by changes in the money supply.
Furthermore, assume that
 e is fixed.
Then
P

L

Y ,
M r
 s
 e

. Price is proportional to money supply.

Money supply doesn’t affect real variables since:
◦ Y is determined by the production function.
r, w, determined by MP
K
, MP
L
, K, and L plus exogenous variables.