The Hotelling rule was developed by Harold Hotelling in its article "“The Economics OF Exhaustible Resources"” of 1931. After their the scarceness pension in timing with the interest rate must rise.

Intuitive explanation

The price of exhaustable resources cannot be identical to (extraction) the neighbouring costs, as it would result according to the model of the complete competition. If this would be the case, then it would be optimal to promote the entire resources existence as fast as possible and the profits to others to invest projects net yield-bringing. An owner of a resources existence is thus only then ready to leave resources in the soil if it can expect that the value of resources lying in the soil increases over the time with the market interest rate. A smaller increase in value would cause it to it to promote in the current period more a higher increase in value would be an incentive the promotion to be reduced. Thus the scarceness pension indicates the to the promotion of an additional resources unit. The development of the scarceness pension with the market interest rate is called as Hotelling rule and/or r-per cent-rule. Many models in the resources economics are based on this principle.

Formal derivation

A goal of the investigation is to be: Non-renewable resources are available in limited quantity. Question: When should be diminished and consumed how much this It is subordinated here that nothing by resources is stored. Which is diminished, one consumes thus immediately. Philosophy: In each period a certain use results from the consumption of resources. Future use can be discounted. Thus there is a welfare function over T periods:

W= \ sum_ {t=0} ^T \ frac {1} {(1+r) ^t} u_t (x_t) here is W the welfare, r the rate of discount of the use and u_t (x_t) the use in period t, dependent on the delivery x_t in period is t.Maximiert the welfare over the deliveries in the periods under the secondary conditions, dassI: the dismantling in all periods equal the entire available existence of resources \ without x to be together smaller must, undII: that it no negative dismantling gives (not W \ rightarrow max! _ s.t {x_0, x_1,"…, x_T}. I: \ sum_ {t=0} ^T x_t \ le \ without x II: x_t \ ge 0 \ quad \ forall t problem: Can be simply discounted future Yes, if applies: 1. All use functions in each period are alike: u_t (x_t) =u_s (x_s) \ quad \ forall t \ ne s2. Use in each period is equal to the maximum Zahlungsbereitschaft: u_t (x_t) =ZB (x_t). For simplification in the following it is accepted that there are only two periods that in each period something is diminished and that at the end resources are completely diminished: x_0 > 0, x_1 > 0, x_0+x_1= \ without x

Then the follows from the maximization problem: u^ \ prime (x_0^*) = \ frac {u^ \ prime (x_1^*)}{(1+r)} \ Leftrightarrow r= \ frac {u^ \ prime (x_1^*) - u^ \ prime (x_0^*)}{u^ \ prime (x_0^*)} This is the Hotelling rule.

Articles in category "Hotelling rule"

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• Marginal Revolution: Oil prices and time
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• Natural Resources, Knowledge and Efficiency: Beyond the Hotelling ...
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