Suppose the economy of a country is described by the following equations:

C = 1000 + 0.75(Y - T)

I = 2000 - 50r

G = 2000

T = 1000

where C is consumption, Y is income, T is taxes, I is investment, r is the interest rate, and G is government spending. All the variables are in billions of dollars.

a) Calculate the equilibrium level of income and the interest rate in this economy.

b) Suppose the government decides to increase its spending by 500 billion dollars. Calculate the new equilibrium level of income and the interest rate.

c) Suppose instead the government chooses to reduce taxes by 10%. Calculate the new equilibrium level of income and the interest rate.