Lecture 3. Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher

Transcription

1 Lecture 3 Chulalongkorn University, EBA Program Monetary Theory and Policy Professor Eric Fisher

2 Inflation Inflation is a sustained and continuing increase in the general price level. It is not a one-time increase in prices It is not an increase in the price of one good, such as imported oil It is a continuing decline in the buying power of money 8/23/2010 Chula, Monetary Theory and Policy 2

3 Winners and Losers Inflation is not bad for everyone. It helps People with flexible incomes Debtors, people who owe money Inflation hurts People with fixed incomes, such as pensioners People who are creditors, such as those who have deposits in banks 8/23/2010 Chula, Monetary Theory and Policy 3

4 Growing supply of money Law of motion for the money supply M t = z M t-1 Here z is the gross rate of growth of money The change in the money supply is M t - M t-1 = (1 1/z) M t 8/23/2010 Chula, Monetary Theory and Policy 4

5 Money transferred to the old The government gives old people this much extra consumption N t-1 a t = v t (1 1/z) M t These are lump-sum transfers, and they distort no economic margins Hence the creation of extra money gives each old person this much extra consumption a t = v t (1 1/z) M t / N t-1 8/23/2010 Chula, Monetary Theory and Policy 5

6 Government budget constraint The government spends N t-1 a t paying for goods to old people It gets these revenues v t (1 1/z) M t from the creation of new money As a matter of fact, the seigniorage from the creation of money by the Fed is transferred to the Treasury 8/23/2010 Chula, Monetary Theory and Policy 6

7 Budget constraint Budget constraint when young Budget constraint when old Unified budget constraint 8/23/2010 Chula, Monetary Theory and Policy 7 y m v c t t 1,t 1 1 1, 2 t t t t a m v c , 1, 1 ) / ( ) / ( t t t t t t t a v v y c v v c

8 The real return on money The savings equation is v t M t = N t (y-c 1,t ) This equation implies v t+1 /v t = (N t+1 /N t )(M t /M t+1 ) = n/z This equation implies that the gross real return on money may be less than unity If the central bank increases the money supply too fast, then negative real interest rates will occur 8/23/2010 Chula, Monetary Theory and Policy 8

9 Stationary budget set The future value of an individual s wealth is y(v t+1 /v t ) + a = yn/z + a The current value of an individual s wealth is y + (v t /v t+1 )a = y + az/n We are using the fact that a stationary budget set entails a constant transfer of a to the old 8/23/2010 Chula, Monetary Theory and Policy 9

10 Price level and inflation Recall that the price level is p t = 1/v t This means that measured gross inflation is p t+1 /p t = z/n So we have net inflation at rate z/n 1 8/23/2010 Chula, Monetary Theory and Policy 10

11 Budget Set with money growth c 2 yn/z + a Real money demand is y c* 1 c* 2 c* 1 y y + za/n c 1 8/23/2010 Chula, Monetary Theory and Policy 11

12 Inefficiency of inflation c 2 ny yn/z + a These points might be chosen it there were no inflation c* 2 The original consumption choice must have been feasible c* 1 y y + za/n c 1 8/23/2010 Chula, Monetary Theory and Policy 12

13 Numerical example Let u(c 1, c 2 ) = c 1 c 2 This utility function has We know that This means that indirect utility is This expression is maximized when z = 1 8/23/2010 Chula, Monetary Theory and Policy / / c c c u c u n z v v c u c u t t / / z z n y 1

14 Some numbers In the last 25 years, the money supply has roughly doubled in the United States Hence z = 2. Fix the term The proportional loss of utility is y n Hence, this level of inflation lowers the utility of a typical generation by 6% /23/2010 Chula, Monetary Theory and Policy 14

15 Policy to fix the price level Since the population is growing at gross rate n, it might be plausible to set the gross money growth rate z = n Now the rate of return on holding money becomes 1. Hence the life-time budget constraint is c 1 + c 2 y + a 8/23/2010 Chula, Monetary Theory and Policy 15

16 Fixed price level c 2 y+ a ny These points might be chosen it there were deflation c* 2 The original consumption choice must have been feasible c* 1 y y + a c 1 8/23/2010 Chula, Monetary Theory and Policy 16

17 Financing government purchases We have maintained the idea that the government uses revenue from seigniorage to buy goods and give them to the old What is the government uses seigniorage to buy government purchases that do not affect agents savings decisions? G t = (1 1/z)v t M t 8/23/2010 Chula, Monetary Theory and Policy 17

18 Implications for the golden rule The monetary authority should set a fixed money supply. Prices will drop at the gross rate of growth of the economy. The gross real return from holding money will be equal to the gross growth rate of the economy. 8/23/2010 Chula, Monetary Theory and Policy 18

19 Old do not receive subsidy Rate of return on money is still v t+1 /v t = n/z Budget constraint is simpler: c 1 + (z/n)c 2 y 8/23/2010 Chula, Monetary Theory and Policy 19

20 Equilibrium with seignioriage revenue c 2 (n/z)y c* 2 c* 1 y c 1 8/23/2010 Chula, Monetary Theory and Policy 20

21 Is an inflation tax efficient? The feasible set: N t c 1 + N t-1 c 2 + G t N t y We will define g = G t /N t-1 These are government purchases per old person Per capita terms: c 1 + c 2 /n + g/n y We assume a stationary equilibrium 8/23/2010 Chula, Monetary Theory and Policy 21

22 Is the inflation tax efficient? c 2 (n/z)y ny - g These points might be chosen if there were no inflation c* 2 The original consumption choice must have been feasible c* 1 y g/n y c 1 8/23/2010 Chula, Monetary Theory and Policy 22

23 A non-distorting tax The government taxes the old a fixed amount τ, denominated in goods The unified budget constraint is c 1,t + (v t /v t+1 )c 2,t+1 y - (v t /v t+1 ) τ If τ = g and z = 1, then we have a stationary equilibrium described by c 1 + (1/n)c 2 y g/n 8/23/2010 Chula, Monetary Theory and Policy 23

24 Non-distorting tax is efficient The last equation is the same as that for the feasible set Hence, if there is no inflation, we can achieve the highest utility for all young generations, given that we must finance exogenous government expenditures Also, the initial old are better off because there money is worth more since the demand for money is higher without inflation. 8/23/2010 Chula, Monetary Theory and Policy 24

25 Limits to seigniorage The real value of seigniorage is (M t - M t-1 ) v t = (1 1/z) M t v t So if the money supply grows at a very large rate, then the inflation tax is almost the entire demand for real balances But (M t - M t-1 ) v t = (1 1/z) N t (y c 1,t ) The inflation tax will decrease the demand for money 8/23/2010 Chula, Monetary Theory and Policy 25

26 Limits of seigniorage c 2 (n/z) y - τ ny - g Money demand, z = 1 If z > 1, then money demand decreases y g/n y (z/n)τ y 8/23/2010 Chula, Monetary Theory and Policy 26 c 1

27 Numerical example u(c 1, c 2 ) = c 1 c 2 People hold q = (y +(z/n) τ)/2 real balances Lump-sum taxes per person: τ = g ((z-1)/z) q These two equations imply q = (y + gz)/(z + 1) Seigniorage per person is ((z-1)/z) q This is a complicated function of z that we must graph 8/23/2010 Chula, Monetary Theory and Policy 27

28 Plausible numbers y = 1 g = 0.1 The US government commands around 10% of the economy for defense and other expenditures, not including transfers Maximum occurs near z = 3 8/23/2010 Chula, Monetary Theory and Policy 28

29 Seigniorage Z 8/23/2010 Chula, Monetary Theory and Policy 29

30 The classical case and the Samuelson case When will money serve as a store of value? Is there anything special about assuming that only the young have any endowment at all? We need to understand money as a store of value even more deeply 8/23/2010 Chula, Monetary Theory and Policy 30

31 Economic environment Period Generation b 1 a b 2 a b 3 a b 4 a b 5 a b Now the old and the young both have some endowment 8/23/2010 Chula, Monetary Theory and Policy 31

32 Equilibrium Conditions The supply of money is a constant M, given to the original old. Utility function u(c 1,c 2 ) = c 1 c 2 Goods market equilibrium: apt 1 bpt ) / 2pt ( 1 demandby old ( apt bpt ) / 2pt demandbyyoung a b 8/23/2010 Chula, Monetary Theory and Policy 32

33 Solving for equilibrium Second-order difference equation: bp t ( a b) pt ap 1 1 t 0 Homogeneous solution t t p t c c a / b) 11 2( 8/23/2010 Chula, Monetary Theory and Policy 33

34 The Unit Root The characteristic equation always has a root equal to the inverse of the growth rate of the economy. Hence an economy without growth will always have a root at unity. If the economy grows at gross rate n, then there will be a root at 1/n 8/23/2010 Chula, Monetary Theory and Policy 34

35 The other root If (a/b) > 1, then the economy is in the Samuelson case. In essence, the young want to save. If (a/b) < 1, then the economy is in the classical case. Now the young people do not need to save. In fact, the may want to borrow. 8/23/2010 Chula, Monetary Theory and Policy 35

36 Autarkic equilibrium c 2 Is the slope less than unity? b a c 1 8/23/2010 Chula, Monetary Theory and Policy 36

37 The deep idea If the autarkic real interest rate is negative, then there is a role for money as a store of value. This is the Samuelson case If the autarkic real interest rate is positive, then there is no (typical) role for money as a store of value. This is the classical case. 8/23/2010 Chula, Monetary Theory and Policy 37

38 Classical case c 2 Slope greater than unity a+ b b a a+b c 1 8/23/2010 Chula, Monetary Theory and Policy 38

39 Samuelson case c 2 a+ b Slope less than unity b a a+b c 1 8/23/2010 Chula, Monetary Theory and Policy 39

40 Champ and Freeman The analysis in your book forces every economy to be in the Samuelson case The real world may be in the classical case. If this is true and money is a store of value, then we must pay taxes on money holdings. This is akin to paying the interest on the national debt. 8/23/2010 Chula, Monetary Theory and Policy 40

41 Summary Inflation is a tax on people who hold money The best monetary policy is to have a constant money supply and let prices decrease at the rate of growth of the economy You should review the classical case and the Samuelson case. The inefficiency of inflation is closely related to how one values money. 8/23/2010 Chula, Monetary Theory and Policy 41