179863074 dornbusch chapter 3 solution docx

WALIA’S THRESHOLD ACADEMY A COMMERCE HUB

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(Ph: 9899924193, 9350341937) By:- T.S. Walia (Ph. No. 9899924193)

CHAPTER – 3 PROBLEMS

1. Here we investigate a particular example of the model studied in Sections 3-2 and 3-3

with no government. Suppose the consumption function is given by C = 100 + 0.8Y,

while investment is given by I = 50.

(a) What is the equilibrium level of income in this case?

(b) What is the level of saving in equilibrium?

(c) If, for some reason, output were at the level of 800, what would the level of

involuntary inventory accumulation be?

(d) If I were to rise to 100 (we discuss what determines / in later chapters), what

would the effect be on equilibrium income?

(e) What is the value of the multiplier, , here?

Ans. C 100 0.8y

I 50

(a) y AD

Y C I

Y 100 0.8 50

0.2y 150

y 750

(b) S Y C

Y 100 0.8Y

0.2Y 100

150 100

50

If Output = 800 (involuntary inventory accumulation)

y AD

800 150 0.8 800

800 150 640

10

(d) I 50( )

Iy

I c

I

I c




50250

1 0.8

income will increase by 250

(e) Value of multiplier

dy 1 15

I C 1 0.8da

2. Suppose consumption behavior were to change in problem 1 so that C = 100 + 0.9Y,

while I remained at 50.

(a) Would you expect the equilibrium level of income to be higher or lower than in

la? Calculate the new equilibrium level, Y’, to verify this.

(b) Now suppose investment increases to I = 100, just as in Id. What is the new

equilibrium income?

(c) Does this change in investment spending have more or less of an effect on Y than

in problem 1? Why ?

(d) Draw a diagram indicating the change in equilibrium income in this case.

Ans. (a) C = 100 + 0.9y , I = 50

MPC increased from 0.8 to 0.9

Ay

1 C

dAy

1 C

Equilibrium income 150

y 15001 0.9

(b) I = 100

I 50

A Iy

1 C 1 C

50500

1 0.9

New equilibrium income = 1500 + 500 = 2000

3. This problem relates to the so-called paradox of thrift. Suppose that I = I0 and that

C C cY .

(a) Draw a diagram where income is measured on the horizontal axis and investment

and saving on the vertical axis,




(b) What is the saving function, that is, the function that shows how saving is related

to income?

(c) Draw the investment function which is flat. Explain why the intersection of the

saving and investment function gives us the equilibrium level of output.

(d) Suppose individuals want to save more at every level of income. Show, using a

figure like Figure 3-4, how the saving function is shifted.

(e) What effect does the increased desire to save have on the new equilibrium level of

saving? Explain the paradox.

Ans. 0I I ,C C CY

(b) S y C

y (C Cyd)

y (C C(y TA Ty TR)

y C Cy CTA CTy CTR

S A (1 C Ct)y

A (1 C(1 t))y

C + I = C + S




(c)

We know that equilibrium is established

When AD = AS

C + I = C + S

I = S

Thus, intersection of the saving and investment function gives us the equilibrium

level of output.




(d) When individuals want to save more at every level of income, the saving income

shifts upwards.

(e)

Autonomous investment induced investment

The paradox of thrift tells us that the desire to save more in the present leads to a reduced

amount of savings in the future.




Autonomous investment:

When the savings of the people increase, the savings curve shifts upwards, from s to s’as

savings increase, consumption decreases and thus income also decreases.

Equilibrium, savings equal autonomous investment which is constant, the level of saving

in the economy remains the same in this case but the level of income decreases.

Induced investment:

As the saving increase, the saving curve shifts upward to s’.

At s1curve, for equilibrium I = S’. Equilibrium is attained at E1, where the amount of

equilibrium, saving and the national income both have decreased.

4. Now let us look at a model that is an example of the one presented in Sections 3-4 and 3-

5: that is, it includes government purchases, taxes, and transfers. It has the same features

as the one in problems 1 and 2 except that it also has a government. Thus, suppose

consumption is given by C = 100 + 0.8yd and that I = 50, while fiscal policy is

summarized by G = 200, TR = 62.5, and t = 0.25.

(a) What is the equilibrium level of income in this more complete model?

(b) What is the value of the new multiplier, ac? Why is this less than the multiplier in

problem 1(e)?

Ans. C 100 0.8yd

I 50,G 200,TR 6.25, t 0.25

(a) y = AD

y C CYd I G

y = 100 + 0.8 (y - 0.25y + 62.5) + 50 + 200

y = 350 + 0.6y + 50

0.4y = 400

y = 1000

(b)

Ay

1 C(1 t)

dy 1

1 C(1 t)dA

1 1

1 0.8(1 0.25) 0.4

2.5




5. Using the same model as in problem 4, determine the following:

(a) What is the value of the budget surplus, BS, when I= 50?

(b) What is BS when I increases to 100?

(c) What accounts for the change in BS between 5b and 5a?

(d) Assuming that the full-employment level of income, Y*, is 1,200, what is the full-

employment budget surplus BS* when I = 50? 100? (Be careful.)

(e) What is BS* if I = 50 and G = 250. with Y* still equal to 1,200?

(f) Explain why we use BS* rather than simply BS to measure the direction of fiscal

policy.

Ans. I = 50

(a) BS TA ty G TR

BS 0.25y 200 62.5

0.25 1000 262.5

250 262.5

12.5

Budget Deficit

(b) When

I 50

y 50 2.5 125

New y1 = 1125

BS = 0.251125 - 262.5

= 18.75 Budget surplus

(d) y*= 1200

When I = 50

* *BS ty G TR

0.25 1200 200 62.5

300 262.5

37.5

(e)

(f) We use full employment budget surplus rather than the simple budget surplus

because the simple budget suffers a serious defect as a measure of the direction of

fiscal policy. The defect is that the surplus can change because of a change in

autonomous private spending.

Thus an increase in the budget deficit does not necessary mean that the govt. has

changed its policy.




6. Suppose we expand our model to take account of the fact that transfer payments, TR, do

depend on the level of income, Y. When income is high, transfer payments such as

unemployment benefits will fall. Conversely, when income is low, unemployment is high

and so are unemployment benefits. We can incorporate this into our model by writing

transfers as TR TR bY , b > 0. Remember that equilibrium income is derived as the

solution to Y = C + I + G = cYD + I + G. where YD = Y + TR - TA is disposable

income.

(a) Derive the expression for v0 in this case, just as equation (22) was derived in the

text.

(b) What is the new multiplier?

(c) Why is the new multiplier less than the standard one, G ?

(d) How does the change in the multiplier relate to the concept of automatic

stabilizers?

Ans. (a) TR TR by , b > 0

y = AD

y = C + I + G

y c cyd I G

y c c(y TA ty TR by)

y c cy cTA c y cTR cby

y cy cty cby A

y[1 c(1 t b)] A

Ay

1 c(1 t b)

(b) New multiplier , 1

1 c(1 t b)

(c) The multiplier is less than the standard one because of the presence of b in the

denominator.

The standard 1

1 c(1 t)

, which is always greater than

, 1

1 c(1 t b)

(d) An automatic stabilizer is any mechanism in the economy that reduces the amount

by which output changes in response to a change in autonomous demand.

If the multiplier is small, it means that the income is changing less than it

would have changed when the multiplier was large.

The use of the new multiplier , 1

1 c(1 t b) reduces the amount by which the

income changes due to a change in the autonomous components of demand.

Thus the presence of ‘b’ in the multiplier plays the role of an automatic stabilizer.




7. Now we look at the role taxes play in determining equilibrium income. Suppose we have

an economy of the type in Sections 3-4 and 3-5, described by the following functions:

C = 50 + 0.8YD

I 70

G = 200

TR 100

t = 0.20

(a) Calculate the equilibrium level of income and the multiplier in this model.

(b) Calculate also the budget surplus, BS.

(c) Suppose that t increases to 0.25. What is the new equilibrium income? The new

multiplier?

(d) Calculate the change in the budget surplus. Would you expect the change in the

surplus to be more or less if c = 0.9 rather than 0.8?

(e) Can you explain why the multiplier is 1 when t = 1?

Ans. C = 50 + 0.8yd

I 70 , G 200 , TR 100 , t = 0.20

(a) At equilibrium, y = AD

y = C + I + G

y c cyd I G

y = 50 + 0.8 (y - 0.20y + 100) + 70 + 200

y = 320 + 0.644 + 80

0.36y = 400

y =1111.11

1 1 1

1 c(1 t) 1 0.8(1 0.20) 1 0.8 0.8

1

2.770.36

(b) BS TA ty G TR

= 0.20 1111.11 200 100

= (-) 77 - 778 (Budget deficit)




(c) t increases 0.25

New multiplier =1

1 0.8(1 0.25

New equilibrium income =A 420

1 c(1 t) 1 0.8(1 0.25)

=1050

(d) 0

1

1 cBS y t

1 c(1 t )

1 0.81111.11 0.05

1 0.8(1 0.25)

(e) When t = 1,

1 1

11 c(1 t) 1 0.8(1 1)

8. Suppose the economy is operating at equilibrium, with Y0 = 1,000. If the government

undertakes a fiscal change so that the tax rate t increases by 0.05 and government

spending increases by 50, will the budget surplus go up or down? Why?

Ans. y0 =1,000

t increases by 0.05, t 0.05

Govt. spending increases by 50, G 50

G 5%of 40

We know that when G increases, y also increases

Thus, the increase in tax (5% of y1) is more than the increase in G (5% of 40)

The budget surplus will increase.

9. Suppose Congress decides to reduce transfer payments (such as welfare) but to increase

government purchases of goods and services by an equal amount. That is, it undertakes a

change in fiscal policy such that G TR .

(a) Would you expect equilibrium income to rise or fall as a result of this change?

Why? Check your answer with the following example: Suppose that initially,

c = 0.8, t = 0.25, and Y0 = 600. Now let G = 10 and TR = - 10.

(b) Find the change in equilibrium income, 0Y .

(c) What is the change in the budget surplus, BS? Why has BS changed?




Ans. G TR

(a)

dAdy

1 c(1 t)

G c TR TR c TR

1 c(1 t) 1 c(1 t)

TR(c 1)dy

1 c(1 t)

As transfers are being reduced, equilibrium income will increase by change in y

(dy).

C = 0.8, t = 0.25, y0 = 600

G 10 , TR 10

10(0.8 1)dy

1 0.8(1 0.25)

(b) 2

dy 50.4

(c) TR(c 1)

BS t1 c(1 t)

= ( 10)(0.8 1)

0.251 0.8(1 0.25)

= 0.25 5 = 1.25




ADDITIONAL PROBLEMS

1. Briefly explain in words the effect of an increase in the marginal propensity to save

on the size of the expenditure multiplier and the level of equilibrium income.

If the marginal propensity to save (s = 1 - c) rises, then the marginal propensity to

consume (c) falls. Therefore one extra dollar in income earned will now affect

consumption by less than before this reduction in c. But if the marginal propensity to save

is larger, then the size of the expenditure multiplier will be smaller, since the expenditure

multiplier is defined as 1/(1 - c) = 1/s. We should expect that when people start to save a

larger portion of their income, spending on consumption goods will decrease, leading to a

decline in equilibrium income.

2. Comment on the following statement:

“When aggregate demand falls below the current output level, an unintended

inventory accumulation occurs and the economy is no longer in an equilibrium.”

When aggregate demand falls below the equilibrium output level, actual production

exceeds desired spending. Therefore firms see an unwanted accumulation in their

inventories, and they respond by reducing their production level. This leads to a decrease

in the level of output up to the point where the new and lower level of desired spending is

again equal to the level of actual output. In other words, in the expenditure sector, the

adjustment from one equilibrium to the next is based on unintended inventory changes,

until the economy eventually reaches a new equilibrium at another output level.

3. Assume a model without any government involvement or external trade, in which

the only two components of aggregate demand are consumption (C) and investment

(I). Show that in this case the equilibrium condition Y = C + I is equivalent to the

equilibrium condition S = I.

We can derive the equilibrium value of output by setting actual output equal to intended

spending, that is, Y = C + I

Y = C0 + cY +I0 (1 - c)Y = C0 + I0 Y = [1/(1 - c)] (C0 + I0) = [1/(1 - c)]A0.

But since S = YD - C = Y - [C0 + cY] = - C0 + (1 - c)Y,

we can derive the same result by setting intended withdrawals equal to intended

injections, that is, S = I0

- C0 + (1 - c)Y = I0 (1 - c)Y = C0 + I0

Y - [1/(1 - c)](C0 + I0) = [1/(1 - c)]A0.




4. For a simple model of the expenditure sector without any government involvement,

derive the multiplier in terms of the marginal propensity to save (s) rather than the

marginal propensity to consume (c). Does this formula still hold when the

government enters the picture and levies an income tax?

The expenditure multiplier for a model without any government involvement was derived

as = 1/(1 - c).

But since the marginal propensity to save is s = (1 - c), the multiplier now becomes

= 1/(1 - c) = 1/s.

In the text, we have also seen that, if the government enters the picture and levies an

income tax, then the simple expenditure multiplier changes to

= 1/[1 - c(1 - t)] = 1/(1 – c’).

By substituting s = (1 - c), this equation can be easily manipulated, to get

= 1/[1 - c + ct] = 1/[s + (1 - s)t] = 1/s'. .

Just as s = (1 - c), we can say that s' = (1 - c'), since

s' = (1 - c') = 1 - c(1 - t) = 1 - c + ct = s + (1 - s)t.

This can also be derived in another way:

S = YD - C = YD - (C0 + cYD) = - C0 + (1 - c)YD = - C0 + sYD

If we assume for simplicity that TR = 0 and NX = 0 and TA = tY + TA0, we can derive

the equilibrium level of output by setting intended withdrawals equal to intended

spending, that is,

S + TA = I + G - C0 + sYD + TA = I0 + G0

- C0 + s(Y - TA) + TA = I0 + G0

s(Y - tY - TA0) + tY + TA0 = C0 + I0 + G0

[s + (l - s)t]Y = C0 + I0 + G0 - (1 - s)TA0

By setting C0 + I0 + G0 - (1 - s)TA0 = A0, we get

[s + (1 - s)t]Y = A0 Y - (1/[s + (1 - s)t]) A0 = (1/s')A0.




5. Using a simple model of the expenditure sector without any government

involvement, explain the paradox of thrift that asserts that an increased desire to

save may not lead to an increase in actual saving.

The paradox of thrift occurs because a higher level of saving can only be achieved if the

level of consumption is lowered. But a lower level of spending sends the economy into a

recession and a new equilibrium is reached at a lower level of output. In the end, the

increase in autonomous saving is exactly offset by the decrease in induced saving due to

the lower income level. In other words, the economy originally is in equilibrium when

S = I0. Since the level of autonomous investment (I0) has not changed, the level of private

saving at the new equilibrium income level must again equal I0, and can therefore not

change.

This can also be derived mathematically. An increase in autonomous saving is equivalent

to a decrease in autonomous consumption, that is, S0 = - C0, so the effect on

equilibrium income is

Y = [1/(1 - c)] (-C0).

In this simple framework saving is defined as S = Y - C

S = Y- (C0 + cY) - C0 + (1 - c)Y.

Therefore the overall effect on total saving is

S = - (-C0) + (1 - c) Y = + C0 + (1 - c)[1/(1- c)](- C0) = + C0 - C0 = 0.

6. The balanced budget theorem states that the government can stimulate the economy

without increasing the budget deficit if an increase in government purchases (G) is

financed by an equivalent increase in taxes (TA). Show that this is true for a simple

model of the expenditure sector without any income taxes.

If taxes and government purchases are increased by the same amount, then the change in

the budget surplus can be calculated as

BS = TA0 - G = 0, since TA0 = G.

The resulting change in national income is

Y = C + G - c(YD) + G = c(Y - TA0) + G = c(Y) - c(TA0) +G

Y = c(Y) + (1 - c) (G) since TA0 = G.

Solving for Y, we get

(1 - c) (Y) = (1 - c) (G) Y = G.




In this case, the increase in output (Y) is exactly of the same magnitude as the increase in

government purchases (G). This occurs since the decrease in the level of consumption

due to the lump sum tax has exactly been offset by the increase in the level of

consumption caused by the increase in income.

7. In an effort to stimulate the economy in 1976, President Ford asked Congress for a

$20 billion tax cut in combination with a $20 billion cut in government purchases.

Do you consider this a good policy proposal? Why or why not?

This was not a good policy proposal. According to the balanced budget theorem, a

decrease in government purchases and taxes of equal magnitude will decrease rather than

increase national income. Therefore the intended result, that is, an increase in economic

activity, will not be achieved.

8. “An increase in government purchases always pays for itself, as it raises national

income and hence the government's tax revenues.” Comment on this statement.

An increase in government purchases increases the budget deficit. If we assume a model

of the expenditure sector with income taxes, the multiplier equals [1/(1 - c')] with

c' = c (1 - t). The change in the budget surplus that arises from a change in government

purchases can be calculated as

BS = t(Y) - G = t[1/(1 - c')] (G) - G = {[t - 1 + c - (ct)]/[l - c + (ct)]}( G)

= - {[(1 - c) (1 - t)]/(1 - c + ct]}( G) < 0, sine G > 0, c < 1 and t < 1.

Therefore, if government purchases are increased, the budget surplus will decrease.

9. In a simple model of the expenditure sector with a positive income tax rate (t), does

a decrease in autonomous investment (I0) affect the budget surplus? Why or why

not?

A decrease in autonomous investment (I0) has a multiplier effect so national income will

decrease. As a result, income tax revenues will decrease, and the budget surplus will

decrease as shown below:

BS = t(Y) = t ( I0) < 0 since I0 < 0

10. Assume the following model of the expenditure sector:

Sp = C – I + G + NX C = 420 + (4/S)YD YD = Y - TA + TR TA = (1/6)Y

TRo = 100 Io = 160 Go = 180 NX0 = - 40

(a) If the government would like to increase the equilibrium level of output (Y) to the

full-employment level Y* = 2,700, by how much should government purchases (G)

be changed?

(b) Assume we want to reach Y = 2,700 by changing government transfer payments

(TR) instead. By how much should TR be changed?




(c) Assume you increase both government purchases (G) and taxes (TA) by the same

lump sum of G = TA0 = + 300. Would this sufficient to reach the full-

employment level of output at Y* = 2,700? Why or why not?

(d) Briefly explain in words how a decrease in the marginal propensity to save would

affect the size of the expenditure multiplier.

(a). Sp = C + I + G + NX = 420 + (4/5) [Y - (1/6)Y + 100] + 160 + 180 – 40

= 720 + (4/5) (5/6)Y + 80 = 800 + (2/3)Y

From Y = Sp Y = 800 + (2/3)Y (1/3)Y = 800 Y = 3*800 - 2,400

the expenditure multiplier is = 3

From Y = (A0) 300 = 3(A0) A0 = 100

Thus government purchases should be changed by G = A0 = 100.

(b) Since A0 = 100 and A0 = c(TR0) 100 = (4/5)( TR0) TR0 - 125.

(c) This is a model with income taxes, so the balanced budget theorem does not apply in its

strictest form, which states that an increase in government purchases and taxes by a given

lump-sum amount increases national income by that same amount, leaving the budget

surplus unchanged. In this model, total tax revenues actually increase by more than 300,

since taxes are initially increased by a lump sum of 300. However, income taxes then also

change due to the change in the income level. Therefore income does not increase by

Y - 300, as we can see below.

Y - (G) + [(- c) (TA0) = 3*300 + 3* [- (4/5)300] - 900 - 720 = 180

This change in fiscal policy will increase income by only Y = 180, that is, from Y0 =

2,400 to Y1 = 2,580, and we therefore will be unable to reach Y* = 2,700.

(d) If the marginal propensity to save s = (1 - c) decreases, people spend a larger portion of

their additional disposable income, that is, the marginal propensity to consume (c) and

the slope of the [C + I + G + NX] line increase. This will lead to an increase in the

expenditure multiplier and the level of equilibrium income.

11. Assume a model with income taxes similar to the model in Problem 10 above. This

time, however, you have only limited information about the model, that is, you only

know that the marginal propensity to consume out of disposable income is c = 0.75,

and that total autonomous spending is A0 = 900, such that Sp = A0 + c'Y = 900 + c'Y.

You also know that you can reach the full-employment level of output at Y = 3,150

by increasing government transfers by a lump sum of TR = 200.

(a) What is the current equilibrium level of output?




(b) Is it possible to determine the size of the expenditure multiplier with the information

you have, and if so, how?

(c) Assume, instead of changing transfer payments, the government wants to change

the income tax rate (t) in order to reach the full-employment level of income Y* =

3,150. How would this change in the tax rate affect the size of the expenditure

multiplier?

(a). If transfer payments are changed by a lump sum TR = 200, then total autonomous

spending is changed by

A = c(TR) = (0.75) 200 = 150.

Therefore the intended spending line, that is, the [C + I + G + NX] line changes to

Sp1 = 1,050 + c'Y.

For each model of the expenditure sector we can derive the equilibrium level of income

by using the following equation:

Y* = A0 = [1/1 – c’)]A0

In this case, we have

3,150 = (1,050) the expenditure multiplier is = 3.

If we now change autonomous spending in this model by A = 150, then the

equilibrium, level of income will have to change by.

Y = a(A) Y = 3*150 = 450.

Therefore the old equilibrium level of income before this change must have been

Y = 3,150 - 450 = 2,700.

(b) From our work above we can see that the size of the expenditure multiplier is = 3.




(c) If we change the tax rate but leave autonomous spending alone, then the new [C + I + G

+ NX] line is of the form Sp2 = 900 + c2Y. This new intended spending line intersects the

45-degree line at the desired equilibrium income level of Y = 3,150. This allows us to

derive the slope of the new intended spending line from the graph below as follows:

c2 = rise/run = (3,150 - 900)/(3,150) = 2,250/3,150 = 5/7.

From Y = Sp2 Y = 900 + (5/7) Y (2/7)Y = 900

Y = (7/2)900 = (3.5)900 = 3,150.

The new value of the multiplier is 1 = 3.5

12. Assume you have the following model of the expenditure sector:

Sp = C + I + G + NX C = 400 + (0.8)YD I0 = 200 G = 300 + (0.1)(Y* - Y)

YD = Y - TA + TR NX0 = - 40 TA = (0.25) Y TR0 = 50

(a) What is the size of the output gap if potential output is at Y* = 3,000?

(b) By how much would investment (I0) have to change to reach equilibrium at Y* =

3,000, and how does this change affect the budget surplus?

(c) From the model above you can see that government purchases (G) are counter-

cyclical, that is, G is increased as national income decreases. If you compare this

specification of G with one that has a constant level of government spending (for

example, G0 = 300), how would the value of the expenditure multiplier differ?

(d) Assume the equation for net exports changes from NX0 = - 40 to NX1 = - 40 - mY.

How would this affect expenditure multiplier, if we assume that 0 < m < 1?

(a) Sp = 400 + (0.8)YD + 200 + 300 + (0.1 )(3,000 - Y) - 40

= 1,160 + (0.8) (Y - (0.25)Y + 50) - (0.1)Y

= 1,200 + [(0.8)(0.75) - (0.1)]Y = 1,200 + (0.5) Y

Y = Sp Y = 1,200 + (0.5)Y (0.5)Y = 1,200 Y = 2*1,200 = 2,400

The output gap is Y* - Y = 3,000 - 2,400 = 600.

(b) From Y = (mult.) (A) 600 - 2( I) I = 300

BuS = TA - TR - G = (0.25)(2,400) - 50 - [300 + (0.1)(600)] = 600 - 50 - 300 - 60 = 190

BuS* = (0.25)(3,000) - 50 - 300 + 0 = 750 - 350 = 400.

Therefore, the budget surplus increases by BuS = 210.




(c) If government purchases are used as a stabilization tool, the size of the expenditure

multiplier should be lower than if the level of government spending is fixed. In the model

of the expenditure sector above, the slope of the [C + I + G + NX] line is c1 = 0.5, and

therefore the size of the expenditure multiplier is = 1/(0.5) = 2. However, if

government purchases are defined as G0 = 300 instead, the slope of the [C + I + G + NX]

line changes to c2 = 0.6 and the size of the expenditure multiplier changes to 2 = 1/(0.4)

= 2.5.

(d) With this change, net exports decrease as national income increases. This additional

leakage implies that the size of the multiplier will decrease. In the model above, the slope

of the [C + I + G + NX] line decreases from c1 = (0.5) to c3 = (0.5) - m, and the

expenditure multiplier decreases from 1/[1 - (0.5)] to 1/[1 - (0.5) + m]. Therefore, if m =

0.14, then the expenditure multiplier decreases from = 1/(0.5) = 2 to 3 = 1/(0.64) =

1.5625.

13. Assume you have the following model of the expenditure sector:

Sp = C + I + G + NX C = Co + cYD YD = Y - TA + TR TA = TA0

TR = TR* I = I0 G = G0 NX = NX0

(a) If a change in income by Y = - 800 leads to a change in savings by S = - 160,

what is the size of the expenditure multiplier?

(b) If a change in taxes by TA = - 400 leads to an change in income by Y = + 1,200,

how large is the marginal propensity to save?

(c) If a change in exports by NX = - 200 is accompanied by a change in consumption

by C = - 800, what is the size of the expenditure multiplier?

The expenditure multiplier for such a simple model can be calculated as: = 1/(1 - c)

(a) (S)/(Y) = s = 1 - c = (-160)/(-800) = 02 1/(1 - c) = 1 /(0.2) = 5

the multiplier is a = 5.

(b) From (Y) = [-c(TA0)] (Y)/( TA0) = (-c) = (- c)/(1 - c)

(1,200)/(- 400) = - 3 = (- c)/(1 - c) - 3(1 - c) = - c c = 3/4

mps = s = 1 - c - 1/4 = 0.25.

(c) Y - C + NX = - 800 + (- 200) = - 1,000

c = (C)/(Y) = (- 800)/(- 1,000) = 0.8 multiplier = = 1/1(1 – c) = 1/(0.2) = 5

14. Explain why the income tax system, the Social Security system, and unemployment

insurance are considered automatic stabilizers.

Income taxation, unemployment benefits, and the Social Security system are often called

automatic stabilizers because they reduce the magnitude by which the level of




equilibrium output changes as a result of a change in aggregate demand. These stabilizers

are a part of the structure of the economy and therefore work even though no explicit

government action is undertaken. For example, when the economy enters a recession, the

level of output declines and the unemployment rate increases. If there was no

unemployment insurance program in place, people out of work would no longer have any

disposable income and consumption would drop significantly. However, since

unemployed workers receive unemployment compensation, consumption and aggregate

demand do not decrease as much. Similarly, as people retire, their income from work

drops, but then they receive Social Security benefits, which means that their disposable

income does not decline by as much and therefore they do not have to reduce

consumption by as much.

15. “A tax cut will increase national income and will therefore always decrease the

budget deficit.” Comment on this statement.

While a tax cut serves to simulate national income, not all of the increase in income is

spent, nor is it completely taxed away. The budget deficit will increase since overall tax

revenue will fall. This can be shown with the help of a simple model of the expenditure

sector that has income taxation:

From BS = TA - G - TR = tY + TA0 - G -TR

ABS = t(Y) + TA0 = t( 1,)(- c)(TA0) + TA0

= t[1/(1 - c + ct)] (- c) (TA0) + TA0 = ([- ct/(1 - c + ct)] + 1)( TA0)

= ([- ct + 1 - c + ct]/[1 - c + ct])(TA0)

= [(1 - c)/(1 – c + ct)]( TA0) < 0, since c < 1 and TA0 < 0.

In other words, a decrease in lump sum taxes will increase the budget deficit, not

decrease it.

16. Assume a model of the expenditure sector with income taxes, in which people who

pay taxes, have a higher marginal propensity to consume than people who receive

government transfer payments. The consumption function is thus of the following

form: C = C0 + c(Y - TA) + dTR, with c < d.

(a) What will happen to the equilibrium level of income and the budget surplus if

government purchases and taxes are both reduced by the same lump sum amount?

(b) What will happen to the equilibrium level of income and the budget surplus if

government transfers are reduced by the same lump sum amount as taxes?

(a). Assume that TA0 - G = -100

Y = [(- c)/(1 - c')( TA0) + [1/(1 - c')](G) = [(1 - c)/(1 - c')](- 100) < 0), that is,

national income (Y) will decrease since c < J and c' = c(l -1).




BS = t(Y) + TA0 - G = t(Y) < 0 since TA0 = G and Y < 0

The budget surplus will decrease by the loss in income tax revenue.

(b). Assume that TA0 = TR0 = - 100

Y = [(- c)/(1 - c')]( TA0) + [d/(1 - c')][ TR0) = [(d - c)/(l - c')](-100) < 0, that is,

national income will increase since c < d and c' = c(1 - t).

BS = t(Y) + TA0 - TR0 = t(Y) < 0 since TA0 = TR0 and (Y) < 0

The budget surplus will decrease.

17. Assume a simple model of the expenditure sector with a positive income tax rate (t).

Show mathematically how an increase in lump sum taxes (TA0) would affect the budget

surplus.

Assume the following model of the expenditure sector:

Sp = C + I + G + NX I = I0

C = C0 + cYD G = G0

YD = Y - TA + TR NX = NX0

TA = TA0 + tY BS = TA - G - TR

TR = TR0

From Y = Sp Y = C0 + c(Y - TA0 - tY + TR0) + I0 + G0 + NX0

Y = C0 - cTA0 + cTR0 + I0 + G0 + NX0 + c(1 - t) Y = A0 + c'Y

Y = [1/(1 - c')]A0 with c' = c (1 - t) and A0 = C0 - cTA0 + cTR0 + I0 + G0 + NX0

Thus Y = [1/(1 - c')]( A0) = [1/(1 - c')][(- c) (TA0)]

From BS = TA - G - TR = tY + TA0 - G - TR

and BS - t(Y) + (TA0) - {[t(- c)]/(l - c') + 1}(TA0)

= t[1/(1 - c + ct)](- c)(TA0) + TA0 = ([- ct/(1 - c + ct)] + 1)(TA0)

= ([- ct + 1 - c + ct]/[1 - c + ct])( TA0) = [(1 - c) /(1 - c + ct)]( TA0) > 0, since c < 1

In other words, a lump sum tax increase would increase the budget surplus.




18. Is the size of the actual budget surplus always a good measure for determining fiscal

policy? What about the size of the full-employment budget surplus?

The actual budget surplus has a cyclical and a structural component. The cyclical

component of the budget surplus changes with changes in the level of income whether or

not any fiscal policy measure is implemented. This implies that the actual budget surplus

also changes with changes in income and is therefore not a very good measure for

assessing fiscal policy. The structural (full-employment) budget surplus is calculated

under the assumption that the economy is at full-employment. It changes only with a

change in fiscal policy and' is therefore a much better measure for fiscal policy than the

actual budget surplus. One should keep in mind, however, that the balanced budget

theorem implies that the government can stimulate national income by an equivalent and

simultaneous increase in taxes and government purchases without affecting the actual or

the full-employment budget surplus. In addition, estimates of the true value of the full-

employment budget surplus largely depend on the assumptions that lead to the calculation

of the full-employment output level.

19. True or false? Why?

“The higher the marginal propensity to import, the lower the size of the multiplier.”

True. Imports represent a leakage out of the income flow. An increase in autonomous

spending will raise income and we will see the usual multiplier effect. However, if

imports are positively related to income, this effect is reduced since higher imports

reduce the level of domestic demand. (Assume for simplicity that TA = TR = 0 in both

cases below.)

Closed Economy Model Open Economy Model

Sp = C + I + G Sp = C + I + G + NX

C = C0 + cY C = C0 + cY

G = G0 G = G0

I = I0 I = I0

NX = NX0 - mY with 0 < m < 1

From Y = Sp

Y = (C0 + I0 + G0) + cY Y = (C0+ I0 + G0 + NX0) + (c - m)Y

Y = A0 + cY Y = A0 + (c - m)Y

Y = [1/(1 - c)]A0 Y = [1/(1 - c + m)]A0

Therefore the multiplier is defined as

[1/(1 - c)] [1/(1 - c + m)]

Clearly the open economy multiplier is smaller than the closed economy multiplier. This

is because leakages reduce demand. If income taxes were included in these models, they

too would reduce the multipliers, as income taxes represent another leakage from the

income flow.

179863074 dornbusch chapter 3 solution docx

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