Consider planned aggregate expenditure model: planned investment, i = $60 billion; government spending g = $50 billion; taxes are equal to $60 billion; the consumption function, c(y-t)= $80 billion + .75(y-t).
a. what is the equilibrium level of output?
b. if output in the economy started at 600 billion, what would happen to inventories and output?
c. at the equilibrium level of output: what are total consumption and savings?
d. if taxes decreased to $50 billion, what would be the new level of equilibrium output? calculate the tax multiplier?
e. if taxes stayed at $60 billion but government spending increased to $60 billion, what would be the new level of equilibrium output? calculate the government spending multiplier? how would your answers change to c, d, and e if the consumption function were instead c(y-t)= $80 billion + 0.80(y-t).

The answer is (a) Y = 520, (b) Y = 2,720, (c) (I) Y = 560, (II) Y = 560, (d) (I) Y = 560, (II) M = 3, (e) (I) Y = 560, (II) Government Multiplier = 40billion, (III) Y = 700

(a)

Explanation:

(a)

Given that

Y = I + G + ca + 0.75 ( Y - T)

Where ca = autonomous consumption, Y - T = disposable income

Substitute into the equation

Y = 60 + 50 + 80 + 0.75 ( Y - 60)

Rearrange the equation

Y - 0.75Y = 60 + 50 + 80 - 60

Factor out the variable Y

(1 - 0.75) Y = 190 - 60

Simplify

0.25Y = 130

Divide both sides by 0.25

0.25Y/0.25 = 130/0.25

Y = 520

(b)

Y = C + I + G

Since the value of output depends on the household's intention to consume

Substitute into the equation

Y = 80 + 0.75 + 600

Rearrange the equation

Y - 0.75Y = 80 + 600

Factor out the variable Y

(1-0.75)Y = 680

Simplify

0.25Y = 680

Divide both sides by 0.25

0.25Y /0.25 = 680/0.25

Y = 2,720

(c)I

Y = C + I

Y = 80 + 60

Rearrange the equation

Y - 0.75Y = 80 + 60

Factor out the variable Y

(1-0.75)Y = 80 + 60

Simplify

0.25Y = 140

Divide both sides by 0.25

0.25Y /0.25 = 140/0.25

Y = 560

(II)

Equilibrium condition S = I

C = 80 + 0.75Y =60

Rearrange the equation

Y - 0.75Y = 80 + 60

Factor out the variable Y

(1-0.75)Y = 80 + 60

Simplify

0.25Y = 140

Divide both sides by 0.25

0.25Y /0.25 = 140/0.25

Y = 560

(d)(I)

Y = I + G + ca + 0.75 (Y -T )

Where ca = autonomous consumption, Y - T = disposable income

Substitute into the equation

Y = 60 + 50 + 80 + 0.75 (Y -50)

Rearrange the equation

Y - 0.75Y = 60 + 50 + 80 - 50

Factor out the variable Y

(1-0.75)Y = 190 - 50

Simplify

0.25Y = 140

Divide both sides by 0.25

0.25Y /0.25 = 140/0.25

Y = 560

(II)

Tax Multiplier = -MPC/(1-MPC)

Because there is a decrease in tax,then the multiplier will be positive, because there is now more money in the circular flow

M= MPC /(1-MPC )

M = 0.75/(1-0.75)

0.75/0.25

= 3

The tax multiplier is 3

(e)(I)

Y = I + G + ca + 0.75 (Y -T)

Substitute into the equation

Y = 60 + 60 + 80 + 0.75 (Y -60)

Rearrange the equation

Y-0.75Y = 60 + 60 + 80 - 60

Factor out the variable Y

(1-0.75)Y = 200 - 60

Simplify

0.25Y =140

Divide both sides by 0.25

0.25Y /0.25 = 140/0.25

Y = 560

(II)

K = ▲Y/▲G

K= 1/1-MPC

K = 1/1-0.75

K = 1/0.25

K = 4

K = ▲Y/▲G

▲G = (60-50) =10

4 = ▲Y/10

Cross multiply

▲Y = 4 × 10

▲Y = 40 billion

(e)(III)

How would the answer change, if consumption function were

C (Y -T )=80billion + 0.80 (Y -T )

Y = I + G + ca + 0.75 (Y -T )

Substitute into the equation

Y = 60 + 50 + 80 + 0.80 (Y -50)

Rearrange the equation

Y - 0.80Y = 60 + 50 + 80 - 50

Factor out the variable Y

(1-0.80)Y = 190 - 50

0.2Y = 140

Divide both sides by 0.2

0.2Y /0.2 = 140/0.2

Y = 700

a manufacturer of printed circuit boards uses exponential smoothing with trend to forecast monthly demand of its product. at the end of december, the company wishes to forecast sales for january. the estimate of trend through november has been 200 additional boards sold per month. average sales have been around 1000 units per month. the demand for december was 1100 units. the company uses α = 0.20 and β = 0.10. make a forecast including trend for the month of january.