Real world example of using difference quotient vs. derivative When would you use the difference quotient in an economic model rather than the derivative to assess the change in some endogenous variable?  Real world examples seem to be lacking in textbooks on basic mathematical economics.
You can see the applications in microeconomics. A tiny example could be on elasticity of demand. 

Let's say 

$$ D = \frac{tC}{P+t} $$

where $P, t, C$ are respectively price, tax and constant. If you like to see the effect of tax change on demand you can use the difference quotient ;

$$\Delta D = \frac{(t + \Delta t C)}{P + t + \Delta t} - \frac{tC}{P + t}$$

I skip the intermediary calculations. This one yields ;

$$\frac{\Delta P}{\Delta t} = \frac{P.C}{(P+t)^{2}+\Delta t.(P+t)}$$

Hope that it helps.