money market

demand

• asset types
  • money
    • currency: coins, bills
    • deposit accounts: bank deposits
  • bonds: interest rate, not used for transactions
• money vs bonds dependent on…
  • level of transactions: need money on hand to avoid having to sell bonds, dependent on spending per month etc
  • interest rate on bonds: holding wealth in bonds is for interest, hassle of managing bonds is dependent on rate
• money market funds pool funds of many people to buy bonds
• terms
  • income: earning from work + interest, dividends; flow over time
  • saving: after-tax income not spent
  • wealth: value of all financial assets minus financial liabilities
  • investment: purchase of new capital goods

derivation

• $M^d$: amount of money people want to hold
• if nominal income increase, transactions increase proportional, $M^d$ increase proportional
• M^d = \YL(i)$
• based on some function of interest rate, $L(i)$
• $M^d$ has negative relationship with $i$

determining interest rate

• focus on supply of money and equilibrium

• in real world, two types of money: deposit accounts supplied by banks, currency supplied by central bank

• assume deposit accounts do not exist, only money is currency

• suppose central bank decides to supply money equal to $M$, thus $M^s=M$, $s$ for supply

• equilibrium requires money supply equals demand, that $M^s=M^d$

  • so $\text{Money supply}=\text{Money demand}$ and M^s = \YL(i)$
  • shows that $i$ must be such that for given income \Y$peoplemustbewillingtoholdmoneyequaltoexistingmoneysupply$M^s$;calledthe$LM$ relationship
  • i.e. increase to supply of money by central bank leads to decrease in interest rate
    • decrease in interest rate leads to increased demand for money, so it equals increased money supply

open market operations

• central banks change suptply of money by buying or selling bonds
• central banks wants increase, buys bond and pays for them by creating money; if wants to decrease, sells bonds and removes from circulation money in exchange for bonds
  • called open market operations as they happen in ‘open market’ for bonds
  • expansionary open market operation → expands supply of money
  • contractionary open market operation → contracts supply of money

bond prices and yields

• suppose one-year bonds with payment of \100$andsomeprice$$P_b$;interestrategivenas$i = \frac{$100 - $P_B}{$P_B}$
• price today from one-year bond paying \100$yearfromtodayis$$P_B = \frac{$100}{1 + i}$
• central bank buys bonds → demand for bonds goes up → price increases → interest rate goes down
• central bank sells bonds → demand for bonds goes down → price decreases → interest rate goes up

liquidity trap

• assume central bank could always affect interest rate by changing money supply
• however, interest rate cannot fall below zero
  • as interest rate decreases, people want to hold more money + less bonds
  • as interest rate becomes zero, people want to hold money equal to $OB$, i.e. right when it hit $0\%$

adding deposit accounts

assets/liabilities

• central bank
  • assets: bonds
  • liabilities: central bank money (reserves + currency)
• banks
  • assets: reserves, loans, bonds
  • liabilities: deposit accounts

cont

• up to this point, assuming only currency supplied by central banks
• banks keep as reserves some funds they receive
  • 1. on given day some depositors withdraw, other deposit cash; no reason for inflows and outflows to be equal
  • 2. on given day, people with accounts write checks to other people with accounts; what bank owes to other banks can be larger or smaller than what is owed to it
  • 3. there are certain reserve requirements applied in areas (europe in this case, with a reserve ratio of 2% on certain deposit types
• loans represent most of banks’ non-reserve assets, bonds account for the rest
  • bonds/loans are approximately equivalent in the model
  • assume only reserves and bonds as assets
• demand for money
  • 
• what determines the demand for deposit accounts vs currency?
  • in the equations, the $c$ vs $(1-c)$ factors, where $c$ is towards demand for currency
• what determines the demand for reserves by banks?
  • based on the amount required by the country, e.g. 2%, and $(1-c)$, the demand for deposit accounts
• what determines the demand for central bank money?
  • based on a negative relationship with a function $L$ of interest $i$
• how does the condition that demand/supply of central money be equal determine interest rate
  • the demand is through M_d = \YL(i)$,soif$M_d$and$Y$areset,$i$hastofollowthrough$L(i)$