Question

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.

2. Determine the Breakeven for the economy.

3. Determine the equilibrium GDP for the economy.

4. Calculate the expenditure multiplier.

5. Now suppose that the potential GDP equals 440, by how much should the government purchases or tax change to reach the potential GDP.

6. Drive consumption or saving equations. (show your work)

Answer 1

(I)

• 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)

In breakeven, Y = AE = 500

(III)

Equilibrium GDP = 500

(IV)

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

Positive output gap = Equilibrium Y - Potential G = 500 - 440 = 60

Required decrease in G = Positive output gap / Spending multiplier = 60 / (5/3) = 36

Required increase in T = Positive output gap / Tax multiplier = 60 / 1.5 = 40

(VI)

(a) Consumption: C = a + bY

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

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

(2) - (1) yields:

50b = 30

b = 0.6

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

Therefore,

C = 70 + 0.6Y

(b) Saving: S = Y - C

S = Y - 70 - 0.6Y

S = - 60 + 0.4Y