Question

a. You are studying an economy with an income tax rate, ti, of 32% and an MPS of 0.3. It is currently suffering from a “recessionary gap” of $500 m. (i.e., Eqm Y Y full employment, FE, aka Yn). Make the necessary calculations for the to policy that it should institute; who does what? Provide the full name of this policy.

b. Compare this economy to one without income taxes to explain the term “automatic stabilizer.” [Hint: Let I change and compare the I multipliers in each of these economies.]

Answer 1

We have the following information

Tax rate (t) = 32% or 0.32

Marginal propensity to save (MPS) = 0.3

Marginal propensity to consume (c) = 1 – MPS = 1 – 0.3 = 0.7

Multiplier = 1/[1 – c(1 – t)]

Multiplier = 1/[1 – 0.7(1 – 0.32)]

Multiplier = 1/[1 – 0.7(0.68)]

Multiplier = 1/0.524

Multiplier = 1.9

It is given that there is recessionary gap of $500m. This gap can be filled using fiscal policy that involves increased government spending.

ΔIncome = ΔGovernment Spending × Multiplier

500 = 1.9ΔGovernment Spending

Government Spending = 263.16

So, government spending need to increase by $263.16 to fill the recessionary gap.

Multiplier without tax = 1/(1 – c)

Multiplier without tax = 1/(1 – 0.7)

Multiplier without tax = 1/0.3

Multiplier without tax = 3.33

ΔIncome = ΔGovernment Spending × Multiplier

500 = 3.33ΔGovernment Spending

Government Spending = 150.15

So, in the situation where there are no taxes government spending need to increase by only $150.15 to fill the recessionary gap.

Automatic stabilizer is an economic mechanism that reduces the amount by which income or output changes in response to a change in autonomous demand, without needing the intervention of the government. Examples of automatic stabilizers include taxes.

For instance, as we have seen above the value of multiplier declines with the addition of tax rate. This means that the change in income or output due to autonomous change in the demand will be lower in the case where there are taxes as compared to no tax situation. For example, an increase in investment will raise income or output by 1.9ΔInvestment in the presence of taxes which is less than the 3.33ΔInvestment in the case where there are no taxes.