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by: Arno Leuschke


Arno Leuschke
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M. Kapicka

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M. Kapicka
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This 80 page Class Notes was uploaded by Arno Leuschke on Thursday October 22, 2015. The Class Notes belongs to ECON 208 at University of California Santa Barbara taught by M. Kapicka in Fall. Since its upload, it has received 19 views. For similar materials see /class/227156/econ-208-university-of-california-santa-barbara in Economcs at University of California Santa Barbara.




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Date Created: 10/22/15
i Econ 208 Marek Kapicka Lecture 10 Ramsey Optimal Taxation Where are we Introduction A model with no Government The Effects of Government Spending Government Taxation and Government Debt Labor Taxation Capital Taxation Government Debt Fiscal and Monetary Policy Optimal Monetary Policy Financial Intermediation Current Account Determination Fiscal De cits and Current Account Announcements PS3 on the web today Read 143 144 for today a US Government Debt r e l 4 1 Ratio of US Public Debt to GDP 1790 2005 w l LO L World War H Z 3 5 08 CL CI k39 73 06 ReaganiBush Deficits E 2 Revolutionary I9 04 War debt 32 War 21812 Great 02 Depression Civil War 0390 I I I I l I I I l OO 25 50 7 3 00 25 SO 75 OO a Ramsey Approach to Taxation Choose optimal welfare maximizing sequences of taxes and debt given that only distortionary tax instruments are available Tax instruments are given Lump sum taxation not allowed Ramsey Taxation Main Results Uniform Commodity Taxation Under certain conditions tax rates should be equated across goods Distortions will be spread evenly Applies to dynamic economies Tax smoothing a Ra msey Taxation We will analyze a problem of a government that Face a given sequence of expenditures G320 Choose a sequence of consumption sales taxes 720 Similar logic applies to labor taxation Ramsey Taxation Household Problem Maximize lifetime utility max 2 t 111Ct Q t0 Subject to PVBC 2 lt 1 t1rtCtZ 0 1r 00 Household Problem a Ra msey Taxation The Lag ra ngean Ct gt39lt1 ma maxi lnC1i 1 K ikll 17 0 7 Assume that 811r 1 oo 1 where W r 1rZ O1r t Household Problem g Ra msey Taxation Indirect Utility Vltr20W i 8 MC CXD r W E 3 1n 0 1 T an 2 2839 1n1z 1 8 Government s Problem g Ra msey Taxation PV Budget Constraint 00 1 00 1 E 7th 2 tTtCt 0 tO 1 1 I r 1 gtr Tr W 1r 11 1 De ne G 29 th Ramsey Taxation Government s Problem Ramsey Problem Choose a sequence of tax rates to maximize agent39s utility subject to the government s budget constraint Tr an 1 G max lnz39 720 6 1 6 lr 17 W First Order Condition Tr u 1 Ra msey Taxation Government s Problem Solution to the Ramsey Problem taxes are constant over time regardless of the time path of government expenditures Solving for the optimal tax rate 7 r G 1 7 1 r W 1r Implications for Government Debt V Ra msey Taxation Example 2 O O GIOtgtO IV Hence W G Ramsey Taxation amp Implications for Government Debt Tax collection each period r 1r Core De cit 1 GO ZZ 1r G T r tgtO 1r Government Debt Bg t 2 O t Ramsey Taxation WWII vs Korean War WWII nanced differently than Korean War 0A OF EXPENDITURES FINANCED BY Direct Taxes Debt and seignorage World War II 41 59 Korean War 100 0 Marginal laxes 0A TAX RATES BEFOREDURING THE WAR Labor Capital World War II 91 8 4460 Korean War 1620 5263 Ramsey Taxation WWII vs Korean War What if WWII were financed like Korean War taxes only Labor taxes would be 6400 rather than 1800 Capital taxes would be 10000 rather than 6000 Welfare costs are 300 of consumption Econ 208 if Marek Kapicka Lecture 1 1 Monetary Economics i Where are we Monetary Economics Money Supply Money Demand Monetary Policy and Output Financial Intermediation Current Account Determination Fiscal Deficits and Current Account i What to read DLS chapter 170 171 today DLS chapter 19 next time i Monetary Economics Explicit treatment of money needed to answer questions like Why people hold money What determines price level and inflation Is there a relation between money and output consumption etc i Money Money is an asset that serves three roles Medium of exchange Store of value Unit of account Distinguishing economic feature medium of exchange i Supply and Demand Money Supply Determined primarily by the central bank Money Demand Chosen by households Depends on price level incomes interest rates Supply Demand i Federal Reserve Bank Created in 1913 Main impulse Banking panics of 1907 Board of Directors FOMC 12 District banks Commercial banks are members of the system i Central Bank s Roles Roles Elastic Currency 39For the Bank of England in J 805 knowing the o ireCtion of the wind was important If the wind was coming from the east shjos would soon be saling up the Thames to unload goods in London The Bank would need to supp y lots of money If a westerly was blowing the Bank would mop up any excess money thereby avoiding in ation Lender of Last Resort Member Bank Oversight i Money Supply Key Players Central Bank Issues Currency holds Reserves of commercial banks Commercial Banks Accept Deposits from households make loans hold Reserves in the central bank Households Hold Currency make Deposits in commercial banks amp Measuring the Money Supply Problem where to draw a line between money and other assets Should checking account be considered a money It is used for transactions What about saving accounts Can be easily converted into checking account Several de nitions of money supply M0 M1 M2 i MO Monetary Base Definition Currency Reserves of commercial banks at the Fed Signi cance of MO Liabilities of the Federal Reserve It is under its control 9 M1 Definition of M1 Currency Checking Deposits at commercial banks Significance of M1 The best measure of money as a medium of exchange 2 M2 Definition of M2 M1 Savings Deposits Small Time Deposits Significance of M2 Can be used for transaction but with some additional effort Monetary Aggregates September 2003 in billions 0f2003 GDP 7207 65 12756 116 60839 553 88545 805 Relationship of MO and M1 Money Multiplier Definitions M0 C R M1 C D C is currency R is reserves D is deposits Money multiplier m 1 C M1DC D1c MO RC RC rc D D amp Increase in M1 Decrease in Reserve requirements Open Market Operations Increase in reserves Buy securities from banks in exchange for reserves Federal funds market Increase in M1 Open Market Operations Example Trade 10 of bonds for reserves rc02 AMOIO AM1m103O 1 AD 1025 7quotC AC 105 7quotC AR r 105 V I C The Money Multiplier During the Great Depression Banking Panic 1933 increase in currency deposit ratio people unwilling to put money in the bank increase in reserve ratio banks hedging against future runs The Money Multiplier During the Great Depression CURRENCYrDEPOSIT RATIO Bank holiday March 1 933 RESERVE DEPOSIT RATIO L y x x x 1928 1929 1930 1931 1932 1933 1934 1935 1936 Year The Money Multiplier During the Great Depression Monetary base in billions of dollars and money multiplier 8 MONETARY BASE 7 6 Bank holiday MONEY MULTIPLIER MarCh 1933 S 4 3 O l 1 1928 1929 1930 1931 1932 1933 1934 1935 1936 Year Econ 208 if Marek Kapicka Lecture 1 5 Financial lntermediation a What to read DLS chapter 174 a Where are we Monetary Policy Financial Intermediation Bank Runs a Financial Intermediation Financial Intermediation has several roles Matching borrowers and lenders Monitoring of loans Matching liquid deposits and illiquid loans Today we will focus on the third role a Bank Runs Two types of effects Monetary effects money multiplier decreases Real effects output decreases Why real effects Banks are forced to liquidate loans prematurely Questions about real effects Is the banking system inherently unstable Are there any tools to prevent banking crises I Bank Runs Bank Runs in the United a States and England Recurrent Banking panics 1873 1884 1890 1893 1907 1933 13 of all depository institutions failed 2007 2008 Northern Rock Bear Stearns Lehman Brothers Liquid Deposits vs Illiquid Loans Problems If everyone wants to withdraw there is not enough resources Sequential Service Constraint If everyone runs incentives to run If nobody else runs no incentive to run Bank runs can be self enforcing Potential Resolutions Bank Holidays Deposit insurance g The Model 3 periods 0 1 and 2 N consumers N is very large Endowed with 1 unit of good in period 0 Production technology 1 unit of good invested in period 0 yields a nothing in period 1 and 1 r units in period 2 or b 1 unit in period 1 and nothing in period 2 interrupted production Goods can also be stored from period 1 to period 2 No consumption in period 0 invest everything The Model Some people want to consume early period 1 early consumers some later period 2 late consumers Probabilities Early 6 Late 1 6 No utility form consumption in the quotwrongquot pe od The type revealed only at the beginning of period 1 a Consumers expected utility 6Uc1 1 6Uc2 c1 consumption if in period 1 c2 consumption if in period 2 Total number of early consumers N6 Total number of late consumers N1 9 Consu mer s Preferences 5392 191 6b 45 a No Banking Each consumer invest on his own If he needs to consume early he interrupts his production expected utility BUG 1 6U1 r Banking A bank offers a deposit contract withdraw all units in period 1 or withdraw d2 units in period 2 The bank needs to choose the banking contract d1 d2 choose resources Xto withdraw in period 1 make sure that it is in the interest of late consumers to wait d1 s d2 g Bank s Problem Let x 261V be a fraction of investment to be interrupted Bank39s decision problem gag 6Ud1 1 6Ud2 SJ 6611 x 1 6d2 1 x1 739 611 S 612 Bank s Problem Eliminate x to get bank39s budget constraint 6 1r d 2 1rd 2 1 1 Optimal Contract C 2 61 6D1r D 45 a Optimal Contract First Order Condition U d1 1 rU i 1 99 1 rd1 If cUquotCU39C gt 1 then One can show that d1 gt 1 and d2 lt 1r Bank provides insurance against the shock The Equilibrium A Good Equilibrium We have all lt d2 in equilibrium late consumers strictly prefer to wait only early consumers prefer to withdraw in period 1 The Equilibrium A Bad Equilibrium Banking Panics Suppose that a late consumer believes that all other late consumers withdraw in period 1 Because all gt 1 even liquidating all assets will not be enough Sequential Service Constraint late consumer prefers to withdraw in period 1 Beliefs are correct gt it is an equilibrium Solution 1 Suspension of a convertibility Suppose that the bank can refuse to pay deposits in period 1 iins exhausted Then waiting guarantees 0 2 Thus no late consumers decide to run Solution 2 Deposit a Insurance Suppose the government guarantees that each depositor will receive d2 Tax all consumers in period 1 to nance this in case bank run happens Then no late consumer will withdraw in period 1 even if he believes that everyone else withdraws in period 1 Bank run will not occur Solution 2 Deposit g Insurance 1934 Federal deposit Insurance Corporation FDIC established deposits up to 250000 insured Raised from 100000 in 2008 No large banking runs on commercial banks since the Great Depression Solution 2 Deposit a Insurance Problems with Deposit Insurance Moral Hazard Bank may take too much risk If successful profits If unsuccessful insured Bear Stea rns Marek Kapicka i Econ 208 Lecture 13 Monetary Policy in the Short Run a What to read DLS chapter 19 DLS chapter 174 next time Lucas What Economists Do on the web a Where are we Monetary Economics Money Supply Money Demand Long Run effects of Monetary Policy Short Run effects of Monetary Policy Financial Intermediation a Main Themes 1 Can central bank use monetary policy to influence output Only in the short run Not by a systematic monetary policy 2 What are the features of a sound monetary policy Ability to commit Eg independent central bankers a Phillips Curve 3 i 60 b 1 0 1 m 50 40 30 l 20 1 0 o 00 1 l l I 3 39 a Phillips Curve c 1 970 1 973 9 80 g 70 60 C 50 40 3 1 I I I 475 500 525 550 5 75 000 a Phillips Curve d 1 974 1 979 125 O 100 g 7 5 50 o 25 I I I 500 6 oo 7 00 B 00 a Phillips Curve 9 1 900 1 3 1 25 1 00 g 75 50 0 C 25 I a I L 4 l 700 750 800 850 900 950 1 000 Phillips Curve 0 Al Y 1 1 1 5095 950 99 0 0 100 0 i 39 O O n quot 39 quot 5 50 4 l I 500 73950 1000 OW m g Phillips Curve No stable relationship in the long run Negative relationship between inflation and unemployment in the short run Our Story It is only unexpected inflation that matters If in ation is expected people will adjust and money are neutral 196039s theories failed didn39t take expectations into account a The Model People do not have perfect information about prices but observe nominal wages can confuse growth in nominal wages with growth in real wages a The Model Preferences Ucz 243 z Budget Constraint P66 W P6 expected price level W nominal wage a The ModeL Solution W F True price level P Real wage w WP Hence labor supply is D W P W P Pe Pe P Pe LS W a The Model Unemployment uzl LS 21 P w P6 Logs 1111 u 111P 111Pe 1nw u 72396 7Z398 where a Znw a Policy Implications Only unexpected monetary policy can reduce unemployment or output rational expectations any systematic component of monetary policy has no effect The cost of anti inflationary policies Depends on whether it is expected or not a Evaluation 1960 S 1970 s Government tried to increase output by increasing in ation In ation expectations adjusted over time Phillips curve shifted upwards Monetary Policy Phillips Curve u u 77Z39e 7Z398 How does should central bank choose in a on Objective function V u2 722 Fed Objectives stable prices maximum employment 9 Monetary Policy Fixed expectations Suppose that expectations are exogenously given by 76 Fed39s problem max u 772396 72392 72392 Solution e 7 7 e 7239 7239 u 7239 12 12


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