Suppose that Cascadias economy is described by the following

Suppose that Cascadia\'s economy is described by the following equations: C-200+.75YD 1-100 Z-C+I+G with YD=Y-T G-200 T= 100 where C is consumption, Yo is disposable income, Y is output (income), T is tax, I is autonomous investment, G is government spending, and Z is aggregate spending (demand)

Solution

(a)

Consumption is as follows -

C = 200 + 0.75Y_D

Coefficient of Y_D in above equation represents MPC.

So,

MPC = 0.75

Calculate the government spending multiplier -

Government spending multiplier = 1/(1-MPC) = 1/(1-0.75) = 1/0.25 = 4

The government spending multiplier is 4.

(b)

At equilibrium,

Aggregate spending equals Income

or,

Z = Y

C + I + G = Y                                [Z = C + I + G]

Y = 200 + 0.75Y_D + 100 + 200

Y = 200 + 0.75(Y - T) + 100 + 200

Y = 500 + 0.75(Y - 100)

Y = 500 + 0.75Y - 75

0.25Y = 425

Y = 425/0.25 = 1,700

The initial equilibrium level of income is 1,700.

Calculate the increase in income -

Increase in income = Increase in government spending * Government spending multiplier

Increase in income = $25 * 4

Increase in income = $100

The increase in income is $100.

Calculate the new level of income -

New level of income = Initial level of income + Increase in income = $1,700 + $100 = $1,800

The new level of income is $1,800.

(c)

Consumption at the initial level of income -

C = 200 + 0.75Y_D = 200 + 0.75(Y - T) = 200 + 0.75(1,700 - 100) = 1,400

Consumption at the new level of income -

C = 200 + 0.75Y_D = 200 + 0.75(Y - T) = 200 + 0.75(1,800 - 100) = 1,475

Increase in consumption = Consumption at the new level of income - Consumption at the initial level of income

Increase in consumption = 1,475 - 1,400 = 75

So,

The increase in consumption is 75.

The new level of consumption is 1,475

(d)

Government spending after increase = $200 + $25 = $225

T = $100

Calculate the budget surplus -

Budget surplus = T - G = 100 - 225 = -125

The Budget Surplus is -125.