# When is the pegged price equal to the market price

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

$$Q_t = P^*$$

• And your question is...? Oct 1 '17 at 19:46
• Can you please explain what you want to show? What is $P^*$? Does it change at every $t$ given you have $Q_t$? Oct 1 '17 at 20:55
• What does this has to do with financial economics? Are you sure those tags are correct? Maybe natural resources? Oct 1 '17 at 21:30
• @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. Oct 1 '17 at 21:49