# Depletion3 - Empirical Evidence for the Optimal Depletion...

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Empirical Evidence for the Optimal Depletion Model

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Following Miller and Upton (1985), let the present value of a resource deposit be where c = constant marginal and average cost t T t t t q r c p V = + = 0 ) 1 ( ) ( (1)
Substituting for in (1) we get where S = the resource stock, and the unit value is t r c p ) 1 )( ( 0 + ) ( c p t t T t t t q r r c p V = + + = 0 0 ) 1 ( ) 1 )( ( = = T t t q c p 0 0 ) ( S c p ) ( 0 = (2) c p S V = 0 (3)

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So we have obtained an expression for the value of the resource that does not depend on future prices or interest rates. To value a resource, all we need to know is the current selling price and extraction cost. This is the implication of the theory (since the rising royalty is “cancelled” by discounting). Miller and Upton test the theory by measuring whether an independent, market indication of the value of oil and gas reserves is consistent with the value calculated as in equation (3).
To do this, they run a regression of the market

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## This note was uploaded on 09/11/2011 for the course ECON 102 taught by Professor Sunding during the Spring '07 term at University of California, Berkeley.

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Depletion3 - Empirical Evidence for the Optimal Depletion...

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