Given the expression $$y_t = \frac{a_t +b_t}{b_t}= 1 +\frac{a_t}{b_t}$$ the change of $y_t$ for the time $t = [0,1]$ may be written
$$\Delta t=y_1-y_0=\biggl(1+\frac{a_1}{b_1}\biggr)-\biggl(1+\frac{a_0}{b_0}\biggr) $$
It is now of interest to investigate how much the respective change in $\Delta a = a_1-a_0$ and $\Delta b = b_1-b_0$ has affected the total change $\Delta y$.
A friend of mine formulated a solution which can be found in the PDF in the link below:
My question to you guys in regards to the solution is
- Is the solution correct?
- If yes, is the solution applicable if either $\Delta a$ or/and $\Delta b$ is negative?
- If no, any other way to approach this issue?