Suppose the government pegs an exhaustible resource, at a price $P^*$. I found out that the shadow price (initial price of the resource if government didn't peg) would be $$Q_t = ( \sigma i S_t )^\frac{-1}{\sigma}$$.

Where $S_t$ is the resources left after time $t$. And $\sigma$ is a parameter, whereas $i$ is the interest rate.

I'm trying to show that if $q(t) = ln Q_t$ and $ \triangle q(t) = i$ (change in q(t)) Then

$$Q_t = P^*$$

  • $\begingroup$ And your question is...? $\endgroup$
    – Giskard
    Oct 1 '17 at 19:46
  • $\begingroup$ Can you please explain what you want to show? What is $P^*$? Does it change at every $t$ given you have $Q_t$? $\endgroup$
    – london
    Oct 1 '17 at 20:55
  • $\begingroup$ What does this has to do with financial economics? Are you sure those tags are correct? Maybe natural resources? $\endgroup$
    – luchonacho
    Oct 1 '17 at 21:30
  • $\begingroup$ @luchonacho, first thing flashed in my mind was Hotelling rule when I read the question, but a google search gave links to the applications of the concept in finance literature. I was going to edit the tags otherwise. $\endgroup$
    – london
    Oct 1 '17 at 21:49

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