Question

The consumption function for a closed economy with a government sector is:

C = $2 trillion + .6Y_d, where Y_d = disposable income = Y – T, and

                        T = lump sum taxes = $2 trillion

Additionally, planned investment, I, is $1.5 trillion and government spending G, is

            $2.5 trillion.

1. Find Y* (equilibrium GDP). Find C and S. Find the size of the multiplier.
2. Assume the Y* you found above is below the full employment level of Y, which is $14.5 trillion. By how much must G be increased to reach full employment?

Answer 1

C = 2 + .6Yd = 2+ .6(Y-T) = 2 + .6(Y - 2) = 2 + .6Y - 1.2 = 0.8 + .6Y

a. Y = C + I + G = 0.8 + .6Y + 1.5 + 2.5 = 4.8 + .6Y
So, Y - .6Y = 4.8
So, .4Y = 4.8
So, Y = 4.8/.4 = 12

So, Y* = $12 trillion

C = 0.8 + .6Y = 0.8 + .6(12) = .8 + 7.2 = $8 trillion

At equilibrium, C + I + G = C + S + T
So, S = I + G - T = 1.5 + 2.5 - 2 = $2 trillion

Multiplier = 1/(1-MPC) = 1/(1-0.6) = 1/0.4 = 2.5
(MPC is taken from consumption function)

b. Change in Y required = 14.5 - 12 = $2.5 trillion

According to multiplier formula,
Change in Y/Change in G = multiplier
So, Change in G = Change in Y/multiplier = 2.5/2.5 = 1

So, G should be increased by $1 trillion to reach the full employment GDP