Chapter 4 Fnancal Markets ECON2123 (Sprng 2012) 14 & 15.3.2012 (Tutoral 5) The demand for money Assumptons: There are only two assets n the fnancal market: money and bonds Prce s fxed and s gven, that s nomnal GDP s gven Wealth = M d + Bond d Money: hgh lqudty, but pays no nterest (currency and checkable deposts) Bond: pays nterest but cannot be used for transactons A person s choce: hold currency or to buy bonds Trade off between holdng money and bonds: lqudty and return Money demand depends on: (1) level of transactons, (2) nterest rate on bonds, (3) other factors, lke transacton cost and lqudty of bonds. Money demand functon: M d = PL(, ) (Overall Money Demand) Money demand postvely depends on and negatvely depends on. The determnaton of nterest rate (1) The supply and demand for currency: M s = PL(, ) (2) The supply and demand for central bank money: = CU d + R d (3) The supply and demand for reserves (Fed fund market): CU d = R d (4) Money Multpler: PL(, ) [ c (1 c)] 1
The determnaton of nterest rate (I): Supply and demand for currency Assume all money s currency, so there are no checkng accounts or banks. Money demand functon: M d = PL(, ) Money supply: M = M s Money supply determned by central bank n most countres. (FED n US). The quantty suppled of money s ndependent of nterest rate. The central bank can change money supply by conductng open market operatons (OMO). If the central bank wants to ncrease money supply, t wll buy bonds. (expansonary) If the central bank wants to reduce money supply, t wll sell bonds. (contractonary) Balance sheet for the central bank: Assets Labltes Bonds Currency Consders open market operatons n terms of ther effect on bond prces. Suppose a bond promses a payment of F (face value) n one year, P B s the current prce of bonds. Then, nterest rate (or rate of return) on ths bond s gven by = (F P B ) / P B P B =F /(1+ ) Nomnal nterest rate and the bond prce are nversely related. For example, when the central bank purchases bonds, t ncreases the demand for them and tends to ncrease ther prce, whch reduces the nterest rate. Money market equlbrum The money market equlbrum s determned by the demand and supply of money. * M s In the money market equlbrum, M d = M s Equlbrum nterest rate = *. M * M d (gven ) M Change n equlbrum (e.g. changes) 2
The determnaton of nterest rate (II): Supply and demand for Central bank money () Assume money ncludes currency and checkng accounts n banks Banks receve funds from depostors (ndvduals and frms) and allow ther depostors to wrte checks aganst (or wthdraw) ther account balances Balance sheet of banks: Assets Bonds Loans Reserves Balance sheet of central bank: Assets Bonds Labltes Checkable deposts Labltes Central bank money = Reserve + Currency Demand for central bank money = demand for currency + demand for reserves by banks Supply of money s controlled by the central bank (: supply of central bank money) Equlbrum: = CU d + R d Demand for currency (CU d ) Recall M d = $L(), people hold money n the form of currency by a fracton of c and n the form of checkable depost by a fracton of (1 c) where 0 < c < 1. M d = CU d + D d = cm d + (1 c)m d Demand for currency: CU d = cm d Demand for reserves (R d ) Banks hold reserves n part to protect aganst daly excesses of wthdrawals (n currency or check form) over deposts and n part because they are requred to do so by the central bank by a fracton of of ther deposts. (reserve rato) Demand for reserves: R d = D = (1 c) M d The demand for central bank money = d = CU d + R d = d = cm d + (1 c) M d = d = [c + (1 c)]pl(, ) The supply of central bank money s equal to the demand for central bank money * In the money market equlbrum, = CU d + R d Equlbrum nterest rate = *. d = CU d + R d 3
The supply and demand for reserves: Fed fund market Fed fund market: the market for bank reserves, and federal funds rate s determned. = CU d + R d CU d = R d Supply of reserves = demand for reserves Money Multpler = [c + (1 c)]pl(, ) M S PL(, ) where [ c (1 c)] 1 [ c (1 c)] s the money multpler The money supply equals central bank money tmes the multpler the central bank can control the money supply by controllng c and are assumed to be fxed, 0 < c < 1 and 0 < <1, money multpler > 1 An ncrease n central bank money leads to a larger ncrease n the overall money supply The Fractonal reserve bankng and the money multpler A gven ncrease n currency deposts creates only a fractonal ncrease n bank reserves. The remander of the depost ncrease s used to purchase bank assets (e.g., bonds). The purchase puts more money n the hands of the non-bank publc and hence creates more checkable deposts, and so on. Assume people hold currency and checkable depost n the proporton of c and (1 c) out of the overall demand for money, reserve raton s Suppose central bank ncreases by $1 by buyng bonds from Seller 1 Seller 1 gets $1, hold $c as currency and depost $(1 c) n a checkable account n Bank A Bank A keeps $ (1 c) n reserves and buys bonds wth $(1 )(1 c) from Seller 2 Seller 2 gets $(1 )(1 c), hold $c(1 )(1 c) and deposts $(1 c)(1 )(1 c) n a checkable account n Bank B Bank B keeps $ (1 c)(1 )(1 c) n reserves and buys bonds wth $(1 )(1 c)(1 )(1 c) from Seller 3 Seller 3 gets $[(1 )(1 c)] 2 Total ncrease n money supply = $1 + $(1 )(1 c) + $[(1 )(1 c)] 2 1 = $1 [ c (1 c)] Total ncrease n money supply = [ c (1 c)] (overall money supply) 4
Example: Assume people only hold checkng account, so c = 0 and = 0.1, so the money multpler s 1/ Suppose ncreases by 100 by buyng bonds from Seller 1 Seller 1 depost 100 n a checkng account n Bank A Bank A keeps 10 n reserves and buys bonds wth 90 from Seller 2 Seller 2 depost 90 n a checkng account n Bank B Bank A keeps 9 n reserves and buys bonds wth 81 from Seller 3 Total ncrease n money supply =100 + 100 (0.9) +100(0.9 2 ) + +100(0.9 n ) = 100 [1/ (1 0.9)] = 1000 = + (1 ) + (1 ) 2 + + (1 ) n = [1/ (1 (1 )] = / (assume c = 0) Examples and Problems Queston 1 Suppose that real money demand s gven by M d = $(0.25 ) where s $100. Also, suppose that the supply of money (M s ) s $20. Assume equlbrum n fnancal markets. (a) What s the real nterest rate? In the equlbrum, M s = M d 20 = 100 (0.25 ) = 0.05 (5%) (b) If the Federal Reserve Bank wants to ncrease by 10% (from 5 to 15%), at what level should t set the supply of money? Let the new money supply be (M s ), (M s ) = 100 ( 0.25 0.15) (M s ) = 10 Queston 2 A bond promses to pay $100 n one year. (a) What s the nterest rate on the bond f ts prce today s $75? 85? 95? P B (1+ ) = 100 Solvng for r When P B = $75, = 33% When P B = $85, = 18% When P B = $95, = 5% (b) What s the relatonshp between the prce of the bond and the nterest rate? Negatve (c) If the nterest s 8%, what s the prce of bond today? P B (1+ ) = 100 P B (1+ 8%) = 100 P B (1+ ) $93 5
Queston 3 Suppose that a person s yearly ncome s $80000. Also suppose that her money demand functon s gven by M d = $(0.3 ). (a) What s her demand for money when the nterest rate s 4%? 8% When = 0.05, M d = 20800. When = 0.1, M d = 17600 (b) Descrbe the effect of the nterest rate on money demand. Explan. Money demand decreases when nterest rate ncreases becauses bonds, whch pay nterest, become more attractve. (c) Suppose that the nterest rate s 4%. In percentage term, what happens to the demand for money f her yearly ncome s reduced by 50%? New ncome = 40000, M d = 10400, that s demand for money drops by 50%. (d) Suppose that the nterest rate s 8%. In percentage terms, what happens to the demand for money f her yearly ncome s reduced by 50%? New ncome = 40000, M d = 8800, that s the real demand for money falls by 50%. (e) Summarze the effect of ncome on money demand. ow does t depends on the nterest rate? A 1% ncrease (decrease) n ncome leads to a 1% ncrease (decerease) n real money demnad. The effect s ndependent of the nterest rate. Queston 4 Suppose that a person s wealth s $50000 and that her yearly ncome s 60000. Also suppose that her money demand functon s gven by M d = (0.35 ). (a) Derve the demand for bonds. What s the effect of an ncrease n the nterest rate by 10% on the demand for bonds? B D = 50000 60000(0.35 ). An ncrease n the nterest rate of 10% ncreases bond demand by $6000. (b) What are the effects of an ncrease n wealth on money and on bond demand? Explan. An ncrease n wealth ncreases bond demand, but has no effect on money demand, whch depends on ncome. (c) What are the effects of an ncrease n ncome on money and on bond demand? Explan. An ncrease n ncome ncreases money demand, but decreases bond demand, snce we mplctly hold wealth constant. (d) When people earn more money, they obvously wll hold more bonds. What s wrong wth ths sentence? When people earn more ncome, ths does not change ther wealth rght away. Thus, they ncrease ther demand for money and decrease ther demand for bonds. 6
Chapter 5 Good and Fnancal Markets: The IS-LM Model The IS curve: Goods market equlbrum IS curve: t captures the relatonshp between output and the nterest rate such that the goods market s n equlbrum. In the goods market equlbrum, Aggregate supply of Goods = Aggregate demand for goods/ Total savng = Investment = C ( T) + I (, ) + G = ZZ I = I (, ): Investment postvely depends on and negatvely depends on. Other factors affectng nvestment ZZ D A 45 ZZ (For ) ZZ Suppose there s an ncrease n nterest rate (cost of borrowng for nvestment) Investment decreases Demand decreases decreases B C (For ) Equlbrum n goods market mples that the hgher the nterest rate, the lower the equlbrum level of output ** * B C IS curve s downward slopng When ncreases Frms borrow less and nvest less Fall n I, snce = C + I + G, therefore falls Movement along the IS curve ED for goods ES of goods Ponts on the left of IS Excess demand for goods (pont D) D A IS (G, T etc) Ponts n the rght of IS Excess supply of goods (Pont C) ** * Factors shftng the IS curve: change n G, T, C 0, I 0 etc Factors affectng the slope of IS curve: MPC, MPI IS curve s flatter wth hgher MPC and MPI 7
The LM curve: Fnancal market equlbrum LM curve: t captures the relatonshp between output and the nterest rate such that the fnancal market s n equlbrum. In the money market equlbrum, Real money demand = Real money supply Ms/P = L() Ms 1 /P ES of money ED for money LM(Ms 1 /P) = 30% = 20% =10% E C B A D =30% = 20% =10% Md/P( 3 =3000) A E B C D Md/P( 1 =1000) Md/P( 2 =2000) M/P At a hgher level of, people demand more money at every nterest rate The demand curve for money shfts out when ncreases, and equlbrum nterest rate rses. and are postvely related All ponts on the left of LM Excess supply of money At 1 = 1000, and = 20% (Pont E) All ponts on the rght of LM Excess demand for money At 3 = 3000, and = 20% (Pont D) 1 =1000 3 =3000 2 =2000 Factors shftng the LM curve: change n Md/P (due to factors other than ), Ms/P, ntroducton of credt card etc Factors affectng the slope of LM: senstvty of money demand to ncome and senstvty of money demand to nterest LM curve s flatter when senstvty of money demand to ncome s lower and senstvty of money demand to nterest s hgher 8
Goods market and fnancal market equlbrum LM(Ms/P) 1 IS (G, T) When the goods market and the fnancal market are smultaneous n equlbrum, nterest rate and output s determned by the ntersecton pont of IS and LM curve. 1 LM( ( Ms / P) Fscal polcy: change n G or T 2 Suppose G ncreases IS curve shfts out Interest rate and ncreases. 1 IS ( G, Taxes 2 ) C ncreases, I may ncrease or decrease, Md/P remans unchanged 1 2 IS ( G, Taxes 1 ) Crowdng out effect 1 LM( ( Ms / P) Monetary polcy: change n Ms/P LM ( 2 Ms / P ) Suppose Ms/P ncreases LM curve shfts out Interest rate falls and ncreases 1 2 IS (G, T) [Ms/P ncreases, then falls. When falls, I ncreases and ncreases] 1 2 C ncreases, I ncreases, M d /P ncreases Effectveness of fscal and monetary polcy It depends on the slope of IS and LM curves Polcy Mx: Combnaton of fscal and monetary polcy 9
Examples and Problems Queston 1 Consder frst the goods market model wth constant nvestment that we saw n Chapter 3: C = c 0 + c 1 D and I, G and T are gven. (a) Solve for the equlbrum output. What s the value of the multpler? In the goods market equlbrum, = c 0 + c 1 ( T) + I + G = ZZ = [1/ (1 c 1 )] [c 0 + I + G + c 1 T] The multpler s 1/ (1 c 1 ) Now, let nvestment depend on both sales and the nterest rate: I = b 0 + b 1 b 2 (b) Solve for equlbrum output. At a gven nterest rate, s the effect of a change n autonomous spendng bgger than what t was n part (a)? Why? (Assume c 1 + b 1 < 1.) In the goods market equlbrum, = c 0 + c 1 ( T) + I + G = Z = c 0 + c 1 c 1 T + b 0 + b 1 b 2 + G = [1/ (1 c 1 b 1 )] [c 0 c 1 T + b 0 b 2 + G] The multpler s 1/ (1 c 1 b 1 ) 1/ (1 c 1 b 1 ) > 1/ (1 c 1 ) Effect of a change n autonomous spendng s bgger than n part (a). An ncrease n autonomous spendng now leads to an ncrease n nvestment as well as consumpton. Next, wrte the LM relaton as follows: M/P = d 1 d 2 (c) Solve for the equlbrum output. (nt: Elmnate the nterest rate from the IS and LM relatons.) Derve the multpler (the effect of a change of one unt n autonomous spendng on output). M/P = d 1 d 2, rearrange the terms, = (d 1 M/P) / d 2 Substtute = (d 1 M/P) / d 2 nto = c 0 + c 1 c 1 T + b 0 + b 1 b 2 + G = c 0 + c 1 c 1 T + b 0 + b 1 b 2 [(d 1 M/P) / d 2 ] + G = [1/ (1 c 1 b 1 + b 2 d 1 / d 2 )] [c 0 c 1 T + b 0 + (b 2 M/P)/d 2 + G] The multpler s 1/ (1 c 1 b 1 + b 2 d 1 / d 2 ) (d) Is the multpler you obtaned n part (c) smaller or larger than the multpler you derved n part (a)? Explan how your answer depends on the parameters n the behavoral equatons for consumpton, nvestment, and money demand. Comparng 1/ (1 c 1 ) and 1/ (1 c 1 b 1 + b 2 d 1 / d 2 ), 1/ (1 c 1 b 1 + b 2 d 1 / d 2 ) s greater than 1/ (1 c 1 ) f (b 1 b 2 d 1 / d 2 ) >0. The multpler n ths part wll be larger f b 1 s large, b 2 s small, d 1 s small, and/or d 2 s large. That s, f nvestment s very senstve to, nvestment s not very senstve to, money demand s not very senstve to, money demand s very senstve to. 1/ (1 c 1 b 1 + b 2 d 1 / d 2 ) s smaller than 1/ (1 c 1 ) f (b 1 b 2 d 1 / d 2 ) < 0. The multpler n ths part wll be smaller f b 1 s small, b 2 s large, d 1 s large, and/or d 2 s small. That s, f nvestment s not very senstve to, nvestment s very senstve to, money demand s very senstve to, money demand s not very senstve to. 10