So far in this chapter, we have assumed that the fiscal policy variables G and T are independentof the level of income. In the real world, however, this is not the case. Taxes typically depend onthe level of income and so tend to be higher when income is higher. In these problems, 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: YD= Y− T T = t0 + t1Y C = c0 + c1YD c0 is autonomous consumption, c1 is the propensity to consume, and t0 is the part of taxes not dependent on income. G and I are both constant. Assume that t1 is between 0 and 1. Solve for equilibrium output. (Y= (c0−c1t0+I+G)/ 1−c1+c1t1) What is the spending multiplier? (The multiplier is 1/1−c1+c1t1.) What is the equilibrium equation for taxes? T= t0 + t1Y = t0 + t1 (c0−c1t0+I+G)/ 1−c1+c1t1) Given the decrease in c0, the level of equilibrium output will decrease Given the decrease in c0, the amount of taxes will decrease Now suppose the government reduces Gto keep a balanced budget. Given the change in G, the level of equilibrium output will decrease even more. When there is a required cut in spending to balance the budget, (this reinforces the decrease in output because the cut in spending lowers the level of output even further.)