Although our development of the Keynesian cross in this chapter assumes that taxes are a fixed amount, in many countries taxes depend on income. Let’s represent the tax system b y writing tax revenue as
T =  + tY,
Where T − and t are parameters of the tax code. The parameter t is the marginal tax rate: if income rises by $1, taxes rise by t × $1.
a. How does this tax system change the way consumption responds to changes in GDP?
b. In the Keynesian cross, how does this tax system alter the government-purchases multiplier?
c. In the IS–LM model, how does this tax sys-tem alter the slope of the IS curve?