Given C=200+0.8Yd, I=300, G=350, T=300

a) Find the equilibrium level of income.

b) Find the value of the tax multiplier.

c) If there is an increase in Government expenditure of $50 that is financed by an equal increase in taxes, show the calculation of the impact on the equilibrium level of income.

d) Explain carefully the principle of your calculated result in (c) above.

Dear David,

1. The equilibrium condition is given as Y = C + I + G

Here, 
                        C         =          100 + 0.8Yd

                        C         =          100 + 0.8(Y – T)

                        C         =          100 + 0.8(Y – 0.10Y)

                        C         =          100 + 0.8(0.9Y)

                        C         =          100 + 0.72Y
Thus,
                        Y         =          100 + 0.72Y + 200 + 180

            Y – 0.72 Y      =          100 + 200 + 180

                        0.28Y  =          480

                        Y         =          480 / 0.28

The equilibrium level of income is $1,714.28 millions.

2. The revenue from taxes at the equilibrium level of income.

The tax function is a proportional income tax function where T = 0.10Y

Thus, T = 0.10(1,714.28)        =          171.42 million dollars

Hence the revenue from taxes at the equilibrium level of income is at $171.42 millions where as the government expenditure is at $180 millions. Therefore, there is a budget deficit of $8.58 millions.

3. When there is an increase in investment from $200 millions to $240 millions,

                        Y         =          100 + 0.72Y + 240 + 180

            Y – 0.72Y       =          100 + 240 + 180

                        0.28Y  =          520

                        Y         =          520 / 0.28

The equilibrium level of income is 1,857.14 million dollars.

4. The revenue from taxes at the new equilibrium level of income is

                           T          =          0.10 (1,857.14)
               
   =          185.714 million dollars

   Hence, the revenue from taxes at the equilibrium level of income is $ $185.714 millions whereas the government expenditure is at 180 million dollars. Therefore, there is a budget surplus of $5.714 millions. Due to the higher income level, there are larger tax revenues leading to a budget surplus.

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