Chapter 5 Notes

February 18, 2025

The quantity theory of money

• A simple theory linking the inflation rate to the growth rate of the money supply.

• Begins with the concept of Velocity.

• Stars with the quantity equation:

  • Assumes V is constant and exogenous: V = V (Repeating)

    • Quantity Equation becomes: M V(Repeating) = P Y

• M * V(Constant) = P*Y

  • How the price level is determined:

    • With V(constant), the money supply determines nominal GDP (PY)

    • Real GDP is determined by the economy’s supplies of K and L and the production function.

    • The price level is P = (Nominal GDP)/(Real GDP)

• π = (∆M / M) - (∆Y / Y)

  • Normal economic growth requires a certain amount of money supply growth to facilitate the growth in transactions.

  • Money growth in excess of this amount leads to inflation.

  • ∆Y/Y depends on growth in the factors of production and on technological progress (all of which we take as given, for now).

    • Hence the quantity theory predicts a one-for-one relationship between changes in the money growth rate and changes in the inflation rate.

Confronting the quantity theory with data

• The quantity theory of money implies:

  1. Countries with higher money growth rates should have higher inflation rates.

  2. The long-run trend in a country’s inflation rate should be similar to the long-run trend in the country’s money growth rate.

Velocity

• Basic concept: The rate at which money circulates.

• Definition: The number of times the average dollar bill changes hands in a given time period.

• Equation for velocity: V = T/M

  • V = Velocity

  • T = Value of all transactions

  • M = Money Supply

• Use nominal GDP as a proxy for total transactions. Then, V = (P * Y)/M

  • P = Price of output

  • Y = Quantity of output (Real GDP)

  • P * Y = Value of output (Nominal GDP)

The Quantity Equation

• The quantity equation: M * V = P * Y

  • Follows from the preceding definition of velocity. It is an identity: it holds by definition of the variables.

Money demand and the quantity equation

• M/P = Real money balances, the purchasing power of the money supply.

• A simple money demand function: (M/P)^d = kY

  • k = How much money people with to hold for each dollar of income.

    • k is exogenous.

    • During periods of economic expansion people would be holding less k and invest the money instead.

    • During harder times people will hold more k.

• Money Demand: (M/P)^d = k Y

• Quantity Equation: M * V = P * Y

• The connection between them: k = 1/V

• When people hold lots of money relative to their incomes (k is large), money changes hands infrequently (V is small).

Seigniorage

• To spend more without raising taxes or selling bonds, the government can create money.

• The “revenue” raised from money creation is called seigniorage.

• The inflation tax:

  • Money creation to raise revenue can cause inflation, paid by holders of money and other nominal assets.

Inflation and interest rates

• Nominal interest rate, i not adjusted for inflation.

• Real interest rate, r adjusted for inflation:

  • r = i - π

The Fisher effect

• The Fisher Equation: i = r + π

  • An increase in π causes an equal increase in i.

    • This one-for-one relationship is called the Fisher Effect.

Two Real interest rates

• Notation:

  • π = Actual interest rate

    • (Not known until after it has occurred)

  • Eπ =8.54 Expected interest rate.

• Two real interest rates:

  • i - Eπ = Ex ante real interest rate:

    • The real interest rate people expect at the time they buy a bond or take out a loan.

  • i - π = Ex post real interest rate:

    • The real interest rate actually realized.

    • Social Security payments are Ex post because they only adjust for cost of living every January instead of doing it throughout the year.

Money demand and the nominal interest rate

• In the quantity theory of money, the demand for real money balances depends only on real income Y.

• Another determinant of money demand: the nominal interest rate i.

  • The opportunity cost of holding money (instead of bonds or other interest-earning assets).

• So, the money demand depends negatively on i.

The money demand function

• (M/P)^d = L(i,Y)

  • (M/P)^d = real money demand, depends

    • negatively on i

      • i is the opportunity cost of holding money

    • positively on Y

      • Higher Y increases spending on goods and services so increases the need for money.

  • L is used for the money demand function because money is the most liquid asset.

• M/P)^d = L(r + Eπ,Y)

  • When people are deciding whether to hold money or bonds, they don’t know what inflation will turn out to be.

  • Hence, the nominal interest rate relevant for money demand is r + Eπ

Equilibrium

• M/P = L(r + Eπ, Y)

  • The supply of real money balances = Real money demand

  • M = Exogenous (The federal reserve)

  • r = adjusts to ensure S = I

  • Y = M/P = L(i, Y)

    • P adjusts to ensure Ŷ = F(Ķ, Ł)

    • i is solved for by i = r + Eπ