Fin 221: Chapter 4

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Fin 221 Chapter 4

• The level of interest rates

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What are Interest Rates?

• Interest rates are
• The price of borrowing money for the use of its
  purchasing power (it is the rental price of
  money).
• To a borrower, they are penalty for consuming
  income before it is earned.
• To a lender , they are reward for postponing
  current consumption until the maturity of the
  loan.
• Interest rates serve an Allocative Function in
  the economy. They allocate funds between SSUs and
  DSUs and among financial markets.

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The Real Rate of Interest

• The interest rate paid on savings basically
  depends on
• 1. The rate of return on investment (The
  rate of return producers can expect to earn on
  investment capital.)
• 2. Savers time preference for current
  versus future consumption Most people prefer to
  consume goods today rather than tomorrow. This is
  known as positive time preference.
• The expected return on investment projects sets
  an upper limit on the interest rate producers can
  pay to savers, whereas consumer time preference
  for consumption establishes how much consumption
  consumers are willing to forgo (save) at the
  different levels of interest rates offered by
  producers.

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The Real Rate of Interest..cont.

• Investment is negatively related to interest
  rate. Other things remaining the same, the higher
  the interest rate, the lower the desired
  investment (desired investment demand curve
  slopes downwards).
• Desired saving is positively related to interest
  rate. The higher the interest rate ,the higher
  the desired savings are (desired saving supply
  curve slopes upwards)..
• The market equilibrium interest rate for the
  economy is determined by the interaction of
  supply and demand for funds (see diagram)

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Determinants of the Real Rate of Interest
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The Real Rate of Interest..cont.

• The market equilibrium rate of interest (r) is
  achieved when desired savings of savers ( S)
  equals desired investments( I) by producers
  across all economic units. ( see diagram)
• The equilibrium rate of interest is called the
  Real Rate of Interest ( this is because it is
  determined by the real output of the economy).
• The real rate of interest is the fundamental
  long-run rate of interest in the economy ( it is
  the base interest rate for the economy).
• Changing economic forces cause interest rates to
  change ( by causing a shift in the savings or
  investment curves)( refer to diagram).

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Loanable funds theory of interest

• The loanable funds ( LFs) is a framework used to
  determine interest rate in the short-run.
• In the shortrun interest rates depend on the
  supply of and the demand for LFs, which in turn
  depend on productivity and thrift.
• The need to sell financial claims issued by DSUs
  constitutes the demand for LFs.
• The SSUs supply LFs to the market ( SSUs purchase
  financial claims offered by DSUs to earn interest
  on their excess funds).

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Loanable funds theory.cont.

• Sources of supply and demand for LFs
• Supply of LFs (SSUs)
• - Consumer savings.
• - Business savings( depreciation and retained
  earnings)
• - Government budget surpluses.
• - C.B actions (increases the money supply).
• Demand for LFs (DSUs)
• Consumer credit purchases.
• Business investment.
• Government budget deficits.

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Loanable funds theory..cont

• In general, higher interest rates stimulate more
  savings and more LFs. The supply curve of LFs
  slopes upward.
• The demand for LFs decreases as the interest rate
  increases. The demand curve for LFS slopes
  downward.
• The intersection of LFs supply and demand curves,
  determine the equilibrium interest rate and the
  equilibrium quantity of LFs savings and demanded
• If the interest rate is below the equilibrium
  rate, there will be shortage of LFs which will
  force the interest rate up. On the other hand, if
  the interest rate is above the equilibrium rate,
  a surplus of LFs will exist forcing the rate
  downward restoring the equilibrium.

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Loanable Funds Theory
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Loanable funds theory.cont.

• Changes in interest rate (other things remaining
  constant) brings changes in quantity of LFs
  demanded and supplied, and thus movements along
  the SL and DL curves.
• Changes in factors other than the interest rate
  will change the supply and demand for LFs. There
  will be a shift in the supply and demand curves,
  and as a result a new equilibrium occurs.

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Factors affecting supply of LFs

• Changes in the quantity of money
• If quantity of money increases, supply of
  LFs increases.The SL curve shifts to the right,
  resulting in a new equilibrium with lower
  interest rate and higher equilibrium quantity.
• 2.Changes in the income tax a decrease in
  income tax increases saving ,Thus the supply of
  LFs increases and the SL shifts to the right (Tax
  is government revenue).
• 3. Changes in government budget from deficit to
  surplus position This will also lead to a shift
  in SL curve to the right.
• 4.Changes in business saving ( depreciation and
  retained earnings). An increase in business
  savings will increase supply of LFs and cause the
  SL curve to shift to the right.

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Factors affecting demand for LFs

• 1.Changes in future expected profits of business
  activities If businesses are expected to
  generate higher profits in the future, the demand
  for investment funds will increase and so the
  demand for LFs.The DL curve shifts to the right
  resulting in a new equilibrium with higher
  interest rate and higher equilibrium quantity.
• 2. Changes in tax level an decrease in taxes,
  will increase government deficit, therefore
  increasing the demand for LFs, hence the DL curve
  will shift to right.
• 3.Changes in government budget from surplus to
  deficit position this occurs due to increase in
  government expenditure (the government must
  borrow to cover the deficit). The demand for LFs
  will therefore increase and this will cause the
  DL curve to shift to the right .

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Price expectations and interest rate

• Changes in price level affect both the realized
  return that lenders receive on their loans and
  the cost that borrowers must pay for them.
• Unanticipated inflation benefits borrowers at
  expense of lenders.
• Lenders charge added interest to offset
  anticipated decreases in purchasing power.
• Expected inflation is to be embodied in nominal
  interest rates.

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Price expectations and interest rate

• How to protect against price changes??
• Protection against changes in purchasing power
  (PP) can be incorporated in the interest rate on
  a loan contract.
• Example
• An SSU and a DSU plan to exchange money and
  financial claims for a period of one year. Both
  agreed that a fair rental price for the money is
  5 and both anticipate an 8 inflation rate
  during the year. What would be the contract rate
  on the loan ?To answer this question we need to
  discuss the Fisher Effect.

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Price expectations and interest rate..cont

• The Fisher Effect
• The Fisher Effect Theory states that the nominal
  interest rate (contract rate) includes real
  interest rate and expected annual inflation rate.
• The Fisher Equation is expressed as
• (1 i ) (1r) ( 1 ?Pe )
• Where i the observed nominal rate of
  interest.
• r real rate of interest in the
  absence of price level changes(
  interest rate where no inflation exists).
• ?Pe expected annual change in
  commodity prices (expected annual rate
  of inflation).

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Price expectations and interest rate..cont

• - Solving the Fisher Equation for ( i) we obtain
  the following equation
• i r ?Pe (r
  ?Pe)
• The equation shows the relationship between
  nominal (contract) rates and rates of expected
  inflation. The inflation component of the
  equation is commonly referred to as the Fisher
  Effect.
• Based on the equation, the contract rate between
  the above mentioned SSU and DSU is
• i 0.05 0.07 ( 0.05 x 0.07 )
  0,123512.35
• - On a loan of 1000 the lender will get
• Total compensation 1000 (1000X5 ) (1000X 7
  ) (1000 X5X7) 1123.5

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Price expectations and interest rate..cont

• The Fisher EquationCont
• 4.The final term of the Fisher equation (r ?Pe
  )is approximately equal to zero. So, in many
  situations it is dropped from the equation
  without creating a critical error.
• The equation without the final term is referred
  to as the Approximate Fisher Equation and is
  stated as
• i r ?Pe
• Therefore, approximately i 57 12

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The Realized Real rate

• The Fisher equation is based on expected
  inflation rate. The actual rate of inflation may
  be different from the anticipated rate. For the
  real interest rate and the nominal interest rates
  to be equal, the expected rate of inflation must
  be zero (?Pe 0).
• The actual inflation rate, more than likely will
  not equal to what was expected.
• This may lead to the realized rate of return on a
  loan to be different from the nominal interest
  rate agreed at the time of the loan contract.
• The realized (actual) real rate is calculated as
  
• r i - ?Pa,
• Where r is the realized real rate of
  return.
• i the nominal interest rate.
• ?Pa is the actual rate of
  inflation.

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Inflation and loanable Funds Model

• Te higher the expected inflation rate ,the higher
  is the demand for LFs ( consumption increases).
  The DL will shift upwards (to the right ). by the
  amount (?Pe) .The shift from DLo to DL1(see
  diagram) implies that borrowers are willing to
  pay the inflation premium ?Pe.
• Similarly, the higher the expected inflation rate
  the lower is supply for LFs ( savings decrease),
  so SL curve will shift upwards ( to the left) by
  the amount ?Pe .The shift from SL0 to SL1 will be
  such that lenders are given a higher nominal
  yield to compensate for their loss of purchasing
  power.

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Inflation and loanable Funds Model
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Inflation and loanable Funds Model

• The net effect of inflation is that the market
  rate of interest will rise from ( r0) to (i1) ,
  where the difference between ( i1 ) and ( r0) is
  the expected inflation rate (?Pe) or
• i1 r0 ?Pe
• Even though the real rate (r0 ) remains
  unchanged, the nominal rate of interest (i1 ) has
  adjusted fully for the anticipated rate of
  inflation (?Pe ) and the quantity of LFs in the
  market has remained the same at Q0

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Interest Rate Movements and Inflation.. Contd

• Historically, interest rates tend to change with
  changes in the rate of inflation, substantiating
  the Fisher equation.
• Short-term rates are more responsive to changes
  in inflation than long-term rates.
• That is Short-term interest rates change more
  than long-term interest rates for a given change
  in inflation.