Two eqn static model with G Two eqn static model with G and T.

Variables:

C consumption; I investment;

G government expenditures; T taxes;

Y real GDP; a,b known constants

Note: In this model the level of government expenditures, taxes and investment are fixed. The purpose of this model is to study the fiscal policy options of government, that is the effect of G and T on Y and C. This model is the simplest model of this type. Equations:

Y = C + I + G       (1)
C = a + b(Y - T)       (2)

Note: This model, useful only for instructional purposes, is slightly more realistic than the two equation model in that it contains a government and consumption is based on disposable income. Solution:

Substitute 2 into 1

Y = a + b(Y -T) + I + G
Y = a + bY - bT + I + G
Subtract bY from both sides
Y-bY = a + I - bT + G
Collect terms
(1 - b)Y = 1(a + I - bT + G)
Y = k(a + I - bT + G)
where k = 1/(1 - b)

Note: The solution to this model has the same form as the simple two equation model. In policy work the analyst is interested in considering the impact of a change in G of T. Using the same type of algebra as for the simple two equation model we can obtain the following equations.

DY = kDG
DY = kDI
DY = kDa
DY = -kbDT
The first shows the impact of a change in government expenditures, the second the impact of private investment, the third shows a shift in consumer confidence, and the last indicates a shift in tax policy. The government has direct control (?) over G and T and indirect influence over a and I through incentives and its policies.

Example: a = 200 b = .8 I = 400 G = 400 T = 400 Find the equilibrium Y and C? Remember: Y = k(a + I - bT + G) where k = 1/(1 - b)

Suppose the government wished to raise Y by 500 to reduce unemployment how could it accomplish this objective? If the government raised G by 100 it would accomplish the objective (500 = 5DG). The government could also lower taxes by 125 (500 = -0.8(5)DT). If the government wished to maintain a balanced budget they could simultaneously raise G by 500 and raise T by 500 using the balanced budget multiplier below:

DY = kDG -kbDT
If DG = DT = D, then
DY = k(1-b)D = (1-b)/(1-b) D = D
Now suppose Da = -100, how much must G be raised in increase Y by 500. DG = 200. 100 compensates for the decrease in a and the other 100 increases Y by 500.

Variables: all the variables for previous model plus t the tax rate. Equations

Y = C + I + G       (1)
C = a + b(Y - T)       (2)
T = tY       (3)
Note: This model adds a fixed tax rate to determine the amount of revenue the government will receive. Solution: Remember to substitute up the stack of equations.

Substitute (3) into (2): C = a + b(Y - tY)

Sub (2) into (1): Y = a + b(Y - tY) + I + G

b(Y - tY) RHS Æ LHS: Y-b(Y - tY) = a + I + G

Collect terms: (1 - b(1 - t))Y = a + I + G

Y = k1 (a + I + G) where k1 = 1/[1 - b(1 - t)]

Example: a = 200 I = 400 G = 400 and t = 0.2 b = 3/4 What is Y and T?

k1 = 1/[1 - (3/4)(1-.2)]

k1 = 1/[1 - (3/4)(0.8)]

k1 = 1/(2/5) = 2.5

Y = 2.5[1000] = 2500

T = .2(2500) = 500.

Note: The fundamental issue for analyzing Reagan's economic policy is can the government ever increase the tax revenues by decreasing taxes as claimed by the devout supply siders.

Suppose t is cut to 1/9, what happens to T?

k1 = 1/[1 - (3/4)(8/9)] = 1/[1 - 2/3] = 3

Y = 3[1000] = 3000 and T = (1/9)[3000] = 333.33

Note: If you have had calculus you will note that

T = tk1 (a + I + G)

dT/dt < 0 for 1 > b > t > 0

This means that if you decrease taxes Keynesian theory indicates that tax revenues must fall. (You do not need to know any calculus to provide an excellent answer to the test question on the subject. You do need to integrate the math with the opinions of both the supply sider and the fiscal conservatives.)  

File translated from TEX by TTH, version 2.25.
On 29 Sep 1999, 15:58.