Economics question

Problem 2. Balanced Budgets and Automatic Stabilizers.
So far in class we have been assuming that the fiscal policy variable T is independent on the level of income. In the real world, however Taxes typically depend on income. Consider the following model of the Economy:
C=c0+c1YD
T=t0+t1Y
I=Ī constant
G is a given number decided by the government.
a) Do you believe t1 should be greater of less than zero? Is it reasonable to assume t1 to be greater of less than one? Explain.
b) A proportional tax system is a system of income taxation where taxes are levied as a fixed percentage on income, independently on its level. In contrast, a tax system is called progressive when income is taxed more heavily (in percentage terms) when its level is high. What is the condition on t0 needed to have a proportional tax system? And what if we want a progressive system? What type of tax system is actually in use in UK?
c) Solve for the equilibrium expressions of output and taxes in our economy.
d) Now set t0=0, t1=0.25, c0=5, c1=0.8, Ī=0, and G=10. Compute the equilibrium levels of Y and T. Does the government balance its budget?
e) What is the Keynesian multiplier of income in this economy?
f) In real world, having a fiscal policy with t1>0 is often called an "automatic stabilizer". According to the result you obtained above, do you agree with this definition? Why?
g) Suppose now that the government cuts spending in order to keep the budget balanced. What will be the effect on Y? (You are not required to do all the algebra, you can answer in words).



Any help with any of that would be much appreciated, I haven't got a clue

C=c0+c1YD
T=t0+t1Y
I=Ī constant
G is a given number decided by the government.
a) Do you believe t1 should be greater of less than zero? Is it reasonable to assume t1 to be greater of less than one? Explain.

C=c0+c1YD
T=t0+t1Y
I=Ī constant
G is a given number decided by the government.
b) A proportional tax system is a system of income taxation where taxes are levied as a fixed percentage on income, independently on its level. In contrast, a tax system is called progressive when income is taxed more heavily (in percentage terms) when its level is high. What is the condition on t0 needed to have a proportional tax system? And what if we want a progressive system? What type of tax system is actually in use in UK?