The regulator of a natural monopoly that sets a two-part tariff and whose marginal cost is stochastic will generally want the price to vary less than marginal cost when the lump-sum charge in the tariff is fixed. A trade-off exists between efficient pricing and an optimal allocation of risk. Pricing at marginal cost is only optimal when the consumer`s marginal utility is independent of the price. When marginal utility increases with the price the mark-up falls monotonically as marginal cost rises. The lump-sum element of the tariff should exceed the fixed cost when demand is inelastic and equals the fixed cost only with unit elasticity. The model may also be applied to optimal commodity taxation.
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