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Extensions of IS-LM Model - Inclusion of Government Sector

Illustration 69

Presume the consumption and investment functions are as below:

C = 100 + 0.75 (Y – 0.45Y)

I = 400 – 4r

G = 200

Find the Equation of the IS Curve and

Find the Equation of the IS Curve when government outlay enhances by $ 80.

Solution

Equation of the IS Curve

Y = C + I + G

Y = 100 + 0.75 (Y – 0.45Y) + 400 – 4r + 200

Y = 700 + 0.75(0.55Y) – 4r

= 700 – 4r + 0.41Y

Y – 0.41Y = 700 – 4r

0.59Y = 700 – 4r

Y = 700 – 4r
0.59

Y = 1,186 – 6.8r

Equation of the IS curve when government outlay enhances by $ 80,

Y = C + I + G

Y = 100 + 0.75(Y – 0.45Y) + 400 – 4r + 280

Y = 780 – 4r + 0.75(0.55Y)

            =          780 + 0.41Y – 4r

                        Y – 0.41Y       =          780 – 4r

Y = 780 – 4r
0.41

Y = 1902 – 9.8r

Illustration 70

Presume the consumption and investment functions and the government outlay are as below:

C = 100 + 0.6 (Y – 40)

I = 300 – 20r

G = $ 240 millions

Suppose that the money supply is $ 392 millions, the money demand function is md = 0.5Y – 12r

Determine the Equation of the IS Curve

Determine the Symmetry of the LM curve

Determine the Concurrent Symmetry for the IS and LM curves

Determine the Concurrent Symmetry for the IS and LM curves when government outlay enhances by $ 110 millions.

Solution

(1) Equation of the IS Curve

Y = C + I + G

Y = 100 + 0.6 (Y – 40) + 300 – 20r + 240

Y = 740 – 20r + 0.6Y – 24

Y = 716 – 20r + 0.6Y

Y – 0.6Y = 716 – 20r

0.4Y = 716 – 20r

Y = 716 – 20r
0.4

Y = 1,790 – 50r

(2) Equation of the LM curve md = 0.5Y – 12r

ms = 392

In symmetry, md = ms.

0.5Y – 12r = 392

0.5Y = 392 + 12r

Y = 392 + 12r
0.5

Y = 784 + 60r

Concurrent Symmetry for the IS curve and LM curves

IS = LM

1,790 – 50r = 784 + 60r

110r = 1790 – 784

r = 1006 / 110

r = 9.2%

Y = 1790 – 50 * 9.2

Y = 1,330

Concurrent symmetry for the IS curve and LM curve subsists when Y = 1,330 and r = 9.2%.

Concurrent symmetry for the IS curve and LM curve when government outlay enhances by $ 110 millions.

IS Equation Y = C + I + G

Y = 100 + 0.6 (Y – 40) + 300 – 20r + 350

Y = 750 + 0.6Y – 24 – 20r

Y = 726 + 0.6Y – 20r

Y – 0.6Y = 726 – 20r

0.4Y = 726 – 20r

Y = 726 – 20r
0.4

Y = 1,815 – 50r

LM Equation stays unaffected at

Y = 784 + 60r

Concurrent symmetry for the IS curve and LM curve is as follows:

IS = LM

1,815 – 50r = 784 + 60r

110r = 1,031

r = 1,031 / 110

r = 9.4%

Y = 1,815 – (50 * 9.4)

Y = 1,815 – 470

Y = 1,345

Concurrent symmetry for the IS curve and LM curves subsists when Y = 1,345 and r = 9.4%.

Illustration 71

Suppose that the consumption and investment functions are as below:

C = 100 + 0.4Yd

I = 400 – 4r

G = 260

Ascertain the following:

The Equation of the IS Curve

The equation of the IS Curve when the following,

Government Outlay enhances by $100 millions
Taxes enhances by $100 millions
Government Outlay enhances by $100 millions and taxes by $100 millions
Ascertain the position of the curve

Solution

Equation of the commodities market symmetry or the IS Curve Y = C+ I + G

Y = 100 + 0.4Yd + 400 – 4r + 260

Y = 760 – 4r + 0.4(Y – 0)

Y = 760 – 4r + 0.4Y

Y – 0.4Y = 760 – 4r

0.6Y = 760 – 4r

Y = 760 – 4r
0.6

Y = 1,267 – 6.7r

Equation of the IS Curve

Government Outlay enhances by $100 millions

                  Y         =          C + I + G

                  Y         =          100 + 0.4Yd + 400 – 4r + 360

Y = 100 + 0.4 (Y-0) + 400 – 4r + 360

Y = 860 + 0.4Y – 4r

Y – 0.4Y = 860 – 4r

0.6Y = 860 – 4r

Y = 860 – 4r
0.6

Y = 1,433 – 6.7r

Taxes enhances by $100 millions

Y = C + I + G

Y = 100 + 0.4Yd + 400 – 4r + 260

Y = 100 + 0.4 (Y – 100) + 400 – 4r + 260

Y = 760 – 4r + 0.4Y – 40

= 720 – 4r + 0.4Y

Y – 0.4Y = 720 – 4r

0.6Y = 720 – 4r

Y = 720 – 4r
0.6

Y = 1,200 – 6.7r

Government outlay enhances by $100 millions and taxes by $100 millions.

This is the case of balanced budget.

Y = C + I + G

Y = 100 + 0.4 (Y – 100) + 400 – 4r + 360

Y = 860 – 4r + 0.4Y – 400

Y = 460 – 4r + 0.4Y

Y – 0.4Y = 460 – 4r

0.6Y = 460 – 4r

Y = 460 – 4r
0.6

Y = 767 – 6.7r

Position of the curve will contain the following points:
1. The nominal IS Curve, Y = 1,267 – 6.7r will be given by the IS1 curve.
2. The IS curve when government outlay enhances by $ 100 millions, Y = 1,433 – 6.7r is given by the IS curve IS2. This denotes a horizontal movement of $ 166 millions.
3. The IS curve when taxes enhances by $100 millions, Y = 1,200 – 6.7r and is given by the IS3 curve. This denotes a horizontal movement towards left of $ 67 millions from the IS1 curve.
4. The IS curve when government outlay enhances by $ 100 millions and taxes by $ 100 millions, Y = 767 – 6.7r is given by the IS4 curve. This denotes a horizontal movement towards the right of $ 100 millions. This is for the reason that ΔG = ΔT = 100 million dollars.

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