8.Suppose that instead of taxes being exogenous (i.e. T = ), instead, assume tax revenue of the government is dependent on income, as T = +tY. and 0 < t < 1 is the tax rate on income.

Assume an economy's consumption function is given as C = + mpc(Y - T) - cr, where is autonomous consumption, mpc is the marginal propensity to consumer, and c is a coefficient representing the elasticity (sensitivity) of interest rates on consumption.

(a)Write an expression for private savings, and calculate the derivative of private saving with respect to the tax rate t. What sign is the derivative? What is the implication for the government raising the tax rate on private saving?

(b)Write an expression for public savings, and calculate the derivative of public saving with respect to the tax rate t. What sign is the derivative? What is the implication for the government raising the tax rate on public saving?

(c)Write an expression for national saving savings, and calculate the derivative of national saving with respect to the tax rate t. What sign is the derivative? What is the implication for the government raising the tax rate on national saving?

*Explain your answers and show shifts of graphs clearly indicating changes in equilibria.