Suppose that the behavior of households and firms in an economy is determined by

Question

Suppose that the behavior of households and firms in an economy is determined by the following equations:

C=30+0.75Y

II = 25

The full employment level of output in the economy is: YFE = 300

i. Find an expression for aggregate demand (This should take the form of AD = a + bY, where a and b are numbers):

ii. What is the equilibrium level of output? YE =

iii. If, for some reason, income is equal to 300, would there be unintended inventory investment (yes or no)?

iv. What would the excess inventory accumulation (+) or depletion (-) be if income were equal to 300?

v. What is the multiplier in this economy?

vi. If intended investment increased by 10 (so the new level of intended investment were equal to II'=35), what would the new equilibrium level of output be? YE' =

Explanation / Answer

(a)

AD = C + I

AD = 30 + 0.75Y + 25

AD = 55 + 0.75Y

(b)

In equilibrium, AD = Y

Y = 55 + 0.75Y

0.25Y = 55

YE = 220

(c) Yes.

When income = 300, there would be unintended inventory investment because aggregate demand (AD) is lower than income (220 < 300).

(d)

Excess inventory accumulation = Income - YE = 300 - 220 = +80

(e)

MPC = 0.75 (From consumption function)

Multiplier = 1 / (1 - MPC) = 1 / (1 - 0.75) = 1 / 0.25 = 4

(f)

In new equilibrium,

Y = 30 + 0.75Y + 35

0.25Y = 65

YE' = 260

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