Question

In: Economics

Given the following data for a hypothetical closed economy: Real GDP (GDP = Y) Taxes Yd...

Given the following data for a hypothetical closed economy:

Real GDP

(GDP = Y)

Taxes

Yd

C

S

I

G

AE

200

50

190

80

50

250

50

220

80

50

300

50

250

80

50

350

50

280

80

50

400

50

310

80

50

450

50

340

80

50

500

50

370

80

50

550

50

400

80

50

600

50

430

80

50

650

50

460

80

50

700

50

490

80

50

  1. Fill-in the table.

  1. Determine the Breakeven for the economy.

  1. Determine the equilibrium GDP for the economy.
  1. Calculate the expenditure multiplier.
  1. Now suppose that the potential GDP equals 440, by how much should the government purchases or tax change to reach the potential GDP.
  1. Drive consumption or saving equations. (show your work)

Solutions

Expert Solution

(I)

Working notes:

  • Disposable income (Yd) = Y - T
  • S = Y - C
  • AE = C + I + G

Y

T

Yd

C

S

I

G

AE

200

50

150

190

10

80

50

320

250

50

200

220

30

80

50

350

300

50

250

250

50

80

50

380

350

50

300

280

70

80

50

410

400

50

350

310

90

80

50

440

450

50

400

340

110

80

50

470

500

50

450

370

130

80

50

500

550

50

500

400

150

80

50

530

600

50

550

430

170

80

50

560

650

50

600

460

190

80

50

590

700

50

650

490

210

80

50

620

(II)

Breakeven occurs when Y = AE, which holds true when Y = 500

(III)

Equilibrium GDP (Y) = 500

(IV)

Government Spending Multiplier = Change in Y / Change in AE = (250 - 200) / (350 - 320) = 500 / 300

= 5/3 = 1.67

(V)

MPC = Change in C / Change in Y = (220 - 190) / (250 - 200) = 30/50 = 0.6

Tax multiplier = - MPC / (1 - MPC) = - 0.6/0.4 = - 1.5

Inflationary gap = Equilibrium Y - Potential G = 500 - 440 = 60

Required decrease in G = Inflationary gap / Government Spending multiplier = 60 / (5/3) = 36

Required increase in T = Inflationary gap / Absolute value of Tax multiplier = 60 / 1.5 = 40

(VI)

(a) Consumption function: C = a + bY

190 = a + 200b..............(1)

220 = a + 250b..............(2)

(2) - (1) results in:

50b = 30

b = 0.6

a = 190 - 200b [using equation (1)] = 190 - (200 x 0.6) = 190 - 120 = 70

Hence,

C = 70 + 0.6Y

(b) Saving function: S = Y - C

S = Y - 70 - 0.6Y

S = - 60 + 0.4Y


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