The Financial Market Introduction to Macroeconomics WS 2011 October 28 th, 2011 Introduction to Macroeconomics (WS 2011) The Financial Market October 28 th, 2011 1 / 22
Recapitulation of last Lecture Last time we looked at the equilibrium on the goods market and determined the level of (real) GDP (Y ) for which production and demand were equal This time we will look at the financial market and try to determine the interest rate (i) for which the demand for money and the supply of money are equal This interest rate will depend on (nominal) GDP ($Y ) Next time, we will consider both markets simultaneously and determine the level of Y and the interest rate for which both markets are in equilibrium Introduction to Macroeconomics (WS 2011) The Financial Market October 28 th, 2011 2 / 22
The Demand for Money At any point in time households have a certain amount of (financial) wealth Wealth is defined as the value of financial assets minus the value of financial liabilities (e.g. mortgages, debt) Wealth is a stock variable (defined at a certain point in time) and determined by past decisions (predetermined) This means that households decisions can only have an effect on their future wealth, but their current wealth is fixed At a certain point in time, the only decision households can make is in which form they want to hold their fixed amount of wealth Introduction to Macroeconomics (WS 2011) The Financial Market October 28 th, 2011 3 / 22
The Demand for Money We assume that households can hold their fixed wealth either in form of money or in form of bonds Holding money is needed to finance transactions (buying goods), in Keynesian models it is also assumed that households have a preference for holding money ( liquidity preference ) Bonds promise to pay a fixed amount of money at a future date (in other words bonds pay a positive interest rate i), i.e. households can increase their wealth in the future by holding bonds The typical household will divide his wealth between money holdings and bond holdings. Everything else equal, it will hold more bonds (and less money) if the interest rate on bonds is higher and it will hold more money (and less bonds) if it wants to buy more goods. Introduction to Macroeconomics (WS 2011) The Financial Market October 28 th, 2011 4 / 22
The Demand for Money More precisely, we assume that money demand (M d ) is given by: M d = $YL (i) with L < 0 That is, we assume that money demand is proportional to nominal GDP. This assumption is made since transactions in an economy should be roughly proportional to the available income of households. money demand depends negatively on the interest rate. This is the case since a larger interest rate implies that the opportunity cost of holding money is higher (people forgo a larger interest payment by holding money), i.e. holding money becomes less attractive compared to holding bonds Introduction to Macroeconomics (WS 2011) The Financial Market October 28 th, 2011 5 / 22
The Demand for Money The function L (i) is a measure for the liquidity preference of households since the value of L captures how strongly agents react to changes in the interest rate: If L is in absolute terms large, households mainly care about the return on holding bonds when making the decision whether to hold money or bonds (they have a weak liquidity preference) If L is in absolute terms small, households care very little about the return on bonds when making the decision whether to hold money or bonds, they simply want to hold a certain amount of money (they have a strong liquidity preference) Introduction to Macroeconomics (WS 2011) The Financial Market October 28 th, 2011 6 / 22
The Demand for Money - Graphical Representation The For simplicity, Demand we for will draw Money money demand as a function of the interest ving ratethe only, Demand changesfor in $Y Money shift the money demand function: d $ YL( i) ( ) Figure 4-1 e Demand for Money a given level of nominal me, a lower interest rate eases the demand for ey. At a given interest rate, ncrease in nominal income ts the demand for money to right. 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 5of 32 Introduction to Macroeconomics (WS 2011) The Financial Market October 28 th, 2011 7 / 22
The Supply of Money We assume that money supply is constant, i.e. M s = M for some fixed value M The central bank can however change the money supply M through open market operations: The central bank can sell bonds to decrease the money supply. This is called contractionary open market operation. The central bank can buy bonds to increase the money supply. This is called expansionary open market operation. Variations in the money supply are also referred to as monetary policy Introduction to Macroeconomics (WS 2011) The Financial Market October 28 th, 2011 8 / 22
The Money Market Equilibrium - A Graphical Analysis 2 Similar The Determination to the goods market, of the the money Interest market is Rate, in equilibrium I if the ney supply Demand, of money Money and the Supply, demand and forthe money Equilibrium are equal, i.e. if M s = M d erest Rate Figure 4-2 he Determination of the nterest Rate he interest rate must be such hat the supply of money which is independent of the nterest rate) is equal to the emand for money (which does epend on the interest rate). 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 8of 32 Introduction to Macroeconomics (WS 2011) The Financial Market October 28 th, 2011 9 / 22
The Money Market Equilibrium - An Algebraic Solution Suppose that the liquidity preference function is given by L (i) = α i, where α is a positive exogenously given parameter, and that money supply is given by M s = M. The money market equilibrium is then characterized by: M = $Y α i i = $Y α M Hence, a nominal GDP of 1000, a money supply of M = 100, and α = 0.01 yield an equilibrium interest rate of i = 1000 0.01 100 = 0.1 = 10% Introduction to Macroeconomics (WS 2011) The Financial Market October 28 th, 2011 10 / 22
The Relationship between the Interest Rate and Bond Prices In order to understand the effect of monetary policy on the money market equilibrium, it is necessary to discuss the connection between bond prices and the interest rate Suppose a bond is promising to pay some amount x in the future and that its current price is given by P B. Then the rate of return on holding the bond is given by: i = x P B P B If the price of bonds increases, the interest rate decreases. (To see this, note that if P B increases, the numerator (x P B ) decreases and the denominator (P B ) increases) Introduction to Macroeconomics (WS 2011) The Financial Market October 28 th, 2011 11 / 22
The Effect of Expansionary Monetary Policy on the Money Market Equilibrium Suppose the central bank increases the money supply by buying bonds: 1 Everything else equal, this action increases the demand for bonds, while leaving the supply of bonds unchanged. 2 An excess demand for bonds implies that their price will increase. 3 A higher bond price implies that the interest rate must decrease. In other words: People are only willing to hold more money if holding bonds becomes less attractive. Introduction to Macroeconomics (WS 2011) The Financial Market October 28 th, 2011 12 / 22
The Effect of Expansionary Monetary Policy on the Money Money Demand, Money Supply, Market Equilibrium and the Equilibrium Interest Rate Graphically, the effects of an expansionary monetary policy can be depicted as follows: Figure 4-4 The Effects of an Increase in the Money Supply on the Interest Rate An increase in the supply of money leads to a decrease in the interest rate. Introduction to Macroeconomics (WS 2011) The Financial Market October 28 th, 2011 13 / 22
A Different Characterization of Monetary Policy Usually central banks do not target a certain money supply, but instead choose a desired level for the interest rate. In order to implement a desired interest rate ĩ, the central bank can use the equilibrium condition M = $YL ( ĩ ) to calculate the money supply M needed for this goal. Introduction to Macroeconomics (WS 2011) The Financial Market October 28 th, 2011 14 / 22
Different Possibilities of Holding Money So far, we have not specified what we mean by money Despite the possibility of holding currency (coins and bills), people may also have checkable deposits at banks Checkable deposits can be used for transactions just like real currency. Therefore, we must distinguish between money that can be used for transactions (currency held by households + checkable deposits) and the money printed by the central bank (coins and bills) However, not only private households hold currency. Also banks need to keep some fraction of the money on checkable deposits as reserves (2% in the Eurozone) in order to finance withdrawals. The rest of the money can be used to make loans or to buy bonds. Introduction to Macroeconomics (WS 2011) The Financial Market October 28 th, 2011 15 / 22
The Demand for Money - Households As before we assume that total money demand (currency and checkable deposits, money used for transactions) is given by: M d = $YL (i) We will now however assume that only a certain fraction c of this total money demand is actually demanded as currency, i.e. CU d = cm d The rest is demanded in form of checkable deposits, i.e. D d = (1 c) M d Introduction to Macroeconomics (WS 2011) The Financial Market October 28 th, 2011 16 / 22
The Demand for Money - Banks As indicated before, banks must hold a certain fraction of the money on checkable deposits as reserves Assuming that this fraction is constant and given by θ < 1 and that the money on checkable deposits is given by D, we get that the amount of currency banks hold as reserves is given by: R = θd Using that the demand for checkable deposits is given by D d = (1 c) M d, we get that the demand for reserves by banks is given by: R d = θ (1 c) M d Introduction to Macroeconomics (WS 2011) The Financial Market October 28 th, 2011 17 / 22
The Demand for Money - Notation Keep in mind the distinction we made: M... stands for the money available for transactions of households. In an economy with banks this is given by the currency held by households (CU) and by the checkable deposits of households (D) H... stands for the money printed by the central bank (coins and bills). In an economy with banks this is given by the currency held by households (CU) and by the currency banks must hold as reserves (R) Introduction to Macroeconomics (WS 2011) The Financial Market October 28 th, 2011 18 / 22
The Total Demand for Central Bank Money and Equilibrium The total demand for central bank money ( monetary base, high powered money, H d ) is given by the demand for currency (CU d ) and by the demand for reserves by the banks (R d ), i.e. by H d = CU d + R d = cm d + θ (1 c) M d = [c + θ (1 c)] $YL (i) In equilibrium, supply of central bank money (H s = H) must equal the demand for central bank money, i.e. in a money market equilibrium the interest rate must be such that: H = [c + θ (1 c)] $YL (i) (1) Introduction to Macroeconomics (WS 2011) The Financial Market October 28 th, 2011 19 / 22
The Money Multiplier - Definition Using that in equilibrium the overall demand for money M d = $YL (i) must equal the overall supply of money (currency plus checkable deposits, M) in condition (1), yields the following relation between the supply of central bank money H and the overall supply of money M: H = [c + θ (1 c)] M or equivalently: M = 1 c + θ (1 c) H Since c + θ (1 c) is smaller than one, the amount of money available for transactions M is actually a multiple of the supply of central bank money H 1 Therefore, the term c+θ(1 c) is referred to as the money multiplier Introduction to Macroeconomics (WS 2011) The Financial Market October 28 th, 2011 20 / 22
The Money Multiplier - Interpretation Suppose that the central bank increases the monetary base (H) by through buying bonds from individual A. Additionally, suppose for simplicity that no one wants to hold currency (i.e. that c = 0 implying that the money multiplier is just given by 1 θ ). Individual A will put on his checkable deposit. Since the bank only keeps θ as reserves it can lend the rest ((1 θ) ) to some individual B (equivalently: the bank can buy bonds of this value from B) Individual B will also put his entire loan on his checkable deposit. Again the bank will only keep a fraction of θ as reserves and can lend the rest ((1 θ) (1 θ) ) to some individual C and so on Introduction to Macroeconomics (WS 2011) The Financial Market October 28 th, 2011 21 / 22
The Money Multiplier - Interpretation In the previous example the total change in money available for transactions is thus given by: + (1 θ) + (1 θ) 2 +... = (1 θ) j Since for 0 < 1 θ < 1 this expression is a geometric series, it can also be expressed as: 1 1 (1 θ) = 1 θ which indeed yields the multiplier effect seen above. j=0 Introduction to Macroeconomics (WS 2011) The Financial Market October 28 th, 2011 22 / 22