The Interest Rate and Money Demand:

Representing the velocity of wealth as a constant or slowly-moving steady trend is misleading. In the real world inflation isn’t always proportional to money growth.

For illustration in the 1980s in the United States both inflation as well as the velocity of money fell sharply however money growth in the 1980s was as fast as in the 1970s. Inflation fell still though money growth didn’t. In the mid of the 1990s there were further rapid declines in velocity, which intended that even relatively high money growth didn’t trigger accelerating inflation. The second half of the 1990s saw evenly rapid increases in velocity and so nominal money supply growth had to dip well below zero in order to keep inflation from rising.

Economic theory suggests that money demand must be inversely related to the nominal interest rate which is the sum of the real interest rate and the current inflation rate. The cash in your purse or wallet doesn’t earn interest. Your checking account balances receive little or no interest as well. Therefore their purchasing power over real goods and services erodes at the rate of inflation. The expected real return on observance your money in readily spendable form is –π^e the negative of the expected inflation rate.

By contrast were you to obtain a dollar out of your checking account and invest it, it’s real return would be the real interest rate r. The dissimilarity 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 total of the inflation rate π^e and the real interest rate r: i.e. the nominal interest rates i. The elevated is this opportunity cost of holding money the lower is the demand for money balances as shows. Economic theory therefore tells us that the velocity of money will be a function like:

V = V^L x (V_o +V_i x (r + π^e))
     
Where V^L is the monetary technology-driven trend in the velocity of money and V₀ + V_i(r+π^e) captures the dependence of the demand for wealth on the nominal interest rate. The higher is the nominal interest rate i = r+πe the higher is the velocity function V and the lower is the demand for money.

Such a function for velocity signifies that the demand for nominal money balances.

For the reason that the level of money demand depends on the current rate of inflation, we require to keep track of two equations to determine the behavior of prices, money, and inflation. The first comes straight from the money demand function and is the equation for the price level:

The subsequent comes from the rate of change of the demand for money. If inflation is constant as well as the proportional rate of change of the velocity trend is v then as before:

π = m + v - y
     
Therefore if the rate of growth of the money stock is +6% per year, the velocity trend is +1% per year and real GDP growth is +4% per year then inflation is 3% per year.

Now presume that the rate of growth of the money stock suddenly increases permanently from 6% per year to 10% per year. When the economy resolve down the new inflation rate will be 4% per year higher--7% instead of 3% per year. However at inflation rate of 7% per year the opportunity cost of holding money was higher. If the real interest rate is steady at 3% per year then the opportunity cost of holding money has just jumped from 6% to 10% per year.

Effects of an Increase in Money Growth:

Legend: A raise in the rate of growth of the money stock leads to an immediate jump in the price level to a step-up of the inflation rate as well as to a fall in the quantity of money demanded as a fraction of nominal GDP.

A higher opportunity cost of holding funds will raise the velocity of money. If the money stock as well as real GDP remains fixed, this raise in the velocity of money will cause the price level to jump suddenly and discontinuously, as is shown in Figure through how much the price level jump will? It depends on how sensitive funds demand is to changes in the nominal interest rate. The more sensitive is funds demand to the nominal interest rate the larger will be the sudden jump in the price level.

Therefore in the flexible-price macro-economy a change in the rate of growth of the money stock not merely changes the long-run inflation rate, it as well causes an immediate jump in the price level at the moment that households and businesses become aware that the rate of money growth has changed.

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