Lecture Notes for Chapter 7 of
Macroeconomics:
An Introduction

• What does ‘demand for money’ mean?
• Why do we need to know about it?
• What is the price of money?
• How the supply and demand for money
  determine the interest rate.
• The Fed controls the supply of money,
  so the Fed can control the interest rate.

• Fed controls the supply of money
  through open market operations.
• The demand for money
  depends on the interest rate.
• Interest rate is a price, and it adjusts to
  balance the supply and demand for money.
• That means the Fed can control interest rates by changing the supply of money.

• Low interest rates stimulate spending on
• plant and equipment
• and consumer durables.
• High interest rates discourage spending,
• affect GDP and employment,
• finally, prices and wages too.
• Control over interest rates gives the Fed
  a lever to move the economy.

• How much money would you like to have?
• One billion?
• Two? That can’t be it.
  
• Instead
  ‘How much money (currency and bank deposits) do you wish to hold,
  given your total wealth.’

• Why hold any money at all?
• It pays no interest.
• It loses purchasing power to inflation.

• 1. To settle transactions.
• Money is the medium of exchange.
  
• 2. As a precautionary store of liquidity.
• Money is the most liquid of all assets.
  
• 3. To reduce the riskiness of your portfolio.
• Money is the least risky of all assets.

• The interest you could have earned!
• That is the opportunity cost.
• At today’s T bill yield, what does it cost you to hold an extra $1,000?
• The optimal amount of money to hold is the amount that balances the benefits of holding money against the opportunity cost.

• The interest rate
• the cost of holding money.
  
• Income
• which affects transactions demand
  
• Wealth
• which affects portfolio demand

• holding income and wealth constant.
• varies inversely with the interest rate
• reflected in negative slope of demand curve.
• What happens at very low interest rate?
• At very high interest rate?

• Transactions demand doubles.
• Portfolio demand doubles.
• Quantity of M demanded doubles.
• Changes in income or wealth shift the demand curve.

• Fed controls supply of M
• Suppose $300 billion.
• Vertical line at $300 b.
• Quantity demanded equals quantity supplied at interest rate of 10%.
• People then willing to hold the money that exists.

• Someone holds each dollar that exists
• You can reduce your holding of money
  by spending it or buying assets
• But individuals cannot changes the total amount of money held by everyone
• Only the Fed can change the total

• If it drops to 9%, we want to hold more money.
• Everybody tries to sell bonds to get cash.
• But cannot all change quantity of money they hold, because total quantity of money is fixed.
• Price of bonds falls, interest rate back to 10%!
• At 10%, we are willing to hold the quantity of money supplied by the Fed.

• You divide your portfolio between
• money, which provides liquidity,
• and bonds, which pay interest but are risky,
• taking into account the interest rate you can earn on bonds.
• The demand for money determines the demand for bonds, and vice versa,
  since your total portfolio is a given.

• What about the stock market? Real estate?
• "Bonds" stand for all non-money assets.
• "The interest rate" represents the return.
• T bill and bond yields are benchmarks.
• Motivation:people always have a choice between bonds and stocks and real estate.

• Fed boosts money supply from $300 b to $600 b
• What will induce them to hold more?
• Income and wealth change slowly, but
• the interest rate falls quickly to 5%.
• How quickly?
  This minute!

• When there is a big orange crop,
  the price of orange juice falls.
• It has to, to clear the market.
• When the Fed expands the money supply,
  the interest rate falls.
• It has to, to clear the market.

• Changes in nominal income or wealth,
• Volume of trading in the stock market
• Seasonal fluctuation in retail sales
• The Fed actually increases the money supply every holiday season.
• What would happen if it didn’t?

• Focus is on key variables, leave out others.
• Summarizes relationships
  using simplifying assumptions.
• Test of a model is not whether it is an accurate description of reality,
• but whether it is useful for
• explaining
• predicting.

• M^d = k(i) • GDP
• "M^d" is the quantity of money demanded,
• "k(i)" is a function of the interest rate "i"
• GDP is the measure of nominal income.
• quantity of money demanded, at a given interest rate, is proportional to GDP.
• k(i) is inversely related to i, giving the demand curve its downward slope.

• Money demand is proportional to GDP
• so money demand doubles at a any "i"
• The new intersection of demand and supply must occur at a higher interest rate
• here at 10%.

• To keep the interest rate constant,
  Fed must increase supply of money
  at the same rate as nominal GDP.
  
• Then both supply and demand curves are shifting to the right at the same rate,
  keeping "i" constant.

• Real income and prices are both growing
• The interest rate will depend on relative growth rates of money and nominal income.
• If money grows more slowly than GDP,
  then interest rates rise;
• If faster than GDP, interest rates fall

• Is k(i) a function of i?
• Let’s calculate k(i) at each point in time
• then plot "k" against "i"
• and see if there is a negative relationship

• The demand for money is M^d = k(i) • GDP
• supply of money is M^s = M,
  quantity supplied by the Fed.
• In equilibrium supply equals demand, so
• k(i) • GDP = M, now solve for k(i):
• k(i) = M/GDP, which is
• the demand for money per dollar of GDP.

• Each point is k & T bond yield during one quarter
• 1960 through mid-1994.
• Pattern downward sloping & concave,
• but not exactly on a curve,
• scattered around a curve.

• Much "noisier"
• Short term interest rates more volatile
• Still see:
  downward sloping
  concave shape

• Left out variables, asset transactions such as volume on the NYSE, home sales.
• More complex models address these issues,
  but simple model is useful approximation.
• Keeps those 247 Fed economists busy!

• Definition: V = GDP/M
• Rate at which dollars circulate through economy.
• Number of times a dollar gets used per year.
• Velocity is higher when the interest rate is higher
  since people will hold less M per dollar of GDP.
• Should be higher in Brazil than in Switzerland,
• It is!

• Substituting [k(i) • GDP] for M we get,
• V = GDP/[GDP • k(i)] = 1/k(i) = V(i)
• Since k(i) varies inversely with i,
  V(i) varies directly with the interest rate.
• In places and times where inflation and interest rates are high,
  the velocity of money is also high.