Hotelling's rule

The Hotelling rule is an important theorem in microeconomics. It was first introduced by Harold Hotelling in his article The Economics of exhaustible resources in 1931. Hotelling's rule states that the price of an exhaustible resource over time with the interest rate must rise.

Definition

The exercise price of exhaustible resources may not be identical to the marginal cost, as it would result, for example, after the model of perfect competition. If this were the case, then it would be optimal to promote the entire resource inventory as quickly as possible and invest the profits into other, higher return projects achieved. An owner of a resource inventory is therefore only willing to resources not for sale, if it can be expected that increases the value of the resource over time with the market rate. A smaller increase in value would cause him to in the current period to sell more, a higher increase in value would be an incentive to reduce supply. The scarcity rent in this case indicates the opportunity cost of selling an additional unit of resources. The development of the scarcity rent at the market rate is called the Hotelling rule. Many models in the resource economics based on this principle.

Mathematical derivation

A non - renewable resource stand in a limited quantity available and there are no storage costs. In each period, creates a certain benefit by consuming the resource. Future benefits are discounted. Thus, there is a welfare function over T periods:

With

  • The welfare
  • The discount rate of the benefit
  • The benefits in period, depending on the flow rate in period
  • Time at which the resource is exhausted.

The welfare maximization function can be represented as follows:

Under the following conditions:

  • That sales in all periods must be together less than / equal to the total available stock of the resource
  • And that there is no degradation of the negative (non- Negativitätsbedingung )

To derive the optimality condition all utility functions must be the same in each period.

At the same time, the benefit must be the maximum willingness to pay in each period equal.

For simplicity, assume in the following that there are only two periods, that in each period is slightly reduced and that, at the end of the resource is completely eliminated:

Then it follows from the maximization problem, the optimality condition ( Hotelling rule ):

Current state of research

It was repeatedly found that the Hotelling rule is not compatible with the actual development of the world market prices of natural resources. This is partly because the original formulation of the Hotelling rule is based on a partial analysis; a derivation of the rule in the context of a general equilibrium model predicts constant prices for finite resources. However, the rule is still used in its simple form in many models of resource and climate economics.

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