Analysing the dependence of a variable on other variables

[musicgold]

Hi,

I am trying to analyze the sensitivity of a variable to three other variables. Please see the attached document explaining the relationship. The document shows how I reached to Eqn 1. It is nothing but a DCF analysis for a one-year period.

I wish to understand how the variables d, g, and T influence the variable C. I wish to know by how much C changes when d or g or T move increases or decreases by 10%.

I kind of did some sensitivity analysis in Excel by changing the values of d, g, and T, but I feel that I still don’t have the whole picturel.

In eqn 2, 3, and 4, I tried to find the derivatives of C wrt to d, g, and T, but they are more confusing than eqn 1. I am not able to interpret the equations.

Also I have the following questions.

Q1. Is this the right way of analyzing such a relationship?
Q2. Are there any other methods for doing this kind of analysis?

Thanks.

 

[fresh_42]

Such investigations are one reason for an entire branch of mathematics: Numerical Analysis.
The simplest approach is to consider $d\pm \varepsilon_1\, , \,g\pm \varepsilon_2\, , \,T\pm \varepsilon_3$ and determine $c$ as a function of your variables and the $\varepsilon_i$. Then you can minimize (maximize) the new function $c(d,g,T,\varepsilon_1,\varepsilon_2,\varepsilon_3)$ w.r.t. the $\varepsilon_i$ by known methods, e.g. using Lagrange multipliers, or if possible, a Simplex algorithm.