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

Suppose that consumption is modeled as in lecture:

C = c0 + c1YD

where YD = 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 ?scal 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 con?dence (c0 drops). What happens to income and taxes?

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

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