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Solved: Let S7 and suppose 4 5 (2143567). Find . What are

Contemporary Abstract Algebra | 8th Edition | ISBN: 9781133599708 | Authors: Joseph Gallian ISBN: 9781133599708 52

Solution for problem 31E Chapter 5

Contemporary Abstract Algebra | 8th Edition

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Contemporary Abstract Algebra | 8th Edition | ISBN: 9781133599708 | Authors: Joseph Gallian

Contemporary Abstract Algebra | 8th Edition

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Problem 31E

Let ? ? S7 and suppose ?4 5 (2143567). Find ?. What are the possibilities for ? if ? ? S9?

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The Monetary System 3/21/16 Monday, March 21, 2016 3:36 PM 1. What money is and why it's important a. Without money, trade would require barter, the exchange of one good or service for another b. Most people would have to spend time searching for others to trade with- a huge waste of resources. c. This searching is unnecessary with money i. Money- The set of assets that people own and use to trade with d. The 3 functions of Money i. Medium of exchange- an item buyers give to sellers when they want to purchase g&s ii. Unit of Account- the yardstick people use to post prices and record debts iii. Store of Value- an item people can use to transfer purchasing power from the present to the future e. 2 Kinds of Money i. Commodity Money- takes the form of a commodity with intrinsic value 1) Ex: gold coins, cigarettes in POW camps ii. Fiat money- Money without intrinsic value, used as money because of govt decree 1) Ex: the U.S. dollar f. The Money Supply i. The money supply (or money stock)- the quantity of money available in the economy ii. What assets should be considered part of the money supply (Two candidates) 1) Currency- the paper bills and coins in the hands of the public 2) Demand Deposits- balances in bank accounts that depositors can access on demand by writing a check (Checking account) g. Measures of the U.S. Money Supply i. M1- currency, demand deposits, travelers' check, and other checkable deposits ii. M2- Everything in M1 plus savings deposits, small time deposits (Certificate of Deposit under 100,000 dollars) , money market funds (Mutual fund that you can write a check on it), and a few minor categories iii. M3- M1 and M2 plus large time deposits (Over 100,000 dollars) , repurchase agreements, and other categories  When we talk about the money supply, we are only talking about M1 and M2 h. Where is all the currency i. 2013: $1.1 trillion currency outstanding 1) Average adult holds about 4,490 of currency 2) Much of currency is held abroad 3) Much of the currency is held by drug dealers , tax evaders, and other criminals i. Central Banks and Monetary Policy i. Central Bank- an institution that oversees the banking system and regulates the money supply ii. Monetary Policy- the setting of the money supply by policymakers in the central bank iii. Federal Reserve (Fed)- the central bank of the U.S. 1) Created in 1913 from the Federal Reserve Act 2) After a series of bank failures in 1907 3) "Panic of 1907" also called "Knickerbocker Crisis"… the failure of the Knickerbocker Trust Company 4) Purpose- to ensure the health of the nation's banking system 5) Made up of a Board of Governors a) 7 members, 14-year terms i) Appointed by the president and confirmed by the Senate i) Appointed by the president and confirmed by the Senate b) The chairman i) Directs the Fed Staff ii) Presides over board meetings iii) Testifies regularly about Fed policy in front of congressional committees iv) Appointed by the president (4-year term) v) Janet Yellen (Current Chairwoman) 6) The Federal Reserve System a) Federal Reserve Board in Washington, D.C. b) 12 regional Federal Reserve Banks i) Major Cities around the country ii) The presidents- chosen by each bank's board of directors  Missouri has 2 regional federal reserve banks 7) The Fed's Job a) Regulate banks and ensure the health of the banking system i) Regional Federal reserve banks ii) Monitors each bank's financial condition iii) Facilitates bank transactions- clearing checks iv) Acts as a bank's bank v) The Fed- Lender of last resort b) Control the Money supply i) Money supply- quantity of money available in the economy ii) Monetary Policy  By Federal Open Market Committee (FOMC) – 7 members of the board of governors – 5 of the twelve regional bank presidents  All twelve regional presidents attend each FOMC meeting, but only five get to vote  NY regional president always votes – Meets about every six weeks in Washington, D.C. – Discuss the condition of the economy – Consider changes in monetary policy  Setting of the money supply 2. Bank Reserves a. In a fractional reserve banking system, banks keep a fraction of deposits as reserves and use the rest to make loans b. The Fed establishes reserve requirements, regulations on the minimum amount of reserves that banks must hold against deposits. Banks can hold the reserves as vault cash or deposits at Fed. c. Banks may hold more than this minimum amount if they choose d. The reserve ratio, R i. =fraction of deposits that banks hold as reserves e. Bank T- account i. T-Account- a simplified accounting statement that shows a bank's assets and liabilities 1) Ex: First national banks assets include Reserves and Loans and liabilities include deposits ii. R would = $10/ $100=10% ○ In a 100% reserve banking system, banks do not affect the size of the money supply because banks do not make any loans. ○ Fractional reserve banking system, by making loans, creates money (But not wealth!!!) f. The Money Multiplier i. Money multiplier- the amount of money the banking system generates with each dollar of reserves reserves 1) =1/R 2) Ex: R=10%, 1/.10=10, $100 of reserve creates $1000 of money The Fed's Tools of Monetary Control 3/23/16 Wednesday, March 23, 2016 3:32 PM 1. Open-Market Operations (OMOs): the purchase and sale of U.S. government bonds by the Fed. a. To increase money supply, fed buys govt bonds, paying with new dollars. i. These are deposited in banks, increasing reserves ii. Which banks use to make loans, causing the money supply to expand b. To reduce money supply, Fed sells govt bonds, taking dollars out of circulation, and the process works in reverse. ○ OMOs are easy to conduct, and are the Fed's monetary policy tool of choice 2. Reserve Requirements(RR)- affect how much money banks can create by making loans a. To increase money supply, Fed reduces RR. i. Banks make more loans from each dollar of reserves, which decreases the reserve ratio and increases the money multiplier and the money supply b. To reduce money supply, Fed raises RR. i. Banks make fewer loans and the process works in reverse. The reserve ratio increases and the money multiplier and the money supply decreases ○ Fed rarely uses reserve requirementsto control money supply: Frequent changes would disrupt banking. 3. The Discount Rate- the interest rate on loans the Fed makes to banks ○ When banks are runninglow on reserves they may borrow reserves from the Fed. a. To increase money supply, Fed can lower discount rate i. Which encourages banks to borrow more reserves from Fed. b. To decrease money supply, Fed can raise discount rate ○ In times of crisis, Discount rate is used more often 4. The Federal Funds Rate (Banks charging other banks) ○ On any given day. Banks with insufficient reserves can borrow from banks with excess reserves ○ The interest rate on these loans is the federal funds rate ○ The FOMC uses OMOs to target the fed funds rate. ○ Many interest rates are highly correlated, so changes in the fed funds rate cause changes in other rates and have a big impact in the economy ○ The Fed does not set the Federal funds rate, but they can cause it to move and influence it using OMOs 5. Problems controlling the money supply a. If householdshold more of their money as currency, banks have fewer reserves, make fewer loans, and money supply falls b. If Banks hold more reserves than required they make fewer loans, the money multiplier decreases, and the money supply falls c. Yet, Fed can compensate for household and bank behavior to retain fairly precise control over the money supply 6. Bank Runs and the Money Supply a. A Run on Banks i. When people suspect their banks are in trouble, they may "run" to the bank to withdraw their funds, holding more currency and less deposits b. Under fractional-reserve banking, banks don't have enough reserves to pay off ALL depositors,hence banks may have to close. depositors,hence banks may have to close. c. Also, banks may make fewer loans and hold more reserves to satisfy depositors d. These events increase R, reverse the process of money creation, cause money supply to fall 7. Financial Crisis of 2008-2009 (The Great Recession) a. Bank Capital i. Resources a bank's owners have put into the institution ii. Used to generate profit b. Leverage i. Use of borrowed money to supplement existing funds for purposes of investment c. Leverage ratio i. Ratio of assets to bank capital ii. (Reserves + Loans +Securities)/ Capital d. Capital Requirement i. Government regulation specifying a minimum amount of bank capital ii. Dependson how risky the investment is e. If bank's assets- rise in value by 5% i. Because some of the securities the bank was holding rose in price ii. $1000 of assets would now be worth $1050 iii. Bank capital rises from $50 to $100 iv. So, for a leverage rate of 20 1) A 5% increase in the value of assets 2) Increases the owners' equity by 100% (20x5) f. If bank's assets- reduced by 5% i. Because some people who borrowed from the bank default on their loans ii. $1000 of assets would be worth $950 iii. Value of the owners' equity falls to zero iv. So, for a leverage ratio of 20 1) A 5% fall in the value of the bank assets 2) Leads to a 100% fall in bank capital g. Banks in 2008 and 2009 i. Shortage of capital 1) After they had incurred losses on some of their assets a) Mortgage loans b) Securities backed by mortgage loans c) "Subprime Mortgage Crisis" (Taking out huge loans when you don’t have the money: high interest rates, generally adjustable) 2) Reduce Lending (Credit Crunch) a) Contributedto a severe downturn in economic activity ii. U.S. Treasury and the Fed 1) Put many billions of dollars of public fundsinto the banking system a) To increase the amount of bank capital b) Called TARP (Troubled asset Relief (Recover) Program) 2) It temporarily made the U.S. taxpayer a part owner of many banks 3) Goal: to recapitalize the banking system a) Bank lending could return to a more normal level (Occurred by late 2009)

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Chapter 5, Problem 31E is Solved
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Textbook: Contemporary Abstract Algebra
Edition: 8
Author: Joseph Gallian
ISBN: 9781133599708

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Solved: Let S7 and suppose 4 5 (2143567). Find . What are