Question

Use the table below to answer the following questions. All data are in $ billions.

Real GDP
Consumption (C)

$ 500
$ 495

510
504

520
513

530
522

540
531

550
540

560
549

Determine the size of the multiplier from the above data. Show your working.

Determine the equilibrium real GDP if taxes are zero, government purchases are $5, investment is $3, and net exports are zero. Show your working and explain your answer.

Determine the equilibrium real GDP if taxes are $10, government purchases are $10, investment is $6, and net exports are zero. Show your working and explain your answer.

Assume investment is $50, taxes are $50, net exports and government purchases are each zero and the full-employment level of GDP is $545. Identify the type of expenditure gap that occur and determine the amount of taxes needed to be changed in order to eliminate the gap. Show your working and explain your answer.

Assume that investment, net exports, and taxes are zero, while the government purchases are $30 and the full-employment GDP is $530. Identify the type of expenditure gap that occur and determine the amount of government spending needed to be changed in order to eliminate this gap. Show your working and explain your answer.

Answer 1

Real GDP	Consumption
500	495
510	504
520	513
530	522
540	531
550	540
560	549

1) now we will find the size of the multiplier.

MPC = Change in Consumption / Change in Real GDP

= (504 - 495) / (510 - 500)

= 9 / 10

= 0.9

Multiplier = 1 / (1 - MPC)

= 1 / (1 - 0.9)

= 1 / 0.1

= 10

Therefore, Multiplier = 10

2)  if taxes are zero, government purchases are $5, investment is $3, and net exports are zero.

Now we will find the equilibrium real GDP

Consumption function: C = a + b x Y ------(1)

When Y = 500, C = 495

495 = a + 0.9 x 500

495 = a + 450

a = 495-450

a = 45

Substitute 'a'value in (1)

C = 45 + 0.9Y

In equilibrium, Y = C + I + G

Y = 45 + 0.9Y + 3 + 5

Y = 53 + 0.9Y

Y - 0.9Y = 53

0.1Y = 53

Y = 53/0.1 = 53*10/1 = 530

Therefore, Equilibrium Y = 530

3) if taxes are $10, government purchases are $10, investment is $6, and net exports are zero.

Now we will find the equilibrium real GDP

C = 45 + 0.9(Y - T)

In equilibrium,

Y = 45 + 0.9 x (Y - 10) + 6 + 10

Y = 61+0.9*Y - 0.9*10

Y = 61 + 0.9Y - 9

Y - 0.9Y = 61-9

0.1Y = 52

Y = 52/0.1 = 52*10/1 = 520

Therefore, Equilibrium Y = 520

4) Assume investment is $50, taxes are $50, net exports and government purchases are each zero and the full-employment level of GDP is $545.

Output gap = 545 - 500 = 45

Tax multiplier = - MPC / (1 - MPC) = - 0.9 / 0.1 = 9

As tax falls by $1, real GDP rises by $9.

To increase real GDP by $45,

required decrease in tax = $45 / 9 = $5

Therefore, required decrease in tax = $5

(5) Assume that investment, net exports, and taxes are zero, while the government purchases are $30 and the full-employment GDP is $530.

Output gap = 560 - 530 = 30

Spending multiplier = 10

As government spending falls by $1,

real GDP falls by $10.

To reduce real GDP by $30,

Government spending should be cut by ($30 / 10) = $3.

Government spending should be cut by = $3.