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).

  • $\begingroup$ Well i dont see how you postulate d(p)=s(p) with d(p)<0 and s(p)>0. $\endgroup$ – Armenthus Jan 10 at 22:29
  • $\begingroup$ Indeed, @Armenthus. There was was a typo, although that relation was still possible (at least for a p*). $\endgroup$ – Rodrigo Remedio Jan 11 at 15:33

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