3) So far we have assumed that the fiscal policy variables G and T are independent of the levels of income. In the real world, however, this is not the case. Taxes typically depend on the level of income, and so tend to be higher when income is higher. In this problem we examine how this automatic response of taxes can help reduce the impact of changes in autonomous spending on output. Consider the following behavioral equations: C = C₁+C₁YD T = t₁ +1₁Y Y₁ = Y-T G and I are both constant. Assume that is between zero and one. a. Solve for equilibrium output. b. What is the multiplier? Does the economy respond more to changes in autonomous spending when is zero or when is positive? Explain. c. Why is fiscal policy in this case called an automatic stabilizer?

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