Answer to Question #236488 in Microeconomics for Marcelo

Question

Given the national income model Y=C+I+G. C=400+0.72Y; I=100 and G=90

a. b. c. d. e.

8. a. b.

Obtain the equilibrium level of output

What is the size of multiplier?

By how much will output increase when investment spending increases by 50%? Graphically demonstrate your answer in 7 (a)

How will your answers in 7 (a)–(d) change if the consumption function is now given as C = 400 + 0.72Yd where Yd = Y – T and the tax function is given as T = 40 + 0.15Y?

Answer 1

a)

$Y=C+I+G\\Y=400+0.72Y+100+90\\Y(1−0.72)=590\\Y=\frac{590}{0.28}\\=2107.14$

Therefore the equilibrium level of output is 2107.14.

b)

The multiplier is calculated as one divided by one minus MPC. The MPC is given as 0.72.

$Multiplier=\frac{1}{1−MPC}\\=\frac{1}{1−0.72}\\=3.57$

Therefore the size of the multiplier is 3.57

c)

If the investment spending increases by 50 percent, the investment spending will become 150. The equilibrium output is calculated as,

$Y(1−0.72)=400+150+90\\0.28Y=640\\Y=2285.71$

The initial equilibrium output is 2107.14 and the new output is 2285.71. The change in equilibrium output is calculated as,

Change in equilibrium output$=2285.71−2107.14=178.57$

Therefore the equilibrium output has increased by 178.57

The equilibrium in the economy occurs at the point where the aggregate expenditure is equal to the output. Graphically the equilibrium occurs when the aggregate expenditure schedule intersects the 45-degree line, as shown in the figure below.

d)

With the new consumption function, the equilibrium level of output is calculated as,

$Y=400+0.72Yd+100+90\\Y=400+0.72(Y−(40+0.15Y))+190\\Y=0.72Y−28.8−0.108Y+590\\Y=0.612Y+561.2\\0.388Y=561.2\\Y=1446.39$

Therefore the new equilibrium level of output is 1446.39. 

The new MPC is 0.612. The multiplier is calculated as,

$Multiplier =\frac{1}{1−0.612}\\=2.58$

The value of the multiplier is 2.58.

When the investment spending increased by 50 percent, the new investment spending becomes 150. The new equilibrium level of output is,

$0.388YY==611.2\\Y=1575.26$

The increase in equilibrium output is calculated as,

Change in equilibrium output$=1575.26−1446.39=128.87$

Therefore the equilibrium level of output has increased by 128.87 or 129 approximately.