1. Under what condition will the nominal interest rate be equal to the real interest rate?

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1 Practice Problems III EC Questions 1. Under what condition will the nominal interest rate be equal to the real interest rate? Real interest rate, or r, is equal to i π where i is the nominal interest rate and π is the inflation rate. If π = 0 (zero inflation rate), nominal interest rate will be equal to the real interest rate. 2. Firms, households, and governments use the credit market for borrowing. The credit demand curve shows the relationship between the quantity of credit demanded and the real interest rate. a. Why does the credit demand curve slope downward? b. What can cause a shift in the credit demand curve? a. The downward slope of the credit demand curve implies that the higher the real interest rate, the lower the quantity of credit demanded. This is because the higher the rate of interest a firm or household must pay to borrow money, the lower the firm s profit. So, fewer borrowers will be willing to obtain a loan at a higher rate of interest. b. Although a change in the real interest rate will lead to a movement along the credit demand curve, the following factors will lead to a shift of the curve: Changes in perceived business opportunities for firms: Businesses borrow to fund their expansions. When more opportunities for expansion are available, the demand for credit at a given real interest rate increases, leading to a rightward shift in the economy-wide, or aggregate, credit demand curve. The opposite a leftward shift would occur if perceived business opportunities decreased. Changes in households borrowing needs: If households grow more optimistic about the future, they ll be more willing to borrow now because they expect that they ll be in a good position to pay back those loans later. This will shift the aggregate credit demand curve to the right. Conversely, if households become more pessimistic about the future, the aggregate credit demand curve will shift to the left. Changes in government policy: All other things being equal, an increase in government borrowing shifts the credit demand curve to the right, while a decrease in government borrowing will shift it to the left. 3. What factors explain why people save for the future? People save for many reasons, some of which are listed below: Retirement: Because the Social Security program pays the typical U.S. household a bit less than half of the household s pre-retirement income, most people save some of their pre-retirement income to keep consumption levels more or less the same after retirement as before retirement. Bequests: Some parents save to leave money for their children. These inter-generational transfers are called bequests. Parents may also save money for their kids college education, etc.

2 Homes and durable goods: People save to buy a home or to buy durable goods, like a new washing machine or a car. Starting a business: In cases where outside funding can t be obtained, small business ownersneed to use their own savings to fund their business idea. Saving for a rainy day: People save for unexpected events they may lose their jobs or need money for a medical expense. 4. Households and firms with savings lend money to banks and other financial institutions. The credit supply curve shows the relationship between the quantity of credit supplied and the real interest rate. a. What is the opportunity cost of saving? b. An increase in the real interest rate leads to a rightward shift in the credit supply curve. Is this statement true or false? Explain your answer. a. The opportunity cost of saving is current consumption forgone. b. False. Change in real interest rate implies a movement along the credit supply curve. An increase in real interest rate encourages more saving, increasing the amount of funds that banks can lend and thereby increasing the quantity of credit supplied. In other words, a higher real interest rate implies an upward movement along the credit supply curve. 5. What functions do banks perform as financial intermediaries in the economy? Banks perform three interrelated functions as financial intermediaries: Banks identify profitable investment opportunities by bringing together credit-worthy borrowers and depositors and channeling depositors savings to borrowers. Banks transform short-term liabilities, like deposits, into long-term investments in a process called maturity transformation. Maturity transformation allows the economy to undertake significant long-term investments. Banks transfer risk from depositors to the bank s stockholders and, in severe financial crises, to the U.S. government. 6. What is stockholders equity? Who bears the risk that a bank faces when stockholders equity is greater than zero? Stockholders equity is defined as the difference between a bank s total assets and total liabilities. Stockholders are the primary risk takers, but it should be noted that if their equity is wiped out, any losses cascade down to either lenders or the government. Hence, undercapitalized banks, that is, banks whose stockholder equity is a very small proportion of assets, run a significant risk that a decline in asset values could not only wipe out stockholders, but also impact others. 7. As the Choice and Consequence box on Too Big to Fail notes, bank regulators worry about the prospect of the failure of large institutions, dubbed systemically important financial institutions (SIFIs). a. How would the failure of a SIFI affect the economy?

3 b. What steps do bank regulators take to prevent SIFIs from failing or to minimize the effect of such failures? a. A SIFI s failure could have repercussions for the entire banking sector and the economy as a whole. All of the banks to which the failed bank owes money will suffer losses. In turn, these losses can cause runs on the banks involved or wipe out the capital (stockholders equity) of these banks, leading to bankruptcy. As one bank after another fails, the ripple effects of financial losses keep spreading through more and more banks. In theory, the failure of one SIFI could bring down the whole financial system. b. To protect the economy from the effects of the failure of a SIFI, bank regulators have adopted two strategies. First, they now require large banks to set up living wills that spell out how the bank would sell its assets and pay off its creditors in the event that it needed to end its business operations. Such living wills are designed to make it more credible and easier for a government to shut down a failing bank, including a failing mega-bank. Second, regulators are now requiring banks to take on less risk and hold more stockholders equity, reducing the likelihood that a large bank will get into trouble in the first place. 8. Imagine two economies Worksa and Relaxsa. In Worksa, people s saving is insensitive to the real interest rate. On the other hand, in Relaxsa, people s saving largely depends on the real interest rate. Both countries have the same credit demand curve slope. a. Referring to the above information, compare the slope of the credit supply curves in these two countries. Now both governments plan to raise $10 billion to finance infrastructure projects in their own countries. To raise the necessary funds, the government will borrow money from the credit market. b. Suppose the loans made by governments in their own countries will not affect people s saving habits. Assume that the initial interest rates for both countries are the same. Plot a graph showing how borrowing from the government affects the interest rate in Worksa and Relaxsa. Compare the results. Which country s real interest rate will be affected more? a. Since people s saving is insensitive to the real interest rate in Worksa, its credit supply curve is steeper than that for Relaxsa. b. An increase in government borrowing leads to a rightward shift in credit demand curve. Given the credit supply curve, an increase in government borrowing will raise the equilibrium real interest rate. As shown in the graph below, the new equilibrium real interest for Worksa will be higher than that for Relaxsa.

4 9. Explain how the equilibrium real interest rate and the equilibrium quantity of credit would change in each of the following scenarios, and illustrate your answer with a well-labeled graph of the credit market. a. As the real estate market recovers from the financial crisis, households begin to buy more houses and condominiums, and apply for more mortgages to enable those purchases. b. Congress agrees to a reduction in the federal deficit, which results in a significant decrease in the amount of government borrowing. c. Households begin to fear that the recovery from the recession will not last, and become more pessimistic about the economy. d. Businesses become more optimistic about the future of the economy, and decide to distribute more of their earnings as dividends to their shareholders. a. As households apply for more mortgages to purchase real estate, the demand for credit increases, and the credit demand curve shifts to the right.this increases the equilibrium real interest rate as well as the quantity of credit, as shown in the graph below.

5 b. As government borrowing decreases, there is a consequent decrease in the demand for credit. The credit demand curve shifts to the left, lowering the equilibrium interest rate and the equilibrium quantity of credit. This is illustrated in the graph below. c. The increase in household pessimism would result in a decline in borrowing by households, reflected in a leftward shift in the credit demand curve. By itself, this would lower the equilibrium real interest rate and the equilibrium quantity of credit. However, households would also tend to increase their saving, thus shifting the credit supply curve to the right. This action further lowers the real interest rate but increases the quantity of credit. Hence, the combination of a decrease in credit demand and an increase in credit supply would definitely lower the equilibrium real interest rate but have an ambiguous effect on the quantity of credit.(note: The graph below shows a small decrease in the equilibrium quantity of credit because the credit demand curve shifted to the left by a greater horizontal distance than the credit supply curve shifted to the right.)

6 d. If the business community becomes more optimistic about the economy, they will tend to increase their borrowing to fund investment and expansion. This will shift the credit demand curve to the right. At the same time, distributing more of their earnings to shareholders as dividends will decrease the supply of credit (assuming that the shareholders spend those dividends), shifting the credit supply curve to the left. The net result of these two effects is shown in the graph below.the equilibrium real interest rate will definitely increase, but the effect on the equilibrium quantity of credit is ambiguous, and depends on which curve shifts by the greater horizontal distance.(note: The graph below shows a situation where the leftward shift in the credit supply curve is exactly offset by the rightward shift in credit demand, resulting in no change in the equilibrium quantity of credit.) 10. Banks that practice narrow banking match the maturity of their investments with the term of the deposits that they collect from the public. In other words, narrow banks take short-maturity deposits and invest in assets that carry a low level of risk and are also of short-term maturity, like short-term government debt. a. Suppose that all FDIC-insured banks decide to adopt narrow banking. How would narrow banking reduce the level of risk in the banking system? b. If narrow banking reduces systemic risk, why do banks still practice maturity transformation? a. Narrow banking would reduce the level of risk in the banking system by reducing the likelihood of bank runs and liquidity problems for banks. Narrow banks match the maturity of their deposits with that of their investments. Becausedepositors money is in the form of short-term, liquid investments, banks will be able to convert these investments into cash easily and return money to their depositors when they ask for it. b. Banks take short-term deposits from savers and make long-term loans to investors. This crucial function allows the economy to undertake significant long-term investments. Maturity transformation allows banks to match savers with investors.

7 11. If you have studied microeconomics, you may recall a concept called moral hazard. Moral hazard occurs when an economic agent is incentivized to take risks because some (or all) of the losses that might result will be borne by other economic agents. Discuss how deposit insurance might lead to moral hazard. Moral hazard occurs whenever a policy changes incentives, which in turn changes behavior. Because of federal deposit insurance, the majority of depositors need not pay any attention to the lending practices of their bank. Depositors are more likely to decide where to bank based on the interest rate offered, or on convenience. Consequently, a bank s customers won t worry about whether a bank is badly run, nor will they worry about whether a bank is making unprofitable longterm investments. The depositors will get their deposits back in any case because of deposit insurance. Likewise, knowing that their depositors funds are covered gives banks management more incentive to acquire riskier assets, e.g., to make riskier loans than they otherwise would. If the assets perform well, the bank will earn higher profits. If the assets decline in value, and lead to losses, the bank s depositors are still covered. 12. The Choice and Consequence box on Asset Price Fluctuations and Bank Failures discusses the relationship between the prices of things like oil and real estate, and the solvency of lending institutions like banks. Consider the following two scenarios. Supply the missing entries, and answer the questions that follow. Assume that Securitas Bank is a large bank in the country of Hyponatremia.The bank s only assets and liabilities at the beginning of the year are given in the following balance sheet: Reserves and Cash Equivalents Assets Securitas Bank Balance Sheet Liabilities $20 Billion Demand Deposits $200 Billion Long-term investments $330 Billion Borrowing from Other Banks Total Assets? Stockholders Equity $50 Billion Philopericulum Bank is another large bank whose only assets and liabilities are summarized in their balance sheet: Reserves and Cash Equivalents Assets Philopericulum Bank Balance Sheet Liabilities $10 Billion Demand Deposits $450 Billion Long-term investments $650 Billion Borrowing from Other Banks Total Assets? Stockholders Equity? $200 Billion

8 Assume now that due to an economic downturn, the value of each bank s long-term investments declines by 10%.Show the resulting situation on each bank s balance sheet. How would you describe the resulting situation for each bank? Relate your answer to the discussion in the chapter of the concept of Too Big to Fail. Before the decline in the banks investments, these were the complete balance sheets: Reserves and Cash Equivalents Assets Securitas Bank Balance Sheet Liabilities $20 Billion Demand Deposits $200 Billion Long-term investments $330 Billion Borrowing from Other Banks Total Assets $350 Billion Stockholders Equity Reserves and Cash Equivalents Assets Philopericulum Bank Balance Sheet Liabilities? $50 Billion $100 Billion $10 Billion Demand Deposits $450 Billion Long-term investments $650 Billion Borrowing from Other Banks Total Assets $660 Billion Stockholders Equity $200 Billion $10 Billion After a 10 percent decline in each bank s long-term investments, here are the resulting balance sheets: Reserves and Cash Equivalents Assets Securitas Bank Balance Sheet Liabilities $20 Billion Demand Deposits $200 Billion Long-term investments $297 Billion Borrowing from Other Banks Total Assets $317 Billion Stockholders Equity Reserves and Cash Equivalents Assets Philopericulum Bank Balance Sheet Liabilities $50 Billion $67 Billion $10 Billion Demand Deposits $450 Billion Long-term investments $585 Billion Borrowing from Other $200 Billion

9 Banks Total Assets $595 Billion Stockholders Equity $55 Billion Securitas Bank is still solvent, with stockholders equity at $67 Billion. This is because the ratio of their assets to equity started at $350 Billion / $100 Billion = 3.5:1; it had $1 of equity for each $3.50 worth of assets. Philopericulum Bank, on the other hand, started with a ratio of assets to equity of $660 Billion / $10 Billion, or 66:1; each dollar of equity supported $66 worth of assets. In other words, Philopericulum Bank had borrowed a much larger proportion of the funds it used to make its investments. In finance jargon, we would say that it had much higher leverage. As discussed in the chapter, any loss of value in assets comes right out of the equity portion of a bank s balance sheet. And when equity falls to zero or below, it means that the bank is insolvent, or has failed. As seen in the balance sheets above, the 10 percent decline in the value of Philopericulum s investments resulted in the bank s failure; it now has negative stockholders equity. This illustrates the danger involved in high leverage. Furthermore, it provides the rationale behind regulatory requirements regarding the amount of stockholders equity that a bank must have as a proportion of its total assets. 13. How does the growth rate of money supply affect the real interest rate? If the growth rate of money supply is greater than the growth rate of real GDP, the inflation rate is positive. Given the nominal interest rate, an increase in inflation rate causes the real interest rate to fall. 14. Bitcoins are defined as a peer-to-peer decentralized digital currency. The supply of bitcoins is not controlled by the government or any other central agency. The value of each bitcoin is determined on the basis of supply and demand and is defined in terms of dollars. New bitcoins can be generated through a process called mining. However, new bitcoins will not be created once there are a total of 21 million bitcoins in existence. Some commentators feel that bitcoins can eventually replace most of the major currencies in the world. Would you agree? Explain your answer. The bitcoin in its present form is not likely to replace any of the major currencies of the world. Bitcoin deposits, unlike bank deposits, are not insured by the government. Also, the value of a bitcoin is highly volatile, so bitcoins may not serve as a reliable store of value. 15. Use the three functions of money to determine whether credit cards constitute money. A credit card serves as a medium of exchange, which is the first function of money, because it is commonly accepted to pay for goods and services. However, a credit card is not a store of value, which is the second function of money, because a credit card simply defers payment and carries the debt that money must eventually be used to settle. Finally, a credit card is not a unit of account, which is the third function of money, because the prices of goods are not expressed in terms of number of credit cards. Since a credit card does not serve the three functions of money, it is not money. 16. How does fiat money differ from commodities like gold and silver that were used as money?

10 Fiat money is intrinsically worthless but is used as legal tender by government decree. Whereas gold and silver have intrinsic value, fiat or paper money is valuable only because other people will accept it as money. 17. Explain the quantity theory of money. The quantity theory of money assumes that the ratio of money supply to nominal GDP is constant. This implies that, if money supply grows by 10 percent, then nominal GDP also needs to grow by 10 percent to keep the ratio of money supply divided by nominal GDP constant. It follows that the growth rate of money supply and the growth rate of nominal GDP will be the same. Growth Rate of Money Supply = Growth Rate of Nominal GDP Substituting the growth rate of money supply for the growth rate of nominal GDP, we find that: Growth Rate of Money Supply = Inflation Rate + Growth Rate of Real GDP Rearranging this equation, Rate= Growth Rate of Money Supply Growth Rate of Real GDP So, according to the quantity theory of money, inflation is equal to the gap between the growth rate of the money supply and the growth rate of real GDP. When this gap widens, the inflation rate increases. 18. What is the most common cause of hyperinflation? Hyperinflation is always related to extremely rapid growth of the money supply. In almost all cases, such extreme monetary growth is brought about by large government budget deficits. If a government s tax revenues fall short of its expenditures, it meets its obligations by borrowing more from the public or printing money. Printing more money and using it to buy goods and services increases the money supply in the economy, leading to rapid increases in the price level. 19. What are the costs associated with inflation? Inflation imposes the following types of costs on consumers and firms. High rates of inflation create logistical costs: Even moderate rates of inflation will necessitate multiple changes to price lists, price tags, and so on over the course of the year. The costs associated with such changes are referred to as menu costs. Higher inflation distorts relative prices, reducing economic efficiency: As a consequence of volatile inflation, firms may adjust their prices differently, causing relative prices to fall out of alignment. Distortion of relative prices leads to economic inefficiencies. Inflation often leads to counterproductive policies like price controls: High rates of inflation are a politically sensitive issue, which may prompt governments to enact economically destructive policies such as price controls. As discussed in earlier chapters, price controls can result in supply disruptions, long lines, and expansion of the underground economy. 20. Does inflation have any benefits? Explain. Yes, inflation does have certain benefits. Government revenue is generated when the government prints money. The government revenue that is obtained from money creation is called seignorage. Seignorage is the difference between

11 the cost of printing paper money and the value of the goods and services that the government can purchase with the newly printed money. Inflation can sometimes stimulate economic activity. If inflation increases when the nominal wage is fixed, a worker s real wage falls. This increases firms willingness to hire more workers. Inflation may therefore give the government a way to stimulate the economy temporarily, which is a useful policy lever during economic slowdowns. In addition, inflation lowers the real interest rate, which increases consumption and investment. 21. How can the central bank reduce the level of reserves? What happens to the supply curve for reserves? A central bank can conduct open market operations to reduce the level of reserves. It would sell government bonds to private banks, who would pay for these bonds with their reserves, thereby reducing their level. 22. How does the growth rate of money supply affect the real interest rate? If the growth rate of money supply is greater than the growth rate of real GDP, the inflation rate is positive. Given the nominal interest rate, an increase in inflation rate causes the real interest rate to fall. 23. During a financial crisis, the central bank increases the supply of reserves, but the overnight call rate (similar to the federal funds rate) also increases. Use a graph to explain how this happens. The central bank controls the level of reserves held by private banks through open market operations. It buys government bonds from private banks, and increases the supply of electronic reserves by paying for these bonds. This causes the overnight call rate to be lower. During a financial crisis, massive withdrawals from private banks are expected. Thus, private banks increase their demand for reserves. As show in the graph, if the increase in demand for reserves is greater than the increase in supply of reserves, the overnight call rate rises. Overnight call rate (%) supply curve for reserves Demand curve for reserves Quantity of reserves ($) 24. Assume there is an increase in the demand for reserves in other words, the demand curve for reserves shifts to the right. Suppose also that the Fed did not change the quantity of reserves supplied.

12 a. Using a graph of the demand and supply of reserves, show the effect of this increase on the equilibrium federal funds rate and the equilibrium quantity of reserves. b. Given your results from part (a), if the Fed wants to restore the fed funds rate to its pre-expansion level, what kind of open market operation would it need to undertake? Show the result of the operation on your graph from part (a). a. An expansion in the demand for reserves shifts the reserve demand curve to the right, from D 0 to D 1.As a result, the equilibrium federal funds rate will increase from f* to f**, as shown in the following graph. Because there has been no action as yet on the part of the Fed, the quantity of reserves will stay constant at Q 0. b. If the Fed wishes to restore the federal funds rate to the level that prevailed before the economic expansion, it will need to buy bonds in an open market operation, shifting the supply curve of reserves to the right from S 0 to S 1 as the quantity of reserves supplied expands from Q 0 to Q 1, which lowers the equilibrium fed funds rate to its previous level. 25. Before 2012, the open market operations were not well-developed in China. Its main tool of monetary policy was the reserve requirement. It required private banks to hold certain portion of their deposits, thereby reducing the amount of loans they could lend. a. How would an increase in the reserve requirement have affected the demand curve for reserves? b. If inflation was high, what would the Chinese banks do to lower the inflation rate raise or reduce the reserve requirement? To answer this question, explain how change in the interest rate lowers the inflation rate and use the demand and supply of reserves graph to show how change in the reserve requirement affects the equilibrium overnight call rate (similar to federal funds rate). For simplicity, assume that the supply of reserves remains unchanged. a. As the central bank increases the reserve requirement, the demand curve for reserves shifts to the right.

13 b. Inflation rate is equal to growth rate of money supply growth rate of real GDP. Lowering the inflation rate implies a slowdown of growth rate of money supply. To reduce the growth rate of money supply, Bank of China has to raise the overnight call rate which implies an increase in interest rate that households and firms face. Then the demand for loans falls, leading to a lower growth of new deposits. (For example, as people are less willing to buy houses, fewer funds are available for house sellers to make new deposits. Therefore, the growth rate of new deposits at the commercial banks falls.) Based on the definition of money supply that includes deposits and currency in circulation, the growth of money supply falls. Overnight call rate (%) Supply curve for reserves Demand curve for reserves Quantity of reserves ($) Given the supply curve of reserves, the demand curve for reserves has to shift to the right. To increase the demand for reserves, the central bank has to raise the required reserve ratio. Thus, the central bank raises the required reserve ratio, thereby raising the interest rate to lower the inflation rate.

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