Eco 200-810

Eco 200
Practice Worksheet: Aggregate Expenditure and the Multiplier

Consider the following model:

At what level of Y is there no saving? (hint: saving is zero when C=Y)

savings = 0 when C=Y = 350 + .75Y

.25Y = 350

Y = 1400

Solve for equilibrium AE.

AE=Y = C+I+G+X-IM = 350+.75Y + 170 + 140 - 10 = 650 + .75Y

Y = 650 + .75Y

.25Y = 650

Y = 2600

What happens to equilibrium expenditure if I falls to 100?

I falls from 140 to 100--a decrease of 40
change in equilibrium expenditure = initial change in spending x multiplier
multiplier = 1/(1-MPC) = 1/(1-.75) = 1/.25 = 4
so,

change in equilibrium expenditure = 40 x 4 = 160

equilibrium expenditures falls by 160 (to 2440)

G rises from 170 to 200--an increase of 30

change in equilibrium expenditure = 30 x 4 = 120

equilibrium expenditure rises by 120 (to 2720)

Suppose we wish to increase equilibrium AE to 3000 (from the original equilibrium AE) How much do we need to increase G?

original AE equilibrium = 2600 so we want an increase of 400

so we want to solve,

400 = change in G x multiplier = change in G x 4

change in G = 400/4 = 100

Consider the following model:

Solve for equilibrium AE. (Hint: do not forget to put taxes (T) is the consumption function!)

AE = Y = C+I+G+X-IM = 1000 + .8(Y- 2000) + 2100 +1600 = 4700 + .8(Y - 2000)

Y = 4700 + .8(Y-2000)

Y = 4700 +.8Y - .8(2000) = 4700 + .8Y - 1600 = 3100 + .8Y

.2Y = 3100

Y = 15,500

Suppose Congress and the President want to balance the budget. What happens to equilibrium if

(a) We balance the budget by increasing taxes so that T=G?

T = 2000 and G = 2100, so we are talking about the effect of a tax increase of 100 on equilibrium

the tax multiplier = MPC/(1-MPC) = .8/(1-.8) = 4

so, the total impact of a 100 tax increase is

4 x 100 = 400

so equilibrium will decrease by 400 if taxes rise to 2100

(b) We balance the budget by decreasing government purchases so that G=T?

T = 2000 and G = 2100, so we are talking about the effect of a decrease in G of 100 on equilibrium

the multiplier = 1/(1-MPC) = 1/(1-.8) = 5

so , the total impact of a 100 decrease in G is

5 x 100 = 500

so equilibrium will decrease by 500 if G falls to 2000

Suppose that when income increases by $1000, we expect consumers to increase their spending by $900. Given that, what is the impact of a $200 tax cut on equilibrium AE? (hint: what does the first sentence imply about the MPC?)

First, if C changes by 900 when Y changes by 1000, then the MPC = 900/1000 = .9
(recall the MPC is the change in consumption relative to a change in income)
Now that we know the MPC, we can calculater the tax mulitplier:

.9/(1-.9) = 9

so the impact of a tax cut = 9 x 200 = 1800
equilibrium AE will rise by 1800 if taxes fall by 200

Given that C = 1000 + 0.60Y, if the level of income is $1000, what is the the level of saving? (hint: Y=C+S)

First, if Y = $1000, then C = 1000 + .6(1000) = 1600
using Y = C + S, then 1000 = 1600 + S
so S = -600, or they are dissaving 600

Given a consumption function of C=25 + 0.75Y, at what level of incomes does C=100?

100 = 25 + .75Y

.75Y = 75

Y = 100

Given that autonomous consumption equals $1000, disposable income equals $20,000, and the MPC equals 0.90, what are the levels of consumption and saving?

first, let's put together the consumption function: C = a + bY. The MPC = b = .9 and autonomous consumption = a = 1000 so

C = 1000 + .9Y

so if Y = 20,000

C = 1000 + .9(20,000) = 19000

S = Y-C = 20000 - 19000 = 1000