Keynesian Multipliers: Suppose the president would like to stimulate the level o

Question

Keynesian Multipliers: Suppose the president would like to stimulate the level of output in the economy by introducing a tax cut. However, he also would like to keep a balanced budget if possible. Let's consider if these two objectives can be consistent with each other. Assume a consumption function C = 100 + 0.75(Y-T), and let G = 100, T = 100, I = 100 (investment is not a function here of the interest rate).

a) First, suppose there is just a tax cut alone, lowering T from 100 to 90. Use the Keynesian multipliers to compute the change in output. Compute also the effect on government saving.Will the president be satisfied (did he get a rise in output and a balanced government budget)?

b) Now suppose he combines the tax cut with spending cuts to keep the budget balanced. So supposed taxes and government spending both are cut from 100 to 90. What is the effect on government saving and output? Will the president be satisfied?

c) Now suppose that the president instead uses a rise in government purchases to stimulate the economy, and then raises taxes to pay for these purchases. In particular, suppose government purchases and taxes both are raised from 100 to 130. Compute the effects on output and government saving. Will the president be satisfied now? Explain how this result is possible and why it is so different from the result in part (b) above.

Explanation / Answer

Given,

C = 100 + 0.75(Y-T)

G = 100

T = 100

I = 100

a)

As per the equation of GDP,

Y=C+I+G

Substituting the given values to get:

Y=100 + 0.75(Y-100)+100+100

Y=300+0.75Y-75

Y-0.75Y=225

0.25Y=225

Y=900

Looking at in terms of multiplier,

Y=100 + 0.75(Y-T)+100+100

0.25Y=300-0.75T

or, Y = 1200-3T

So, one unit decrease in T will decrease Y by 3 units.

So, when T falls by 10 units, Y increases by 30 units.

Looking at it numerically, after tax-cut, T becomes 90.

Thus, Y changes to:

Substituting the given values to get:

Y=100 + 0.75(Y-90)+100+100

Y=300+0.75Y-67.5

Y-0.75Y=232.5

0.25Y=232.5

Y=930

Government savings become: T-G = 90-100 = -10

Since government savings are negative, budget is not balanced and thus president will not be satisfied.

b)

Now G is also cut from 100 to 90.

Change in Y becomes:

Substituting the given values to get:

Y=100 + 0.75(Y-90)+90+100

Y=290+0.75Y-67.5

Y-0.75Y=222.5

0.25Y=222.5

Y=890

Thus, output falls.

Looking at in terms of multiplier,

Y=100 + 0.75(Y-T)+100+G

0.25Y=200-0.75T+G

or, Y = 800-3T+4G

So, one unit decrease in T and G simultaneously will decrease Y by 1 units (i.e. 3 minus 4).

So, when T and G fall by 10 units, Y decreases by 10 units.

Government savings become: T-G = 90-90 = 0

Thus, budget becomes balanced, but output or real GDP falls.

So, president will again not be satisfied.

c)

Now both G and T are raised to 130.

Change in Y becomes:

Substituting the given values to get:

Y=100 + 0.75(Y-130)+130+100

Y=330+0.75Y-97.5

Y-0.75Y=232.5

0.25Y=232.5

Y=930

Thus, output increases.

Looking at in terms of multiplier,

Y=100 + 0.75(Y-T)+100+G

0.25Y=200-0.75T+G

or, Y = 800-3T+4G

So, one unit increase in T and G simultaneously will increase Y by 1 units (i.e. 4 minus 3).

So, when T and G increase by 1.3 units, Y increases by 1.3 units.

Government savings become: T-G = 130-130 = 0

Thus, budget becomes balanced and output or real GDP also increase.

So, president will be satisfied.

This result is different from result in part(b) as there is an increase in the output, keeping the budget balanced.

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