Answer to Question #111450 in Macroeconomics for Yoon Lee

Question

Y*=[C0-C1T+A0/i+G]/(1-C1)
FIND THE DERIVATIVE dY*/di Assuming that a0>0

Answer 1

$\frac{dY*}{di}=(\frac{C0-C1T+\frac{A0}{i}+G}{1-C1})'=\frac{([C0-C1T+\frac{A0}{i}+G])'\times(1-C1)-([C0-C1T+\frac{A0}{i}+G])\times(1-C1)'}{(1-C1)^2}=\frac{((-C1-\frac{A0}{i^2}+1)\times(1-C1)-0)}{(1-2C1+C12)}=\frac{(1-C1-\frac{A0}{i^2})\times(1-C1)}{(1-C1)(1+C1)}=\frac{(1-C1-\frac{A0}{i^2})}{(1+C1)}$