Tutorial 6 - Answers

8/11/2019 Tutorial 6 - Answers

1/8

ECON 211 FC 2011

Tutorial 6 Answers

1. (a) Total planned expenditure is

E C Y T I G

Plugging in the consumption function and the values for investment I, government

purchases G, and taxes T given in the question, total planned expenditureE is

E = 200 0.75 100 100 100Y

= 0.75 325Y

(b) To find the equilibrium level of income, combine the planned-expenditure equation derived

in part (a) with the equilibrium condition Y E :

Y = 0.75 325Y

Y =1,300

The equilibrium level of income is 1,300.

(c) If government purchases increase to 125, then planned expenditure changes to

0.75 350E Y . Equilibrium income increases to 1,400.Y Therefore, an increase in

government purchases of 25 (i.e., 125 100 125 ) increases income by 100. This is what

we expect to find, because the government purchases multiplier is 1/ 1 MPC : becausetheMPC is 0.75, the government-purchases multiplier is 4.

(d) A level of income of 1,600 represents an increase of 300 over the original level of income.

The government purchases multiplier is 1/ 1 MPC : the MPC in this example equals0.75, so the government-purchases multiplier is 4. This means that government purchases

must increase by 75 (to a level of 175) for income to increase by 300.

325

45

0.75 325E Y

Y E

E

*1,300Y

Income, output

Y

Planned

expenditure


2/8

-2-

2. (a) If the central bank increases the money supply, then the LM curve shifts downward.

Income increases and the interest rate falls. The increase in disposable income causes

consumption to rise; the fall in the interest rate causes investment to rise as well.

(b) If government purchases increase, then the government-purchases multiplier tells us that theIS curve shifts to the right by an amount equal to 1/ 1 MPC G . Income and the

interest rate both increase. The increase in disposable income causes consumption to rise,

while the increase in the interest rate causes investment to fall.

2r

1r

Interestrate

1Y

2Y

Y

2IS

1IS

LM

B

A

1

G

MPC

r

Income, output

B

IS

A1r

2r

1Y

2Y

Income, output

Y

1LM

2LM

r

Interestrate


3/8

-3-

(c) If the government increases taxes, then the tax multiplier tells us that the IS curve shifts to

the left by an amount equal to / 1MPC MPC T . Income and the interest rate both

fall. Disposable income falls because income is lower and taxes are higher; this causes

consumption to fall. The fall in the interest rate causes investment to rise.

1r

2r

Interestrate

2Y

1Y

Y

1IS

2IS

LM

A

B

1

MPCT

MPC

r

Income, output


4/8

-4-

(d) We can figure out how much the IS curve shifts in response to an equal increase in

government purchases and taxes by adding together the two multiplier effects that we used

in parts (b) and (c):

1/ 1 / 1Y MPC G MPC MPC T

Because government purchases and taxes increase by the same amount, we know that

G T . Therefore, we can rewrite the above equation as:

1/ 1 / 1Y MPC MPC MPC G

Y G

This expression tells us how output changes, holding the interest rate constant. It says that

an equal increase in government purchases and taxes shifts the IScurve to the right by the

amount that Gincreases.

Output increases, but by less than the amount that G and T increase; this means that

disposable income Y T falls. As a result, consumption also falls. The interest rate rises,

causing investment to fall.

2r

1r

Interestrate

1Y

2Y Y

2IS

1IS

LM

B

A

G

r

Income, output


5/8

-5-

3. (a) TheIScurve is given by:

Y = C Y T I r G

We can plug in the consumption and investment functions and values for Gand Tas given

in the question and then rearrange to solve for theIScurve for this economy:

Y = 200 0.75 100 200 25 100Y r 0.75Y Y = 425 25r

1 0.75 Y = 425 25r

Y = 1 / 0.25 425 25r Y =1,700 100r

(b) The LM curve is determined by equating the demand for and supply of real money

balances. The supply of real balances is 1,000/ 2 500 . Setting this equal to money

demand, we find:

500 100Y r

500 100Y r

(c) If we take the price level as given, then theISand theLMequations give us two equations

in two unknowns, Yand r. We found the following equations in parts (a) and (b):

: 1, 700 100IS Y r

: 500 100LM Y r

Equating these, we can solve for r:

1,700 100r = 500 100r

1,200 20r = 20r

r = 6

Now that we know r, we can solve for Y by substituting it into either the IS or the LM

equation. We find

1,100Y

Therefore, the equilibrium interest rate is 6 percent and the equilibrium level of output is

1,100.

r

6

8

0 500

1,100

1,700 Y

IS LM

Interestrate

Income, output


6/8

-6-

(d) If government purchases increase from 100 to 150, then theISequation becomes:

200 0.75 100 200 25 150Y Y r

Simplifying, we find:

Y = 1,900 100r

We see that theIScurve shifts to the right by 200

By equating the new IScurve with the LMcurve derived in part (b), we can solve for the

new equilibrium interest rate:

1,900 100r = 500 100r

1,400 = 200r

7 = r

We can now substitute r into either the IS or the LM equation to find the new level of

output. We find

Y =1,200

Therefore, the increase in government purchases causes the equilibrium interest rate to risefrom 6 percent to 7 percent, while output increases from 1,100 to 1,200.

0500 1,100 1,200 1,700 1,900 Y

200

LM1

IS 2

IS

6

7

8

r

Interestrate

Income out ut


7/8

-7-

(e) If the money supply increases from 1,000 to 1,200, then theLMequation becomes:

1, 202 / 2 100Y r or

600 100Y r

We see that the LMcurve shifts to the right by 100 because of the increase in real money

balances.

To determine the new equilibrium interest rate and level of output, equate the IScurve from

part (a) with the newLMcurve derived above:

1,700 100r = 600 100r

1,100 = 200r

5.5 = r

Substituting this into either theIS or theLMequation, we find

Y = 1,150

Therefore, the increase in the money supply causes the interest rate to fall from 6 percent to

5.5 percent, while output increases from 1,100 to 1,150.

IS1

LM

2LM

1,700 Y1,1006005000

5.5

Interestrate

100

r

6.0

1,150

Income, output


8/8

-8-

(f) If the price level rises from 2 to 4, then real money balances fall from 500 to

1,000/ 4 250 . TheLMequation becomes:

250 100Y r

The LM curve shifts to the left by 250 because the increase in the price level reduces realmoney balances.

To determine the new equilibrium interest rate, equate the IS curve from part (a) with the

newLMcurve from above:

1,700 100r = 250 100r

1,450 = 200r

7.25 = r

Substituting this interest rate into either theISor theLMequation, we find

Y = 975

Therefore, the new equilibrium interest rate is 7.25, and the new equilibrium level of output

is 975.

________________________

7.25

6.0

r IS

2LM

1LM

250

0250 600 1,100 1,700 Y

Intere

strate

Income, output

975

Documents

Tutorial 6 - Answers