# Consumption Function

I would really appreciate if anyone of you could guide me as to whether I my solution is right or not.

Q. Consider the following consumption function:

C=a+b(Y-T)

Assuming a>0, show using calculus that APC falls as the disposable income increases.

Also show from the answer to above that APC>MPC

My take:

MPC = dC/dy = b (I have expanded the consumption function and taken derivative with respect to Y)

APC = C/Y = a+bY-bT/Y =a/Y -bt/Y + b

Now taking derivative of the APC derived above

i.e. dAPC/dY= -a/Y^2 + bt/Y^2

as it has negative sign it is < 0

Thanks.