equilibrium in the money market

• Equilibrium in the money market

  Occurs when money supply (MS) equals money demand (Md)

  
• Money demand (Md)


  Sum of transactions demand for money (Mt) and speculative demand for money (MSP)

  
• At equilibrium, MS = Mt + MSP
• MS is taken as an exogenous variable determined by the Central Bank's monetary policy
• Equilibrium in the money market

  1. Md = MS

  2. Md = Mt + MSP

  3. MS = Mt + MSP

  
• Interest rate below equilibrium (Md > MS)

  Interest rate must increase to reduce money demand and bring about equilibrium

  
• Interest rate above equilibrium (Md < MS)

  Interest rate must decrease to increase money demand and bring about equilibrium

  
• Increase in money supply


  Leads to a fall in the interest rate
• Increase in money supply beyond the liquidity trap level is ineffective in bringing about a fall in interest rate
• Increase in income


  Leads to increase in interest rate if speculative demand for money (MSP) and nominal supply of money (MS) are fixed

  
• Decrease in income


  Leads to transactions balances exceeding desired levels if money supply is held constant
• Deriving the LM equation

  1. Md = Ms

  2. Md = Mt + Msp

  3. Mt = kY

  4. Msp = l(r) = α - βr

  5. Ms = λ

  6. βr = α - λ + kY

  7. r = (α - λ)/β + k/β * Y
• The LM equation is upward sloping
• Deriving the IS-LM equation

  1. LM equation: r = (α - λ)/β + kY/β

  2. IS equation: r = α + I0/k - (1 - β)/k * Y

  3. At equilibrium: r = (α - λ)/β + kY/β = α + I0/k - (1 - β)/k * Y

  4. Y* = (α + I0/k - α - λ/β)/(k/β + (1 - β)/k)
• Given equations for the economy

  • Consumption function
  • Investment function
  • Tax function
  • Money supply
  • Money demand

  
• Solving for equilibrium income and interest rate


  1. Derive IS and LM equations

  2. Set LM = IS and solve for Y*

  3. Substitute Y* into IS or LM to find r*

  
• Changes in the general equilibrium may result from:
• Increase in aggregate Investment

  Increases income but also raises the transactions demand for money, causing interest rate to rise
• Increase in money supply

  Raises the level of income and lowers interest rates
• Simultaneous shifts in IS and LM

  Income Y will rise, but whether the interest rate r falls or rises depends on the extent of the change in Money supply