3. Although our development of the Keynesian cross in this chapter assumes that taxes are a fixed amount, in many countries (including the United States) taxes depend on income. Let’s represent the tax system by writing tax revenue as T = 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 system alter the slope of the IS curve?