Question

Table 6.9 shows some of the expenditure amounts in the economy of Arkinia. The MPC, the MTR, and the MPM are all constant, as are the values of the three injections.

Y	T	YD	C	S	I	G	X	IM	XN	AE (C + I + G + XN)
0					60	150	50
100		50		−10					30
200	75		120	5
300	100		180					40
400	125			35				50
500			300					60
600		425
700			420
800		575		95					−40
TABLE 6.9

a) Complete Table 6.9, and in Figure 6.12 graph a 45° line and the aggregate expenditure function, labelled AE₁. Identify expenditure equilibrium with the letter e₁.

Answer 1

It shall be noted that MPC, MTR, and MPM are constant.

(C1,Y1) = (120, 200)

(C2, Y2) = (180, 300)

The MPC = (C2-C1)/(Y2-Y1) = (180-120)/(300-200) = 60/100 = 0.6

C = MPC*Y

YD = Y - T

C + S = YD

(Y1, T1) = (200 , 75)

(Y2, T2) = (300, 100)

The MTR = (T2-T1)/(Y2-Y1) = (100-75)/(300-200)

= 25/100

=0.25

T = 25 + MTR*Y

(M1, Y1) = (40, 300)

(M2, Y2) = (50, 400)

The MPM = (M2-M1)/(Y2-Y1) = (50-40)/(400-300)

=10/100

=0.10

M = 10 +MPM*Y

I = 60

G = 150

X = 50

XN = X - M

Thus, the complete table is:

Y	T	YD	C	S	I	G	X	IM	XN	AE
										(C + I +
										G + XN)
0	25	-25	0	-25	60	150	50	10	40	250
100	50	50	60	-10	60	150	50	20	30	300
200	75	125	120	5	60	150	50	30	20	350
300	100	200	180	20	60	150	50	40	10	400
400	125	275	240	35	60	150	50	50	0	450
500	150	350	300	50	60	150	50	60	-10	500
600	175	425	360	65	60	150	50	70	-20	550
700	200	500	420	80	60	150	50	80	-30	600
800	225	575	480	95	60	150	50	90	-40	650

On graphing the 45-degree line and AE1, the result is:

The expenditure equilibrium is identified with the letter e₁