Money and Banking
Econ 165: Money and Banking Homework 2 VERY IMPORTANT: Must submit via Gradescope. Due January 21st, 5pm Make references to materials in the readings or lecture slides as needed when answer the ques ons below. For problems where you are asked to calculate something show the formula or calculaƟon that you are using, not just the answer. Homework is due by the beginning of class. Late assignments will be penalized by 25% of the total score for each day past the deadline. For example, an assignment submi ed four days a er the deadline would have a score of zero. All ques ons and parts are weighted equally. 1. Assume the annual interest rate on a loan is 5%, compounded monthly. a. What is the monthly interest rate? b. What is the 30‐year interest rate? c. Assume that infla on is 2%. If 5% is the nominal rate, what is the real annual interest rate you are paying on the loan? 2. Assume you have $5,000 in credit card debt where the interest is compounded daily (like in real life). The annual interest rate on this debt is 28%. Assume there are 365 days in a year. a. What is the future value of this debt a er 30 days? b. How much will you need to pay a er 30 days if you wanted to pay off everything you owe? 3. Assume you run a business. You are thinking of making an investment in new equipment that would cost $15M in the first year, but which would then produce $5M in addi onal profits for the next five years. By the end of year six, the equipment would be obsolete. Assume the annual nominal discount rate (interest rate) is 7% and the annual infla on rate is 0% (and assumed to stay there). a. What is the NPV (net present value) of this investment? b. Should you do this investment or not? c. If the infla on rate jumps to 3% (assume the cash flows for the equipment do not change). What is the exact real discount rate? d. Does this change your decision about the equipment? Explain why or why not (two sentences). e. Do you think increases in real rates encourage or discourage investment? Why? (two sentences) 4. Private and central bank balance sheets (see the lecture slides). a. If a bank makes addi onal loans to the public, does anything change on the liability side? b. Does this represent an increase or a decrease in broader money supply? c. Now imagine that the CENTRAL BANK (this is NOT the exercise we did in class) sells some of its holdings of government debt. What can change on the central bank liabili es? (Hint: how will people buy the securi es, there are two possible answers.) d. What effect does this have on money supply? 5. Remember the mul plier rela onship 𝑀 𝐵 where 𝜒 and 𝜌 . a. Discuss two economic factors that could affect 𝜒 and how. (2‐3 sentences) b. Discuss two economic factors that could affect 𝜌 and how. (2‐3 sentences) 6. Go to FRED. Find the M2 measure of money (M2SL), CPI (CPIAUCSL), and real GDP (GDPCI). a. Calculate the total growth rates from January 1960 to January 2023 (for GDP do 1960‐Q1 to 2023‐Q1). b. If we assume the velocity of money has not changed over this me, would these data be consistent with the QTM as Fisher saw it? c. What is the implied change in velocity over this period? d. What do you think could explain these changes in velocity? (three or four sentences max.) 7. Consider a Keynesian money‐demand curve that depends on the interest rate on bonds, the level of income, and expected future income: 𝐿 𝑖, 𝑌, 𝐸 𝑌 along with a simplified, completely ver cal money supply curve. a. Draw the money market equilibrium figure (interest rate on the ver cal axis, real balances on the horizontal axis). b. Imagine households become worried about the risk of a recession in the future so that their expected income temporarily declines. What would the precau onary mo ve imply about money demand in response to this decline in expected income? c. What would the transac ons mo ve suggest in response to this decline in expected income? d. Do they move in the same direc on? If not, which one do you think would dominate? e. Draw the net effect of this shock to expected income, as you interpret it. f. What is the effect on interest rates? Interpret this change (i.e. why do you think the interest rate on bonds moves the way it does). 8. Now assume that the money demand func on includes expecta ons of future interest rates as with the specula ve money demand mo ve: 𝐿 𝑖, 𝐸 𝑖 , 𝑌, 𝐸 𝑌 . a. If expected interest rates go up, what does it imply about what may happen to current interest rates? b. What will happen to the price of bonds today if interest rates increase? (Hint: remember that bonds offer a fixed payment over a number of periods in the future). c. What do you think this would do to the money demand curve today (show this using the figure). 9. Now consider Friedman’s PIH and the cri cal implica on that people will smooth their consump on across their lives. a. Imagine that households become concerned about a permanent decline in expected income. What should happen to their consump on and money demand today? b. Imagine someone who is young and s ll in college, but expects to earn a high income throughout their career. Assume this person follows the PIH, will they consume more or less than their current level of income? c. Does this suggest the person will be borrowing or saving? d. What are some poten al complica ons in reality that could limit how much people want to or are able to smooth their consump on according to their permanent income? (three to four sentences max). e. If permanent income is rela vely stable, what does that imply about money demand? (two sentences max) f. What does this suggest about being able to use monetary aggregates (like M1) to implement monetary policy?
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