In: Economics
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 |
(I)
Working notes:
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