In a closed economy, given the consumption function C = 100+ 0.9YD, when investment I = 30 billion yuan, government purchase G = 16 billion yuan, tax rate t '= 0.2, T0 = 0, calculate:

(1) What is the equilibrium level of national income when the government is in balance? What is the multiplier for government purchases? What is the tax multiplier?

(2) Assuming that the government purchase of G increases to 30 billion yuan, what is the new equilibrium level of national income?

(3) Suppose that the investment increases from 30 billion yuan to 40 billion yuan, what is the new equilibrium national income?

(4) Assuming that investment is not an exogenous variable but is internally determined by the equation I = 300+ 0.2y, what is the new equilibrium national income and multiplier?

(5) Assuming that the tax rate t '= 0.4, what is the new equilibrium national income and multiplier?