Question

The data in the table below are for the economy of Nubia.

a. Complete the AE column.

Y	T	YD	C	S	I	G	X	IM	XN	AE
0	80	−80	20	−100	40	105	170	60	110
300	95	205	260	−55	40	105	170	75	95
600	110	490	500	−10	40	105	170	90	80
900	125	775	740	35	40	105	170	105	65
1,200	140	1,060	980	80	40	105	170	120	50

b. Write out expressions for the tax function, the consumption function (related to national income [Y]), the net export function, and the AE function. Round your answers to 2 decimal places.

T	=	(Click to select)  +  −    (Click to select)  C  G  S  Y
C	=	(Click to select)  +  −    (Click to select)  C  G  S  Y
XN	=	(Click to select)  +  −    (Click to select)  C  G  S  Y
AE	=	(Click to select)  +  −    (Click to select)  C  G  S  Y

c. Use algebra to find out the value of equilibrium income. Round your answer to the nearest whole dollar.

    Equilibrium income is $  .

Answer 1

(a)

Y	T	YD	C	S	I	G	X	IM	Xn	AE
0	80	-80	20	-100	40	105	170	60	110	275
300	95	205	260	-55	40	105	170	75	95	500
600	110	490	500	-10	40	105	170	90	80	725
900	125	775	740	35	40	105	170	105	65	950
1200	140	1060	980	80	40	105	170	120	50	1175

AE = C + I + G + Xn

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(b)

Tax function:

T = T0 + tY

Where T0 is autonomous tax revenue. It is equal to tax revenue at Y=0

t is tax rate. i.e., t = ΔT/ ΔY

---

When Y=0, then T is 80. It means T0 =80

When Y = 300, then T is 95

=> ΔY = 300 - 0

=> ΔY = 300

and

ΔT = 95 -80

=> ΔT = 15

Hence, t = ΔT/ΔY

=> t = 15 / 300

=> t = 0.05

Tax function: T = T0 + tY

=> T = 80 + 0.05Y

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Consumption function:

C = C0 + MPC * Y

Where C0 is autonomous Consumption. It is equal to consumption at Y=0

MPC is marginal propensity to consumer. i.e., MPC = ΔC/ ΔY

---

When Y=0, then C is 20. It means C0 =20

When Y = 300, then C is 260

=> ΔY = 300 - 0

=> ΔY = 300

and

ΔC = 260 - 20

=> ΔC = 240

Hence, MPC = ΔC/ΔY

=> MPC = 240 / 300

=> MPC  = 0.8

Consumption function: C = C0 + MPC * Y

=> C = 20 + 0.8Y

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Net export function (Xn)

Xn = Xno + xn * Y

Where Xno is net export at zero level of Y

xn is slope of net export fucntion; i.e., xn = ΔXn / ΔY

When Y=0, then Xn is 110. It means Xno is 110

When Y = 300, then Xn  is 95

=> ΔY = 300 - 0

=> ΔY = 300

and

ΔXn = 95 -110

=> ΔXn = -15

Hence, xn = ΔXn/ΔY

=>xn = -15 / 300

=> xn = -0.05

Net export function: Xn = Xno + xn * Y

=> Xn = 110 - 0.05 * Y

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Aggregate expenditrure function:

AE = AE0 + ae * Y

Where AE0 is aggregate expenditure at zero level of Y

ae is slope of AE function.

----

When Y=0, then AE is 275. It means AE0 is 275

When Y = 300, then AE is 500

=> ΔY = 300 - 0

=> ΔY = 300

and

ΔAE = 500 - 275

=> ΔAE = 225

Hence, ae = ΔAE /ΔY

=>ae = 225/ 300

=> ae = 0.75

Aggregate expenditure function: AE = AE0 + ae *Y

=> AE = 275 + 0.75Y

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(c) At equilibrium, Y = AE
=> Y = 275 + 0.75Y

=> Y - 0.75Y = 275

=> 0.25Y = 275

=> Y = (275 / 0.25)

=>Y = 1100

The equilibrium level of income is 1100