The total market demand is given by the sum of the two destinations ($e$ and $f$) given to the product.
Given these conditions:
Demand: $d(p) = e(p) + f(p)$ where:
- $d(p) > 0$, $d'(p) \leq 0$;
- $e(p) > 0$, $e'(p) \leq 0$;
- $f(p) > 0$, $f'(p) \leq 0$;
Supply: $s(p)$ where $s(p) > 0$ and $s'(p) \geq 0$;
Equilibrium: $d(p) = s(p)$;
How can the condition below be interpreted?
- $\frac{f'(p)}{f(p)}-\frac{d'(p)}{d(p)}> \frac{e(p)}{f(p)}\frac{s'(p)}{s(p)}$
It may be helpfull to see that's possible to multiply by $p$ and get some elasticities:
$p*\big(\frac{f'(p)}{f(p)}-\frac{d'(p)}{d(p)}> \frac{e(p)}{f(p)}\frac{s'(p)}{s(p)}\big) \Rightarrow$ $\varepsilon_{f}-\varepsilon_{d} > \frac{e(p)}{f(p)}\varepsilon_{s}$
This is a simplification of the whole situation from the The Ethanol-subsidy Multiplier example (or notebook file).
