CS代写 ECOS3010: Tutorial 1 (Answer Key)

ECOS3010: Tutorial 1 (Answer Key)
Question 1-5. Answer True, False or Uncertain. Brieáy explain your answer.
1. The main di§erence between Öat money and commodity money is that Öat money is intrinsically useless.
True. Historically, commodity money takes many forms including shell, bead, silver, gold and etc.. Commodity money has its own value. Unlike commodity money, Öat money is intrinsically useless. Fiat money is often issued by the government.

2. The golden rule allocation maximizes the utilities of both the future generations and the initial old.
False. The golden rule maximizes the utilities of the future generations, but does not maximize the utilities of the initial old. In our model, the initial old consume only when old. So they would like allocate all consumption to old. In contrast, all future generations prefer to consume both when young and when old.
3. In a monetary equilibrium, individuals maximize their utilities subject to the resource constraints.
False. In a monetary equilibrium, individuals maximize their utilities subject to the lifetime budget constraints.
4. Our model of money is consistent with the quantity theory of money.
True. Quantity theory of money says that the price level is proportional to the quantity of money in the economy. In our model, the equality of money supply and money demand determines the equilibrium price level, which is proportional to the quantity of money.
5. When money supply is constant and population is growing at a constant rate Nt = nNt1, the allocation from a monetary equilibrium is not the golden rule allocation.
False. When the population is growing and money supply is constant, the allocation in a monetary equilibrium still achieves the golden rule allocation. One can Önd that the resource constraint coincides with an individualís budget constraint. So individuals in a monetary equilibrium consume the same consumption bundle as the golden rule allocation chosen by the planner.
6. Consider an economy with a constant population of N = 100. Individuals are endowed with y = 20 units of the consumption good when young and nothing when old.
(a) What is the equation for the feasible set of this economy? Portray the feasible set on a graph. With arbitrarily drawn indi§erence curves, illustrate the stationary combination of c1 and c2 that maximizes the utility of future generations.
Feasible set:
Point A in on the graph maximizes the utility of future generations.
100c1 +100c2 10020 ! c1 +c2 20:

(b) Now look at a monetary equilibrium. Write down equations that represent the constraints on Örst- and second-period consumption for a typical individual. Combine these constraints into a lifetime budget constraint.
First-period budget constraint:
c2 mt20c1 ! c1+ vt c220: vt+1 vt vt+1
(c) Suppose the initial old are endowed with a total of M = 400 units of Öat money. What condition represents the clearing of the money market in an arbitrary period t? Use this condition to Önd the real rate of return of Öat money.
Aggregate real demand for money in period t:
N (y c1) = 100 (20 c1):
Aggregate real supply of money in period t:
vtM = 400vt:
The value of money is determined by the equality of money supply and money demand. Therefore, we have
c1 + vtmt 20: c2 vt+1mt:
Second-period budget constraint:
Lifetime budget constraint: using the Örst- and second-period budget constraints
Similarly,
400vt = 100 (20 c1) and vt = 100 (20 c1): 400
vt+1 = 100(20c1): 400

We can now Önd that the real rate of return of Öat money is
v 100(20c1 )
t+1 = 400 =1:
vt 100(20c1 ) 400
The value of money is constant.
Now suppose that preferences are such that u (c1; c2) = c1=2 + c1=2.
(d) Find an individualís real demand for money. Use the assumption about preferences and your answer in part (c) to Önd an exact numerical value.
In a monetary equilibrium, an individual maximizes his utility subject to the budget constraint. Mathematically,
max c1=2 + c1=2 subject to c1 + c2 = 20; c1;c2 1 2
where we have substituted vt=vt+1 in the budget constraint by 1. From the budget con- straint, c2 = 20 c1. We substitute the expression of c2 into the utility function to have the unconstrained maximization problem:
The Örst-order condition is
max c1=2 + (20 c1)1=2 : c1;c2 1
1c1=2 + 1 (20 c1)1=2 (1) = 0 212
! c1=2 = (20 c1)1=2 1
! c1 = 20 c1 !c1 =10:
It follows that an individualís real demand for money is
yc1 =2010=10:
(e) What is the value of money in period t, vt? What is the price of the consumption good pt?
The value of money in period t is
vt = 100(20c1) = 100(2010) =2:5:
400 400 pt = 1 = 1 = 0:4:
(f) Suppose instead that the initial old were endowed with a total of 800 units of Öat money. How do your answers to part (e) change? Are the initial old better o§ with more units of money?
If the initial old is endowed with 800 units of money, it wonít a§ect the choice of (c1; c2).
Therefore, the price level is

(You can try to verify it.) The value of money in period t is thus
vt = 100(20c1) = 100(2010) =1:25:
800 800 pt=1= 1 =0:8:
The initial old consume c2 = 10, which is the same as before. So they are not better o§ with more units of money. In this economy, money is neutral. The change in the stock of money does not a§ect any real variables such as c1 and c2. Only nominal variables such as vt and pt are a§ected.
7. In this chapter, we modeled growth in an economy by a growing population. We could also achieve a growing economy by having an endowment that increases over time. To see this, consider the following economy: Let the number of young people born in each period be constant at N. There is a constant stock of Öat money, M. Each young person born in period t is endowed with yt units of the consumption good when young and nothing when old. The individual endowment grows over time so that yt = yt1 where > 1. For simplicity, assume that in each period t, individuals desire to hold real money balances equal to one-half of their endowment, so that vtmt = yt=2.
(a) Write down equations that represent the constraints on Örst- and second-period consumption for a typical individual. Combine these constraints into a lifetime budget constraint.
First-period budget constraint:
c1+ vt c2yt: vt+1
The price level is
budget constraint:
c1 + vtmt yt : c2 vt+1mt:
Second-period budget constraint:
As before, we combine the previous two budget constraints to get an individualís lifetime
(b) Write down the condition that represents the clearing of the money market in an arbitrary period t. Use this condition to Önd the real rate of return of Öat money in a monetary equilibrium. Explain the path over time of the value of Öat money.
Aggregate real demand for money in period t: N (yt c1) :
Aggregate real supply of money in period t: vtM:
When money market clears, we have
N(yc1)=vtM ! vt=N(ytc1): M
We know that the preferences are such that vtmt = yt=2. It implies that c1 = yt vtmt = 4

yt=2. The value of money in period t is
Similarly,
It follows that the real rate of return of Öat money is
t+1 = 2M = t+1 = :
vt Nyt yt 2M
The value of Öat money grows at a constant rate . In our lecture, we modeled growth in the economy by growth in the number of young people born each period. We found that in that case, the rate of return of Öat money equal to n, the growth rate of the economy. In this example, is the growth rate of the economy (it is the gross rate of change of the total endowment.). We discover that even in this more complicated setup, the rate of return of Öat money is equal to the growth rate of the economy when the money supply is Öxed.
N yt yt Nyt vt= 2=:
M 2M vt+1 = Nyt+1:

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

Related Posts