3a)Y= C+I+G+NX Y= C0 + C1YD + b0 + b1Y + G +NX =Y(b1 ) + C0 + b0 + C1 (Y-T)+ G +NX = Y(b1 ) + C0 + b0 + C1 Y - C1T +G+NX Y = Y(b1 + C1) + C0 + b0 - C1T +G+NX Y(1- b1 - C1) = C0 + b0 - C1T +G+NX Y= (1/ 1- b1 - C1)C0 - C1T + b0 +G+NX

b) Y= (1/ 1- b1 - C1)C0 - C1T + b0 +G+NX 1/ 1- b1 - C1 = Y/ C0 - C1T + b0 +G+NX c) From the equation, I= b0 + b1Y, hence I is proportionate with Output which is equivalent to Y. If I and Y increase, b1 ,which is the propensity to increase Investment with respect to Income, will also tend to increase. With an increase in b1, which makes it closer to 1, the denominator of the multiplier becomes smaller. Assuming C1 will also increase with increase in Y, multiplier will become greater in value.
(b1 + C1) must be less than or equal to 1.

d) There will be a decrease where the change in equilibrium output will be multiplied with the multiplier which is (1/ 1- b1 - C1).
As this is an open economy, Investment may not equal to National Savings. National Savings = Public Savings + Private Savings = T-G + Y – T – C = T-G + Y – T - C0 - C1 (Y-T) = T-G + Y – T - C0 - C1 Y+ C1 T = Y(1- C1 ) – G - C0 + C1 T
As National Savings is proportional to Output, National Savings will also decrease in this case.

e) Y= (1/ 1- b1 - C1)C0 - C1T + b0 +G+NX = (1/ 0.4)(100-0.5(50)+100+ 50+ 50) = 275(2.5) =687.5 National Savings = 687.5(1-0.5) – 50 – 100 + 0.5(50)) = 218.75 a. Y=C+ I+G+NX = c0 + c1YD + b0+ b1Y +G+NX = c0+ c1 Y-T + b0+ b1Y +G+NX =c0+ c1Y- c1T+ b0+ b1Y+G+NX
Y- c1Y- b1Y= c0- c1T+ b0 +G+NX
1- c1- b1Y= c0- c1T+ b0 +G+NX
Y= c0 - c1T + b0 + G + NX1- c1- b1

b. Y= c0 - c1T + b0 + G + NX1- c1-