Question

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

C=30+0.75Y_d

I_I = 15

G = 10

T=30

TR=10

The full employment level of output in the economy is: Y_FE = 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? Y_E =

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 government spending multiplier in this economy?

vi. If government spending increased by 10 (so the new level of government spending were equal to G'=20), what would the new equilibrium level of output be? Y_E' =

Answer 1

(i) Disposable income (YD) = Y - T + TR = Y - 30 + 10 = Y - 20

Aggregate demand (AD) = C + I + G

AD = 30 + 0.75(Y - 20) + 15 + 10

AD = 55 + 0.75Y - 15

AD = 40 + 0.75Y

(ii) Equilibrium holds when Y equals AD.

Y = 40 + 0.75Y

(1 - 0.75)Y = 40

0.25Y = 40

YE = 40/0.25 = 160

(iii) Unintended inventory investment: Yes

An Income of $300is more than the equilibrium income (YE) computed above, so the firms are unable to sell all of their production and output. This leads to unintended (unplanned) inventory accumulation.

(iv) Excess inventory accumulation ($) = Income - YE = 300 - 160 = 140

(v) Government Spending multiplier = 1 / (1 - MPC) = 1 / (1 - 0.75**) = 1 / 0.25 = 4

**Coefficient of YD in consumption function is the MPC.

(vi) When Government spending increases by $10, Y increases by ($10 x 4) = $40. Therefore,

New value of YE (YE') = $160 + $40 = $200