Type of fiscal policy be called an automatic stabilizer

Question

Assignment:

1. Automatic Stabilizers

Suppose that consumption is modeled as in lecture:

C = c₀ + c₁Y_D

where Y_D = Y - T is disposable income. Now suppose that instead of treating taxes (T) as exogenous, tax policy is conducted according to the following equation:

T = t₀ + t₁Y

that is, taxes depend on income. Assume that 0 < t₁ < 1. Continue to treat government spending (G) and investment (I) as exogenous.

1. Solve for equilibrium output.

2. What is the multiplier? Does the economy respond more to changes in autonomous spending when t₁ is 0 or when t₁ is positive? Explain.

3. Why would this type of fiscal policy be called an automatic stabilizer?

2. Balanced Budget vs. Automatic Stabilizers

Suppose tax policy is conducted as in the above problem.

1. Solve for taxes in equilibrium.

2. Suppose that the government starts with a balanced budget (ie. G = T) and that there is then a drop in consumer confidence (c₀ drops). What happens to income and taxes?

3. Suppose that the government adjusts spending (G) to keep the budget balanced. What will the effect be on Y ? Does this effect counteract or reinforce the effects of the drop in consumer confidence?