ECON 304 HW 8

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Name _______________________________________________ Date_________ last 4 PSU ID _______ Economics 304WD -- Homework - Lesson 8 – Demand for Money - 85 points total  You need to show your work, not just the final answer  Use the template to complete your work or points will be taken off.  Please put your name and PSU ID number at the top of the page  Save the file on your computer ( .PDF is the only format allowed ) and then upload it to the Canvas dropbox for this homework assignment.  Be sure your assignment is all on one file. Failure to submit a single file will result in points being deducted 1. (65 points total) Suppose the real money demand function is: Assume M = 4000, P = 2.0, π e = 0.01, and Y = 5000. Note: we are holding P and Y constant in this problem until we get to case #2 below. a) (5)What is the market clearing real interest rate? r = b) (10)Show your results on a real money supply, real money demand diagram and label this initial equilibrium point as point A. Be sure to label your graph completely! Correctly drawn and completely labeled diagram is worth 10 points total. Be sure to put relevant shift variables in parentheses next to the appropriate function. Case #1 7/8/2022 1,500 + .2 ( 5,000 ) − 10,000 ( r + 0.0 = 0.04 m/p R 0.045 0.04 2,000 1

c) (5 points) Suppose Janet Yellen and the Fed were successful in their campaign to decrease inflationary expectations to 0.5% (.005). Why would they want to do this? Use the Fisher equation to support your argument. d) (5 points) Solve for the real interest rate that clears the money market given the change in inflationary expectations. Please show work and Label this new point as point B on your diagram above. r = Fisher equation r = i − π π = inflation i = nominal interest rate r = realinterest rate Fed decline inflationary expectations then real rates will rise. ideal to do this to pull back on a growing economy. 1500 + 0.2 ( 5,000 ) − 10,000 ( r + .005 ) = 4000 2 − 10000 r + 2450 = 2000 r = − 450 − 10000 = 9 200 .045 2

e) (10 points) Explain how this strategy of decreasing inflationary expectations is supposed to pull back on the economy. Recall that output is equal to C + I + G! Be very specific. Hint: The price of current consumption in terms of future consumption and the user cost of capital most definitely need to be in your response. Case #2 f) (5 points) We now experience an economic slowdown so that Y = 4000. This is the only change. Resolve for the market clearing real rate of interest and label on your diagram as point B. Please show all work and label this as point B on the graph above. Correctly Higher real interest rate will pull back the economy over investment. When real interest rate inclines the user cost of capital increase. Firms must decrease the level of capital investment to maintain profit maximization circumstances. When the desired capital stock decreases, the investment decreases. I = K ¿ − Kf + dk . An incline in real rates will cause an incline in the price of current consumption. The greater r will draw back investment. Let us return to our original conditions. Please redraw the original graph locating point A (this is with  e = 0.01, we are holding expected inflation constant in case #2) r 0.04 0.03 0.02 2000 1800 3

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drawn and completely labeled diagram is worth 10 points total. Be sure to put relevant shift variables in parentheses next to the appropriate function. r = g) (5 points) Now explain exactly why the real rate of interest had to change the way it did to clear the money market. Please be clear with the intuition being sure to refer to the bond market in your answer. You should begin your response with "At the same real rate of interest, the money market is no longer clearing. In particular money demand ..." you can finish the rest. h) (5 points) Suppose the Fed wanted to keep real interest rates constant at their original level. Suppose also that the money multiplier is 0.8, which is consistent with reality since the Fed began paying interest on reserves beginning in October 2008. What exactly would the Fed have to do to keep real interest rates constant at their original level? Be 2000 = 1500 + 800 − 10000 r − 100 − 10000 r =− 200 r = 1 50 1 50 = .02 Through constant inflationary potentials, the lower nominal rate will transfer into lesser real rates. Rates will maintain lowering thus leading the money market to clear. Money demand is less than money supply which means households will begin purchasing non-monetary asset or bonds causing their price to incline and yield interest for growth. 4

specific with regard to the type and quantity of open market operations the Fed would need to conduct to be successful in keeping real interest rates constant at their original level. i) (5 points) Finally, explain the movement to the new equilibrium in the money market given the Fed expansion and show on your diagram as point C. Be sure to refer to the bond market as you did in part f). In fact, you should start your response the same way. 2. (10)Using the percent change of the equation of exchange, explain what assumptions need to be made to make the argument that the Fed should allow for the nominal money supply to grow at 5%. m d p = 1500 + 0.2 y − 10,000 ( r + π ) 1500 + 0.2 ( 4000 ) − 10000 ( .04 + .01 ) m = 3600 percent ∆ = % ∆m + % ∆Y = % ∆ P + % ∆Y FED target 2% inflation rate and 3% in growth with velocity at a constant rate. 5

3. This question will dig deeper into the velocity of money. a. (5)Define the velocity of money. b. (5)What does it mean if the percent change in velocity is negative? c. (5)Give a real-life example of how this could be possible? d. (5)What central banking nightmare can occur if we see the percent change in velocity of money turn negative and the Fed does not react? Measure of how recurrent the monetary stock turns over during each period. When velocity of money percent change is negative this means the economy is slackening with real output declines. With a negative inflationary effect people save money rather spending the money. A real-life example is when the quantity of money is growing at a quicker rate than the growth rate of GDP which is negative. The velocity of money turns negative deflation occurs. 6

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