UNIVERSITY OF GRONINGENFACULTY OF ECONOMICS & BUSINESSEBB130A05 – MONETARY MACROECONOMICSACADEMIC YEAR 2020-2021SEMESTER 1.AProblem Set 1with Suggested AnswersExercise 1: The IS-LM model with money targetingIn this exercise we depart from the assumption that the central bank targets the interestrate. This clearly illustrates the role played by nominal money supply.Consider the following set of equations characterizing the goods and money markets of aclosed economy:• Consumption: C = c0 + c1(Y – T); 0 < c1 < 1• Investment: I = b0 + b1Y – b2i; 0 < b1 < 1 – c1; b2 > 0• Government Spending: G = G• Taxes: T = T• Real Money Demand: (M=P)d = f0 + f1Y – f2i; f1; f2 > 0• Real Money Supply: (M=P)s = M=P(a) Identify the endogenous and exogenous variables. Given this information, can themodel be solved to find a unique value for the equilibrium level of income? If not,state the missing equation(s).Answer:The model has six equations and eight endogenous variables. So, the model can notbe solved. We should the equilibrium condition for the goods market Y = C + I + G,and the equilibrium condition for the money market. (M=P)d = (M=P)s.Endogenous variables: C; Y; T; I; G; i; (M=P)d; (M=P)s.Exogenous variables: T ; G; M; P.(b) Derive the equations of the IS curve and the LM curve, and illustrate the IS-LMmodel in a graph.Answer:The goods market equilibrium requires thatY = C + I + G:1Making the necessary substitutions we obtain that:Y = c0 + c1(Y – T) + b0 + b1Y – b2i + G )(1 – c1 – b1)Y = c0 – c1T + b0 + G – b2i )i =c0 – c1T + b0 + Gb2 – 1 – cb12- b1 Y:The slope in a graph with i on the vertical axis, -(1 – c1 – b1)=b2, is negative: the IScurve slopes downward.The money market equilibrium requires thatMP s = MP d :Making the necessary substitutions we find:f0 + f1Y – f2i = MP) i =f0 – M=Pf2 +f1f2Y:The slope in a graph with i on the vertical axis, f1=f2, is positive: the LM curve slopesupward.(c) Identify the factors that shift the curves parallel to the original curves. Also explainin each case the direction of the shift.Answer:Parallel shifts imply that coefficients c1; b1; b2; f1; f2 are constant.The IS curve shifts to the right if government spending G increases and taxes T godown. Also an increase the autonomous parts of consumption and investment (c0; b0)shift the IS curve to the right.The LM curve shifts to the right if nominal money supply M increases and the pricelevel P goes down. An increase of autonomous real money demand f0 shifts the LMcurve to the left.2(d) Illustrate the impact of an increase in government spending. How do the equilibriumlevels of income and the interest rate change? Explain your answer.Answer:The IS curve shifts to the right, and the equilibrium levels of income and the interestrate both are higher. The increase of government spending increases demand whichrequires output to increase to maintain goods market equilibrium. If income goes upreal money demand increases which requires an increase of the interest (lowering realmoney demand) since money supply and price are constant.(e) Assume that the central bank targets the nominal interest rate i. What is the newLM curve? How does an increase in government spending affect the equilibrium levelof income and the interest rate? What is the role of nominal money supply? Illustratethis graphically and compare with question (c).Answer:The equation i = i is added, this is the LM curve is i = i which is a horizontal line.Now, money supply is M endogenous. An increase in government spending shifts theIS curve to the right increasing income. Higher income increases real money demand.The interest rate does not change, so in order to maintain money market equilibriumthe central bank increases nominal money supply. This implies that nominal moneysupply is an endogenous variable, and the interest rate is an exogenous variable.3Exercise 2: The External Finance PremiumConsider the following set of equations characterizing the goods and money markets of aneconomy:• Consumption: C = c0 + c1(Y – T), where 0 < c1 < 1• Investment: I = b0 + b1Y – b2ρ, where 0 < b1 < 1 – 1 – c1 < 1, b2 > 0• Government Spending: G = G• Taxes: T = T• Money Market: i = i• Bank’s lending rate: ρ = i + xwhere x denotes the external finance premium.(a) Identify the endogenous and exogenous variables. Given this information, can themodel be solved to find a unique value for the equilibrium level of income? If not,state the missing equation(s).Answer:Assuming x is among the exogenous variables, the model has six equations and sevenendogenous variables. So, the model can not be solved. We should add the accountingidentity (good’s market equilibrium condition) as seventh equation: Y = C + I + G.Endogenous variables: C; Y; T; I; ρ; G; i.Exogenous variables: T ; G; i; x.(b) Assume that x = 0. Derive the IS curve and the LM curve. Solve the IS-LM modelfor the equilibrium level of income.Answer:From the goods market equilibrium condition we derive the IS curve:Y = c0 + c1(Y – T) + b0 + b1Y – b2i + G) (1 – c1 – b1)Y = -b2i + c0 – c1T + b0 + GY = 1 –c1b2- b1 i + 1 – c11 – b1 c0 – c1T + b0 + G (IS)From the money market equilibrium we know that i = i (LM).Combining these curves gives the equilibrium level of income:) Y = 1 –c1b2- b1 i + 1 – c11 – b1 c0 – c1T + b0 + G4(c) What is the equilibrium level of investment and corresponding cost of bank loans?Answer:Plugging in both equilibrium values in the investment function we obtain the equilibrium level of investment:I = b0 + b1 1 –c1b2- b1 i + 1 – c11 – b1 c0 – c1T + b0 + G – b2i= 1 –cb11b-2 b1 – b2 i + b0 + 1 – cb11- b1 c0 – c1T + b0 + GI = -1 b-2(1 c1–cb11) i + b0 + 1 – cb11- b1 c0 – c1T + b0 + GNote, that in the absence of an external finance premium the cost of bank loans tofirms is equal to equilibrium interest rate i.Suppose now that capital of firms drops following a severe slump in stock prices and bankscharge an external finance premium x > 0 on loans. As a reaction the central bank reducesthe nominal interest to i0. However, the cost of bank loan increases: i0 + x > i.(d) Calculate the changes in the equilibrium level of income and investment.Answer:After the rise in the external finance premium and the drop of the nominal interestrate, equilibrium income, say, Y1 is lower since i0 + x > i:Y1 = -b21 – c1 – b1 i0 + x + 1 – c11 – b1 c0 – c1T + b0 + G∆Y ≡ Y1 – Y0 = -b21 – c1 – b1 i0 + x – i < 0;where Y0 is the initial equilibrium level of income. The higher cost of bank loanslowers equilibrium investment to, say, I1, because income is lower and the lending rateis higher:I1 = -1 b-2(1 c1–cb11) i0 + x + b0 + 1 – cb11- b1 c0 – c1T + b0 + G∆I ≡ I1 – I0 = -b2(1 – c1)1 – c1 – b1 i0 + x – i < 0;where I0 is the initial equilibrium level of investment.5(e) How much should the central bank lower the interest rate to keep income constantafter the increase in the external finance premium? Are there reasons the central bankcan not manage to keep income constant?Answer:The original equilibrium level of income is Y = 1 –c1b2- b1 ρ + 1 – c11 – b1 c0 – c1T + b0 + Gwith ρ = i + x. To keep income constant, ρ has to be kept constant:∆ρ = ∆i + ∆x = 0 ) ∆i = -∆x < 0However, it is required that the new interest rate should be non-negative (assumingthe lower bound is zero).Exercise 3: Bond PricesConsider two types of bonds, a 5-year coupon bond of face-value e1000 with a coupon rateof 2% and a 2-year discount bond of the same face value.(a) Compute the prices of the two bonds assuming a constant nominal interest rate of 4%over the period of interest. Which bonds sells at a higher price, and why?Answer:The price of the coupon bond corresponds to the discounted future streams of couponpayments and its discounted face value. Given a 4% nominal interest rate this equals:e20(1 + 0:04) +e20(1 + 0:04)2 +e20(1 + 0:04)3 +e20(1 + 0:04)4 +e20(1 + 0:04)5 +e1000(1 + 0:04)5 ==e20(1 + 0:04) “11–1+0 1+0 11:04 :045# + (1 + 0 e1000 :04)5 =6e200:04 “1 – 1 + 0 1 :045# + (1 + 0 e1000 :04)5 = e910:96:The price of the discount bond equals just its discounted face value:e1000(1 + 0:04)2 = e924:56:The price of the latter exceeds the former as at the prevailing interest rate environmentthe earlier repayment of the face value is valued as more important relative to thecoupon payments of the former.(b) Suppose that the above discount bond sells currently at a price of e900. Compute itsyield to maturity. Assuming that during the current year the nominal interest rate willremain at 4%, what does the computed yield imply about the nominal interest ratenext year?Answer:The bond’s yield to maturity is the constant annual interest rate that makes the priceof the bond today equal to the present value of all resulting payments. Let’s definetoday’s period as period t. In our context this meanse900 = e1000(1 + i2t)2 ;which corresponds to a yield to maturity of 5.4% :i2t = ree1000 900 – 1 = 0:054:Given the prevailing interest rate i1t = 0:04, this yield implies that the bond marketexpects a nominal interest for the next year of 6.8% :e1000(1 + i2t)2 =e1000(1 + i1t)(1 + ie 1t+1) ) ie 1t+1 = (1 + 1 +ii21tt)2 – 1 = 0:068:Exercise 4: Stocks Price MovementsConsider the stock of a company which is expected to pay a dividend of e1,000 each yearstarting next year, and for which the value of dividend payments is expected to increase by3% per year every year. For sake of convenience we assume that there is no equity premium.(a) What should be the current price of the stock if the nominal interest rate is expectedto remain constant at 5%? How will the price differ if the nominal interest rate wouldbe raised to 7%?Answer:7The current price of the stock, eQt; must equal the expected future stream of dividendpayments, eDte+s; discounted at the prevailing nominal interest rate. Therefore: eQt =+++ : : : =eDet+1eDet+2eDet+3(1 + i)(1 + i)2(1 + i)3 eDet+1(1 + i) +eDet+1(1 + g)(1 + i)2 +eDet+1(1 + g)2(1 + i)3 + : : : =eDet+1(1 + i) “1 + 1 + 1 +gi + 1 + 1 +gi 2 + : : :# = (1 + eDte+1 i) 1 -11+ 1+gi = eiD-te+1 g :If the growth rate of dividends, g, is 3% and the nominal interest rate, i is 5%, theabove expression implies that the current price of the stock should be e50,000. If thenominal interest rate is raised to 7%, then the price of the stock will drop to e25,000as future dividends will now be more heavily discounted.Suppose that the company announces an expansion of its economic activity which is expectedto make dividend payments now rise every year. Suppose that the price of the stock remainsunchanged following the company’s announcement.(b) Can you provide an explanation for this response of the market. Use the IS-LM modelto explain your argument.Answer:If the current stock price of the company remains unchanged despite the announcedexpansion of activity and profits, this must be due to expectations of higher futureinterest rates as well. This expectation can be justified if the whole economy is experiencing a period of economic expansion, and the central bank reacts by increasing theinterest rate (monetary contraction).8

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