编程代考 ECOS3010

Topic 2: Ináation
Monetary Economics ECOS3010
Monetary Economics (ECOS3010) Topic 2: Ináation 1 / 50

Copyright By PowCoder代写 加微信 powcoder

Measuring Money
The deÖnition of money as anything that is generally accepted in payments for goods and services does not tell us how we should measure money.
Which assets shall we include when we measure money? Each countryís central bank provides precise deÖnitions.
In Australia, the Reserve Bank of Australia (RBA) is responsible for monetary policy.
Monetary Economics (ECOS3010) Topic 2: Ináation 2 / 50

Measuring Money
RBAís deÖnition of monetary aggregates:
currency: notes and coins held by the private non-bank sector;
M1: currency + current deposits with banks;
M3: M1 + all other deposits at banks;
Broad money: M3 + other borrowings from private sector by AFIs.
In general, currency < M1 < M3 < broad money. Monetary Economics (ECOS3010) Topic 2: Ináation 3 / 50 Australian Monetary Aggregates Insert Data Monetary Economics (ECOS3010) Topic 2: Ináation 4 / 50 Introduction: Ináation In our simple model of money, money supply is constant. From data on monetary aggregates, money supply seems to grow over time. The supply of Öat money is usually controlled by the central bank. Printing new money is an important way to Önance government spending needs. In this topic, we will examine the consequences of increasing money supply; the link between government spending and ináation; seigniorage: theory and evidence. Monetary Economics (ECOS3010) Topic 2: Ináation 5 / 50 Some Evidence Money growth is the main determinant of ináation. A few examples of extraordinarily high ináation rates ñhyperináations: Germany in 1923: ináation hits 3.25  106 percent per month ! prices double every two days; Greece between 1941 and 1944: ináation hits 8.55  109 percent per month ! prices double every 28 hours; Yugoslavia between Oct 1993 and Jan 1994: ináation hits 5  1015 percent per month ! prices double every 16 hours; Hungary after the end of WWII: ináation peaks at 4.19  1016 percent per month ! prices double every 15 hours; other examples include eastern European countries in the period of economic transition in the early 1990s, Chile from 1972 to 1974, Mexico from 1982 to 1988, and ...... A more recent example is Zimbabwe. Monetary Economics (ECOS3010) Topic 2: Ináation 6 / 50 Australian Ináation Insert Data Monetary Economics (ECOS3010) Topic 2: Ináation 7 / 50 Some Evidence There could also be deáation. Examples: United States from 1930 to 1933; from late 1997 to 2004; Japan in the early 1990s. To understand the causes and consequences of changing money growth rate, we will develop a theory. Monetary Economics (ECOS3010) Topic 2: Ináation 8 / 50 A Growing Money Supply: to the Public Consider the OLG economy that we developed so far. Suppose that money supply grows at a rate z Mt = zMt1. The amount of new money introduced into the economy in period t is MtMt1=MtMt =11Mt. New money is introduced into the economy by means of lump-sum transfers to each old individual in every period t worth at units of consumption goods. To Önd the value of at , in aggregate the government budget constraint is Nt1at =1z1vtMt. ) a t = 1 z1
v t M t . Monetary Economics (ECOS3010) Topic 2: Ináation 9 / 50 A Growing Money Supply: to the Public A Monetary Equilibrium Budget constraints: Örst period of life second period of life c1,t +vtmt y; c2,t+1  vt+1mt + at+1; lifetime budget constraint c1,t + vt c2,t+1 y+ vt at+1. vt +1 vt +1 What is the value of vt+1/vt? As before, we Örst solve for vt from money market clearing condition. vtMt =Nt(yc1,t) ! vt =Nt(yc1,t). Monetary Economics (ECOS3010) Topic 2: Ináation 10 / 50 A Growing Money Supply: to the Public A Monetary Equilibrium As usual, we focus on stationary allocations. Assume for now that the population is constant. The value of money is then vt =N(yc1). Mt It follows that Furthermore, the price level p1v t+1=vt+1 = t =z. pt 1 vt+1 vt When money supply is growing at a rate z, the price level increases at a rate z. Quantity Theory of Money! vt+1= . vt Monetary Economics (ECOS3010) Topic 2: Ináation 11 / 50 A Growing Money Supply: to the Public A Monetary Equilibrium An individualís budget constraint simpliÖes to c1 + zc2  y + za. Monetary Economics (ECOS3010) Topic 2: Ináation 12 / 50 A Growing Money Supply: to the Public A Monetary Equilibrium The solution (c1,c2) are functions of (z,y,a). To close the model, we need to Önd the value of a. Recall that from the government budget constraint Nt1at =1z1vtMt. a is solved from 1 1
v M 1 1
N (y c1 ) Mt  1  a= ztt= z Mt =1(yc1). In a monetary equilibrium, (c1,c2) maximizes an individualís utility subject to the lifetime budget constraint. The government transfer a is such that the government budget constraint is satisÖed in every period. Monetary Economics (ECOS3010) Topic 2: Ináation 13 / 50 A Growing Money Supply: to the Public A Monetary Equilibrium: an Example Anexample: ifu(c1,c2)=c1c2,anindividual max c1c2 subject to c1 +zc2  y +za. Following similar steps as we did in last lecture, we have c1 = y + za and c2 = y + za . 2 2z We can also Önd a by solving a=11yy+za ! a=y1z1
. z21+z Substituting a into (c1,c2), we have c1= yz andc2= y . 1+z 1+z Monetary Economics (ECOS3010) Topic 2: Ináation 14 / 50 A Growing Money Supply: to the Public Is the Monetary Equilibrium E¢ cient? Consider the model with a constant population and a growing money supply, Mt = zMt1. An individualís budget constraint c1 + zc2  y + za. The golden rule allocation: a planner maximizes an individualís utility subject to the resource constraint. Resource constraint Nc1+Nc2Ny ! c1+c2y. Monetary Economics (ECOS3010) Topic 2: Ináation 15 / 50 A Growing Money Supply: to the Public Is the Monetary Equilibrium E¢ cient? Graphically, Monetary Economics (ECOS3010) Topic 2: Ináation 16 / 50 A Growing Money Supply: to the Public Is the Monetary Equilibrium E¢ cient? Compare monetary equilibrium allocation at point B with the golden rule allocation at point A. Monetary equilibrium at point B: intersection of the budget constraint and the resource constraint. Why? Monetary Economics (ECOS3010) Topic 2: Ináation 17 / 50 A Growing Money Supply: to the Public Is the Monetary Equilibrium E¢ cient? With a growing money supply, the allocation in a monetary equilibrium is not the golden rule allocation. Young consume more ! noncash goods. Old consume less ! cash goods. In a monetary equilibrium, all future generations are worse o§: utility at point B is lower than utility at point A. The initial old are also worse o§. Some more to think about Why donít individuals choose point A? What is the optimal growth rate of money supply? Monetary Economics (ECOS3010) Topic 2: Ináation 18 / 50 A Growing Money Supply: to the Public Cost of Ináation In general, e§ects of ináation: people are less willing to hold money & economize the use of money, transactions that are conducted using money are adversely a§ected, violates "smooth consumption" assumption welfare fall. Ináation is e§ectively a tax. Monetary Economics (ECOS3010) Topic 2: Ináation 19 / 50 A Growing Money Supply: to the Public A Growing Population Suppose that population grows such that Nt = nNt1. Budget constraints: Örst-period budget constraint: c1 + vt mt  y ; second-period budget constraint: c2  vt+1mt + a; lifetime budget constraint: c1+ vt c2y+ vt a. vt +1 vt +1 Value of money vt : Nt(yc1)=vtMt !vt=Nt(yc1). Monetary Economics (ECOS3010) Topic 2: Ináation 20 / 50 A Growing Money Supply: to the Public A Growing Population Moneyís rate of return vt+1/vt: v Nt+1(yc1) N M n t+1=Mt+1 =t+1t=. vt Nt(yc1) Nt Mt+1 z The value of money may increase or decrease over time depending on the values of n and z. An individualís lifetime budget constraint simpliÖes to c 1 + nz c 2  y + nz a . Monetary Economics (ECOS3010) Topic 2: Ináation 21 / 50 A Growing Money Supply: to the Public A Growing Population Graphically, we depict the budget constraint and the allocation B that is chosen in a monetary equilibrium. Allocation A is the golden rule allocation. Monetary Economics (ECOS3010) Topic 2: Ináation 22 / 50 A Growing Money Supply: to the Public A Growing Population Golden rule allocation: a plannerís resource constraint Ntc1+Nt1c2Nty ! c1+n1c2y. The resource constraint is di§erent from the individualís budget constraint. The allocation in a monetary equilibrium is not the golden rule allocation. Again, the expansion of money supply makes individuals consume more when young and less when old. The overall utility is lower than the utility at the golden rule allocation. Monetary Economics (ECOS3010) Topic 2: Ináation 23 / 50 A Growing Money Supply: to the Public Consider the case in which government set z = n, which implies vt+1 = n = 1. The value of money and the price level are constant in this vt z case. Is the monetary equilibrium e¢ cient? Monetary Economics (ECOS3010) Topic 2: Ináation 24 / 50 A Growing Money Supply: to the Public A Growing Population What is the optimal growth rate of money supply in an economy with a growing population? To make the individualís budget constraint identical to the resource constraint, it requires vt+1 =n=n. vt z It means that z = 1. A constant money supply allows the economy to achieve the golden rule allocation. Monetary Economics (ECOS3010) Topic 2: Ináation 25 / 50 A Growing Money Supply: to the Public A Growing Population Why is z = 1 the optimal policy in an economy with a population growth? Some intuition: Plannerís resource constraint: if each young gives up 1 unit of consumption, the old can receives n units. Individualís budget constraint: if the young gives up 1 unit of consumption, he will receive n/z units when old. To convey the message that the economy can o§er n units of goods to the old for each good not consumed by the young, the budget constraint has to be adjusted so that it coincides with the resource constraint. The value of money needs to increase at a rate n. That is vt+1 = n. vt Monetary Economics (ECOS3010) Topic 2: Ináation 26 / 50 A Growing Money Supply: to the Public Summary So far, we have shown that when money supply grows at a rate z with z > 1, the allocation in a monetary equilibrium generally di§ers from the golden rule allocation.
Ináation reduces individualsíincentives to hold money and adversely a§ects transactions using money. As a result, ináation may reduce output and welfare.
In our model, the optimal growth rate of money supply is always
z = 1, no matter the population is constant or growing. That is, a constant money supply is the best policy.
Why might a government want to increase money supply?
The government may need to print money to Önance its own expenditure.
Monetary Economics (ECOS3010) Topic 2: Ináation 27 / 50

A Growing Money Supply: to Finance
Government Purchases A Monetary Equilibrium
Government needs to create revenue to Önance various types of expenditures. The use of money creation as a revenue device is called “seigniorage”.
We focus on stationary allocations and a constant population. Suppose that money supply grows at a constant rate z: Mt = zMt1.
The amount of new money created in period t is
M t M t 1 = M t z1 M t =  1 z1  M t .
The amount of goods that the government can purchase in period t is G t = v t ( M t M t 1 ) =  1 z1  v t M t .
This is also the government budget constraint.
Suppose that Gt does not a§ect an individualís consumption choice.
Monetary Economics (ECOS3010) Topic 2: Ináation 28 / 50

A Growing Money Supply: to Finance
Government Purchases A Monetary Equilibrium
An individualís budget constraint: Örst-period budget constraint
c1+vtmt y; second-period budget constraint
c2 vt+1mt; lifetime budget constraint
c1+ vt c2y. vt +1
Notice that in this model, individuals do not receive government transfers.
Monetary Economics (ECOS3010) Topic 2: Ináation 29 / 50

A Growing Money Supply: to Finance
Government Purchases A Monetary Equilibrium
Moneyís rate of return vt+1/vt:
value of money vt is determined when money market clears
N(yc1)=vtMt ! vt=N(yc1). Mt
moneyís rate of return
vt+1=Mt+1 =Mt=1.
vt N(yc1) Mt+1 z
We simplify the individualís budget constraint to c1+zc2 y.
Monetary Economics (ECOS3010) Topic 2: Ináation 30 / 50

A Growing Money Supply: to Finance
Government Purchases A Monetary Equilibrium
Graphically, we depict the budget constraint and add a typical indi§erence curve.
Monetary Economics (ECOS3010) Topic 2: Ináation 31 / 50

A Growing Money Supply: to Finance
Government Purchases A Monetary Equilibrium
In a monetary equilibrium, the amount of goods that the government can purchase in period t can be found from
Gt =1z1vtMt =1z1N(yc1). Notice that Gt is also stationary because Gt = Gt+1 for any t.
Monetary Economics (ECOS3010) Topic 2: Ináation 32 / 50

A Growing Money Supply: to Finance
Government Purchases Golden Rule Allocation
To discuss the optimality of monetary equilibrium, we need to Önd the golden rule allocation.
The plannerís resource constraint
Nc1 + Nc2 + G  Ny ,
where Gt = G for stationary allocations. Divide both sides by N and let g  G/N. The resource constraint can be rewritten as
c1 + c2 + g  y .
Notice that when the government uses new money to Önance its own purchases, G or g is in the resource constraint. The government competes with individuals for resources.
Monetary Economics (ECOS3010) Topic 2: Ináation 33 / 50

A Growing Money Supply: to Finance
Government Purchases Golden Rule Allocation
Graphically, we depict the resource constraint and add a typical indi§erence curve.
Monetary Economics (ECOS3010) Topic 2: Ináation 34 / 50

A Growing Money Supply: to Finance
Government Purchases Golden Rule Allocation
We compare monetary equilibrium at point B with the golden rule allocation at point A.
When the government prints new money to Önance its own purchases, the allocation in a monetary equilibrium achieves a lower level of utility than the golden rule allocation.
Ináation makes individuals trade less goods for money when young, which leads to
higher consumption when young; lower consumption when old.
Note that in comparison with the golden rule allocation, ináation hurts all future generations, as well as the initial old because c2 is lower in a monetary equilibrium.
Monetary Economics (ECOS3010) Topic 2: Ináation 35 / 50

A Growing Money Supply: to Finance
Government Purchases Ináation Tax v.s. Nondistorting Tax
Creating new money is one way to Önance government purchases ! e§ectively an ináation tax. As we have shown, ináation leads to the monetary equilibrium allocation at point B, which is inferior to the golden rule allocation at point A.
Given the need for the government to raise revenue, are there other ways to raise revenue and make the golden rule allocation attainable?
Consider a lump-sum tax. Suppose that the government collects a Öxed tax of τ goods from each old individual in every period.
Monetary Economics (ECOS3010) Topic 2: Ináation 36 / 50

A Growing Money Supply: to Finance
Government Purchases Ináation Tax v.s. Nondistorting Tax
Monetary equilibrium:
Örst- and second-period budget constraints
c1+vtmty and c2vt+1mtτ; lifetime budget constraint
c1+ vt c2y vt τ. vt +1 vt +1
How can the government choose the values of vt+1/vt and τ so that monetary equilibrium can be the same as the golden rule allocation;
the government can still Önance its own purchases G?
Monetary Economics (ECOS3010) Topic 2: Ináation 37 / 50

A Growing Money Supply: to Finance
Government Purchases Ináation Tax v.s. Nondistorting Tax
The government can keep a constant money supply by imposing
τ = g. In this case, we can verify vt+1/vt = 1 and the individualís budget constraint becomes
c1+c2 yg.
Now the budget constraint is identical to the plannerís resource constraint. The allocation in a monetary equilibrium is the same as the golden rule allocation.
Ináation tax (creating new money) and lump-sum taxes:
ináation tax: inferior equilibrium allocation but easy to implement ñ low cost
lump-sum taxes: golden rule allocation but hard to implement in reality.
Money creation has been a popular means to raise government
Monetary Economics (ECOS3010) Topic 2: Ináation 38 / 50

A Growing Money Supply: to Finance
Government Purchases Seigniorage: Theory and Evidence
Recall: government revenue generated by money creation is called
seigniorage.
The use of seigniorage as a source of government revenue varies from country to country and from time to time.
For most developed countries during normal times: seigniorage contributes little to government revenue. For example, seigniorage in U.S. accounted for about 2% of total government revenue and for about 0.3% of gross national product from 1948 to 1989.
For countries that experience high ináation episodes like Argentina, Chile and etc., seigniorage contributes signiÖcantly to government revenue. For example, seigniorage accounted for about 46% of Argentinian government revenue and 6.2% of gross national product from 1960 to 1975.
An extreme case: Germany during its hyperináation of the early 1920s. Seigniorage was about 10% to 15% of gross national product.
Monetary Economics (ECOS3010) Topic 2: Ináation 39 / 50

A Growing Money Supply: to Finance
Government Purchases Seigniorage: Theory and Evidence
Can the government simply print enough money to Önance any purchase without the bother of direct taxation?
The government can print any amount of dollars.
The value of those dollars may shrink as the supply of money increases. Seigniorage revenue in terms of real goods is limited by the real value of money.
To formally examine how seigniorage revenue depends on the speed of money creation, we revisit the government budget constraint
G=(MtMt1)vt =11vtMt . | {zz}|{z}
tax base tax rate
Monetary Economics (ECOS3010) Topic 2: Ináation

A Growing Money Supply: to Finance
Government Purchases Seigniorage: Theory and Evidence
There are two terms in seigniorage revenue collected:
11/z: tax rate ñthe fraction of the real value of the money stock that becomes government revenue;
example: if z = 1.05, then 1 1/z = 1 1/1.05 = 0.0476.
vt Mt : tax base ñ the real value of the money stock (the value of the
money stock in terms of goods).
When the government increases the speed of printing money by
raising z,
the tax rate 1 1/z will increase;
but what is the e§ect of z on the tax base vtMt?
Monetary Economics (ECOS3010) Topic 2: Ináation 41 / 50

A Growing Money Supply: to Finance
Government Purchases Seigniorage: Theory and Evidence
Recall: from the money market clearing condition vtMt =N(yc1).
We need to know how c1 depends on z.
Monetary Economics (ECOS3010) Topic 2: Ináation 42 / 50

A Growing Money Supply: to Finance
Government Purchases Seigniorage: Theory and Evidence
Consider z1 and z2 where z2 > z1. How does c1 respond to an increase in z from z1 to z2?
(c1,c2) in a monetary

程序代写 CS代考 加微信: powcoder QQ: 1823890830 Email: powcoder@163.com