ECON2123 Tutorial 3: Financial Market, IS-LM Model Department of Economics HKUST September 27, 2018 ECON2123 Tutorial 3: Financial Market, IS-LM Model 1 / 14
Money Demand A comparison b/w two assets: Money vs. Bonds: Money: can be used for transaction; pay no interest rate. Bonds: cannot be used for transactions; pay a positive interest rate. (price and interest rate) Question: Which (combination of) assets to hold? Case 1: Bonds pay no interest, and you need to do transactions. Case 2: Bonds pay positive interest and you don t need to do any transaction. Case 3: Bonds pay positive interest rate and you need to do transactions. ECON2123 Tutorial 3: Financial Market, IS-LM Model 2 / 14
Money Demand In reality, demand for money increases with overall level of transactions in the economy and decreases with interest rate. Assumption that overall level of transactions in the economy is proportional to nominal income. Demand for money increases with nominal income and decreases with interest rate: Example: M d = $Y (0.35 i) M d = $Y L(i) ECON2123 Tutorial 3: Financial Market, IS-LM Model 3 / 14
Market Equilibrium: LM relation Money Supply: M s = M Money Demand: M d = $Y L(i) Market Equilibrium: M s = M d, or M = $Y L(i). ECON2123 Tutorial 3: Financial Market, IS-LM Model 4 / 14
Market Equilibrium: LM relation M = $Y L(i) Determination of Interest Rate: Question 1: Suppose M d = $Y (0.35 i), the supply of money is $20, and the nominal income is $ 100. What is the interest rate? Comparative Static Analysis: (Identify the channel of impact: demand side vs. supply side.) Question 2: What is the impact on the interest rate if nominal income increases, i.e. from $100 to $200? Question 3: What is the impact on the interest rate if money supply increases, i.e. from $20 to $30? ECON2123 Tutorial 3: Financial Market, IS-LM Model 5 / 14
Market Equilibrium: LM relation Question 1: Suppose M d = $Y (0.35 i), the supply of money is $20, and the nominal income is $ 100. What is the interest rate? Answer: 20=100(0.35-i); i=15%. Question 2: What is the impact on the interest rate if nominal income increases, i.e. from $100 to $200? Answer: If nominal income increases, money demand curve shift to the right, which gives a higher equilibrium interest rate. i=25%. Question 3: What is the impact on the interest rate if money supply increases, i.e. from $20 to $30? Answer: If money supply increases, the money supply curve shift to the right, which gives a lower equilibrium interest rate. i=5%. ECON2123 Tutorial 3: Financial Market, IS-LM Model 6 / 14
Money Supply: Monetary Policy Money Supply a. Central bank buys bonds: market bonds decrease + market money increases, thus money supply increases. (expansionary) b. Central bank sells bonds: market bonds increase + market money decreases, thus money supply decreases. Interest Rate a. Central bank increases bond prices: bond interest rate decreases (money demand increases). b. Central bank decreases bond prices: bond interest rate increases (money demand decreases). ECON2123 Tutorial 3: Financial Market, IS-LM Model 7 / 14
Liquidity Trap: When Monetary Policy Fails Liquidity trap: When the interest rate is down to zero, monetary policy cannot decrease it further. ECON2123 Tutorial 3: Financial Market, IS-LM Model 8 / 14
IS-LM Model IS Relation(Goods Market): Y = Z. Y = C + I + G = c 0 + c 1 (Y T ) + I + G LM Relation(Financial Market): M s = M d M = $YL(i) IS-LM relation: Try to connect goods market and financial markets. Question: How to connect these two markets? ECON2123 Tutorial 3: Financial Market, IS-LM Model 9 / 14
IS Relation Recall: Y = c 0 + c 1 (Y T ) + I + G; Now we add one assumption: I = I (Y, i) The eq m condition becomes: Y = c 0 + c 1 (Y T ) + I (Y, i) + G IS curve characterizes Y and i at goods market eq m : for any level of Y, i is the interest rate that clears the goods market. IS curve is downward sloping: When i increases, investment decreases, output decreases; IS curve implies eq m output as a function of interest rate; ECON2123 Tutorial 3: Financial Market, IS-LM Model 10 / 14
LM Relation Recall: M = $YL(i); Now we add one assumption: $Y = YP The eq m condition becomes: M = YPL(i), or M P = YL(i) LM curve characterizes Y and i at financial market eq m : for any level of income (Y), i is the interest rate that clears the financial market. LM curve is upward sloping: When income (I) increases, demand for money increases, given a money supply level, eq m interest rate increases; LM curve implies eq m output as a function of interest rate; ECON2123 Tutorial 3: Financial Market, IS-LM Model 11 / 14
IS-LM Model IS Relation(Goods Market): Y = c 0 + c 1 (Y T ) + I (Y, i) + G LM Relation(Financial Market): M P = YL(i) IS-LM relation: ECON2123 Tutorial 3: Financial Market, IS-LM Model 12 / 14
IS-LM Model: Exercise Consider the following IS-LM model: C = 200 + 0.25Y D ; I = 150 + 0.25Y 1000i G = 250; T = 200 M d = 2Y 8000i; M s = 1600 a. Derive the IS relation. b. Derive the LM relation. c. Solve for equilibrium output. d. Solve for the equilibrium interest rate. e. Solve for the equilibrium values of C and I. f. Now suppose that the money supply increases to M s = 1,900. Solve for new equilibrium Y and i. ECON2123 Tutorial 3: Financial Market, IS-LM Model 13 / 14
IS-LM Model: Exercise a. IS Relation: Y = C + I + G = 200 + 0.25(Y T ) + 150 + 0.25Y 1000i + 250; Y = 1100 2000i; b. LM Relation: M s = M d ; 1600 = 2Y 8000i; Y = 800 + 4000i. c&d. 1100-2000i =800+4000i; i= 0.05; Y= 800+4000i=1000. e. C=200 + 0.25(Y-T) = 400; I= 150 + 0.25Y - 1000i=170. f. IS Relation Unchanged: Y =1100-2000i; LM: 1900 = 800+4000i; Y=950+4000i; i=0.025; Y=1050. ECON2123 Tutorial 3: Financial Market, IS-LM Model 14 / 14