Suppose that the model of the economy is given by

Y = C + I + G + X

C = a + bYd

Yd = (1-t)Y

X = g - mY

Where I = 900 billion, G = 1,200 billion, and the constants take the following values: a= 220, b = 0.9, t = 0.3, g = 500 and m = 0.1.

a. Show that the value of GDP at the point of spending balance is 6,000 billion.

b. What proportion of investment is private saving? Government saving? Saving by the rest of the world?

c. Now, suppose that I increase by 100 billion. By what proportion of the increase in investment do each of the three categories of saving increase?