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[ Intermediate Macroeconomics ]

Exercise 1. IS-LM model. Part 1. Consider the IS-LM model with the following consumption and investment functions: C=co+c,(Y-T) I=by+byY byi Moreover, government spendings are denoted G and taxes net of transfer T. We shall assume that the central bank operate so has to mimic what is happening under the modern LM curve. i) Solve for equilibrium output Y when i = 7. Write Y as a function of 7. ii) What is the multiplier in this scenario? iii) Assume c; + by 0; and by > 0, is the multiplier larger or smaller compared to the case with exogenous investment? iv) If the equation characterizing equilibrium in financial markets is % =d;Y d,i, what is the equilibrium real money supply needed to achieve i = 7? v) How does the real money supply change if the government decreases spending? Part 2. Take the same IS-LM model from part 1, but now assume that the central bank fixes the money supply so that we get the traditional LM curve. i) Suppose that the government is increasing taxes to reduce its deficit. Draw the fiscal consolidation on the IS-LM diagram and describe the policy in words. ii) Is the equilibrium output and interest rate lower or higher relative to the situation where the LM relation would have been flat? Explain why. Part 3. Consider the IS-LM model characterized by the following equations: =200+25(Y-T) [ =150 +.25Y 1000i G=25 T =200 With the central bank behaving under the modern LM-relation. i) Write the expression for Z(Y, ). ii) Derive the IS curve, Y (i). iii) Discuss the relationship between output and the real interest rate along the IS curve and discuss the intuition behind it. iv) What is the equilibrium output if 7 = .05 v) Suppose real money demand is described by % = 2Y 8000i. What is the level of real money supply when the IS-LM model is in equilibrium? vi) Solve for and [ in equilibrium. vii) Verify those are the correct equilibrium values by addingup C + 1+ G. viii) Suppose the central bank cuts to interest rate to 3%. How would this change the LM curve? ix) Solve for the new equilibrium values of Y, I, C, and real money supply. x) Draw the monetary policy expansion on the IS-LM diagram and describe the policy in words. Part 4. Fill in the table below and answer the questions that relate to the data in the table: Nominal Nominal Real policy Expected Real Policy Risk borrowing borrowing Situation interest rate inflation interest rate Premium interestrate interest rate A 3 0 3 0 3 3 B 4 2 2 1 3 3 C 0 2 -2 4 4 2 D 4 3 1 2 6 3 E 0 -2 2 & &> 5 i) Which situations correspond to the zero lower bound? ii) Which situation corresponds to the highest risk premium? Why does the risk premium might vary? iil) Why is it important at the zero lower bound to maintain a positive expected rate of inflation? Part 5. Consider the extended IS-LM diagram with the modern LM relation with the real policy interest rate on the vertical axis. i) Draw and label the vertical axis of an IS-LM diagram if the nominal interest rate is 5% and the expected rate of inflation is 3%. ii) Suppose the nominal policy interest rate is 5% and expected inflation falls from 3% to 2%. If the Fed wanted to keep the LM curve from shifting, what do they have to do to the nominal policy rate? iii) Suppose the expected rate of inflation falls from 3% to 2% with the nominal policy rate unchanged, does the IS curve shift? iv) If the expected rate of inflation were to decrease from 3% to 2%, does the LM curve shift? v) If the risk premium on risky bonds increases from 5% to 6%, does the LM curve shift? vi) If the risk premium increases, draw the implications in the IS-LM diagram. vii) What fiscal policy options could prevent the fall in output associated with the increase in the risk premium? Exercise 2. Risk premium. (1+4i) =0 -p)(A+i+x)+p-0, where p is the probability that the bond does not pay, i is the nominal policy interest rate, and x is the risk premium. i) If the probability of bankruptey is zero, what is the rate of return on the risky bond relative to the safe asset? ii) Calculate the probability of bankruptcy when the nominal interest rate for a risky borrower is 8% and the nominal policy rate of interest is 3%. iii) Calculate the nominal interest rate for a borrower when the probability of bankruptcy is 5% and the nominal policy rate of interest is 4%. iv) Calculate the risk premium if the nominal policy rate is 6% and the probability of bankruptcy is 8%