Assume That GDP (Y) Is 5,000 $C , l$ , And $r$

Assume that GDP (Y) is 5,000. Consumption (C). is given by the equation C = 1,200 + 0.3(Y - T) - 50r, where r is the real interest rate. Investment (I) is given by the equation I = 1,500 - 50r. Taxes (T) are 1,000 and government spending (G) is 1,500.

a. What are the equilibrium values of $C , l$ , and $r$ ?
b. What are the values of private saving, public saving, and national saving?
c. Now assume there is a technological innovation that makes business want to invest more. It raises the investment equation to $I = 2,000 - 50 r$ . What are the new equilibrium values of $C$ , $I$ , and $r$ ?
d. What are the new values of private saving, public saving, and national saving?