1. Proof that

Question

A. tax multiplier= -mpc/1-mpc
B. government multiplier = 1/1-mpc

Answer 1

I can provide the proof for A. tax multiplier = -mpc / (1 - mpc):

The tax multiplier is the change in real GDP divided by the change in taxes. It can be represented by the formula:

Tax multiplier = ΔY / ΔT

Given the consumption function equation: C = a + (mpc * (Y-T)), where:
- C is consumption
- a is autonomous consumption
- mpc is the marginal propensity to consume
- Y is real GDP
- T is taxes

If we take the derivative of the consumption function with respect to Y, we get the marginal propensity to consume:

dC/dY = mpc

Now, let's differentiate the consumption function with respect to taxes T:
dC/dT = -mpc

Therefore, the change in consumption with respect to a change in taxes (ΔT) will be:
dC = -mpc * ΔT

Substitute this back into the tax multiplier formula:
Tax multiplier = ΔY / ΔT
ΔY / ΔT = -mpc * ΔT / ΔT
ΔY / ΔT = -mpc

Therefore, the tax multiplier is equal to -mpc / (1 - mpc).

I hope this helps with the understanding of the tax multiplier formula. Let me know if you would like me to explain the government multiplier formula as well.