Chapter 5 - good PDF

Preview

Summary

good...

Description

chapter 5 Question 1 Suppose you are interviewed by BusinessThink. You are asked to explain the concept of a balanced budget multiplier. Write out your responses to the following questions. Interviewer: Can you explain to our readers the basic idea of a balanced budget fiscal policy? Answer: We do a case where T and G are changed so that the initial level of BS (budget surplus) is unchanged. Might want to do this if worried about increasing the size of the deficit. Interviewer: It has always seemed to me that the balanced budget multiplier should be zero. Can you provide a simple explanation as to why this is not the case? Answer: Although G and T are changed by equal (initial) amounts, they have different sized multipliers and this produces non-zero BB multiplier.

Question 2 This question illustrates the workings of automatic stabilisers. Suppose the components of planned spending in an economy are given by:

C=C0 +c(Y−T)

Ip=I0

G=G0

T=t Y

M=mY

X= X0

m=0 where t is the tax rate and m the marginal propensity to import is zero (i.e. M=0). In this economy, the tax system acts as an automatic stabiliser, because tax revenues automatically decline when national income falls. a. Solve for an equation that determines the short-run equilibrium output for this economy. Answer: In this example there are no numbers so we just need to solve using a bit of algebra. Write out the equation for PAE:

PAE=C+IP+G+X−M Now just substitute the various components of aggregate expenditure into the above equation.

PAE=C0+c(Y−t×Y)+I0+G0+X0 Collecting terms

PAE=C0+I0+G0+X0+c(1−t)Y

Notice that, in this model, autonomous aggregate demand is C0+I0+G0+X0 and induced aggregate expenditure is c(1−t)Y. The second step is use the equilibrium condition that Y = PAE to solve for equilibrium output:

Y=PAE Y=C0+I0+G0+X0+c(1−t)Y Y[1−c(1−t)]=C0+I0+G0+X0 Ye=1/[1−c(1−t)][C0+I0+G0+X0] The last line above gives an algebraic expression for short-run equilibrium output in the model in which taxes are proportional to output. b. Find the expression for the multiplier, i.e. the amount that output changes when exogenous expenditure changes by one unit. Answer: From the expression for short-run equilibrium output in part (A), we can see that a one-unit increase in autonomous aggregate demand, [C0+I0+G0+X0], increases short-run equilibrium output Ye by 1/[1−c(1−t)] units, so 1/[1−c(1−t)] is the multiplier (k). c. Compare the formula for the multiplier in (ii) with the case when taxes are exogenous. Show that making taxes proportional to income (i.e. endogenous) reduces the size of the multiplier. Answer: If taxes are exogenous (or autonomous), it means that they do not depend on income. If we write our general version of the tax function as

T=T0+tY T0 is the exogenous part of taxes and tY is the induced (or endogenous) part of taxes. If all taxes are exogenous then t=0 and the multiplier in this case would be 1/(1−c). Multiplier with exogenous taxes:

k1=1/(1−c) Multiplier with endogenous taxes:

k2=1/[1−c(1−t)] Suppose c=0.5, then k1=2, but if marginal tax rate t is greater than zero, say t=0.3, the size of the multiplier is reduced to k2=1.54. d. Explain how reducing the size of the multiplier (or increasing the tax rate t) helps to stabilise the economy. Answer: Short-run equilibrium output equals the multiplier times autonomous expenditure (see part (a)). For given fluctuations in autonomous expenditure, the smaller the multiplier, the less output will fluctuate. So changes in the economy that reduce the multiplier, such as introducing taxes that are proportional to output, tend to stabilise output (for given fluctuations in autonomous expenditure). e. Suppose that c=0.8 and t=0.25, calculate the multiplier. Answer: Substitute the numbers into our formula.

k2=1/[1−c(1−t)] k2=1/[1−0.8(1−0.25)] k2=1/[1−0.6]=2.5

Question 3

The following equation is a version of the government budget constraint from Chapter 5.

Gt+TRt+rDt−1=Tt~+Dt−Dt−1 The one change to the equation is that in the above case the real interest rate is not constant over time. a. What does each variable in above equation denote? Answer: The variables in the government budget constraint are:

G = government purchases TR = transfer payments rt−1Dt−1 = interest payments on government debt Tt~ = tax revenue Dt−Dt−1 = new government borrowing (also budget balance) b. Explain in words the implications of the government budget constraint. Does it mean that a government must balance its budget on a year to year basis? Why not? The government budget constraint can be used to think about the Greek debt crisis. Answer: The government budget constraint implies that total government expenditures (G t+TRt+rt−1Dt−1) must be financed either by taxes or by government borrowing. Provided the government can borrow (and lend) then the budget does not need to be balanced on an annual or yearly basis. c. We can think of the Greek situation as being one in which additional government borrowing (at least from financial markets) is no longer possible. In terms of the above equation we have Dt−Dt−1=0. If this is the case, then what are the only options available to the Greek government to solve the crisis? Answer: If (Dt−Dt−1)=0 the government budget constraint becomes

Gt+TRt+rt−1Dt−1=Tt~ Now the Greek government has to fund its government spending, transfers and interest payments out of its taxation revenue. Obviously one possibility is that it does not meet interest payments (and any repayments of debt) and so effectively defaults on its debt. The other options are to: o

Reduce spending and/or transfer payments

o

Raise taxes.

d. In terms of the government budget constraint how does a “bailout 紧急财政援助” of Greece by the other Eurozone countries work? Answer: Another possible option (that is not in the above constraint) is for a Greek bailout – by other countries in the Euro zone. Basically the other countries just make a transfer of Euros to Greece so that it can meet its debt obligations (this is a form of foreign aid or charity really). e. Although it is not included in the above equation, some countries have at times used the option of printing money to finance a budget deficit. Does Greece have this option? Explain. Answer: If Greece issued its own currency (like Australia) there would be an additional term in the government budget constraint, which reflects (what is commonly called) “printing money”. In this case the Greek government could always pay-off its debts (borrowings) by printing (or requiring its central bank to print) some more of its currency. However, since Greek debt is denominated in Euros and Greece cannot just print additional Euros at will, it does not have this option. Of course what Greece could do (and what is roughly equivalent) is to leave the Euro area and introduce its own currency.

Question 4 The government budget constraint can be re-arranged to describe the evolution of public debt in an economy.

Dt=Dt−1+rDt−1−[Tt~−Gt−TRt] or

Dt=Dt−1+rDt−1−PBBt where the term PBB is the primary budget balance and is equal to [Tt~−Gt−TRt]. Suppose that PBB is always equal to zero, the real interest rate r=0.04 and the initial stock of debt equals 50 (i.e. D0=50). a. Fill-in the numbers for the level of public debt in the following table.

Time

Dt

0

50

1

52

2

54.08

3

56.24

4

58.49

b. Answer: See above and as follows: Since PBB = 0, we just have to use: Dt=Dt−1+rDt−1 Time 1

D1=D0+rD0 D1=50+0.04×50=52 Time 2

D2=D1+rD1 D2=52+0.04×52=54.08 Time 3

D3=D2+rD2 D3=54.08+0.04×54.08=56.24 Time 4

D4=D3+rD3 D4=56.24+0.04×56.24=58.49 c. Calculate the growth rate of public debt for each of the periods 1 to 4. What do you notice?

Answer: The growth rate of debt is constant in each period and equal to 0.04 (4%). For example, growth rate of debt between period 3 and 4 equals:

(58.49−56.24)/(56.24)=0.04 The growth rate of debt equals the real interest rate. d. In order to stabilize the public debt to GDP ratio Dt/Yt in the economy, what would the growth rate of GDP need to be? Answer: If Dt is growing at 4% then to stabilize the debt to GDP ratio we need Yt to grow at 4% as well. e. Suppose the primary budget balance was always in deficit (PBB...