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RAMSEY PRICING IN THE PRESENCE OF EXTERNALITY COSTS

RAMSEY PRICING IN THE PRESENCE OF EXTERNALITY COSTS. Tae Hoon Oum and Michael W. Tretheway. Presentation by C. Philipps. Premise. “First Best” pricing creates a financial deficit and is potentially unsustainable.

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RAMSEY PRICING IN THE PRESENCE OF EXTERNALITY COSTS

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  1. RAMSEY PRICING IN THE PRESENCE OF EXTERNALITY COSTS Tae HoonOum and Michael W. Tretheway Presentation by C. Philipps

  2. Premise • “First Best” pricing creates a financial deficit and is potentially unsustainable. • Ramsey (1927) proposes a pricing method that can maximize social welfare without harming the firm.

  3. Premise • Simple Ramsey pricing model: output shares should be equal to those in the first-best case. • The “Inverse Elasticity” rule suggests that markup should be inversely proportional to the price elasticity of demand; and that the proportion should be equal across goods. • This simple case assumes independent demand functions

  4. Premise • The simple Ramsey pricing method has other limitations due to simplicity of the model and its implicit assumptions. • Ramsey’s results do not account for the possibility of externality costs.

  5. Premise • Oum and Tretheway propose and derive a generalization of the Ramsey rule with two modifications: • They allow for the existence of costs external to the firm. • They allow demand for any good to be dependent on other goods.

  6. Implications? • The generalized pricing rule suggests that markups are not applied only to social costs, but to a weighted average of social costs and private costs. • In other words, the markup rule is based on private (firm) costs plus some fraction of externality costs.

  7. Derivation • We intend to maximize social benefit (welfare) subject to some budget constraint on the firm. • This suggests a composite Lagrangian function of familiar form.

  8. Derivation

  9. Derivation

  10. Derivation

  11. Derivation

  12. Derivation

  13. Derivation If there are no external costs, then MPC=MSC and the following is true:

  14. Derivation If, in addition to MSC=MPC, all cross-price elasticities are zero, then we find ourselves in familiar territory.

  15. Derivation Without the two simplifying conditions, the pricing rule simplifies only somewhat and can be written in the following form.

  16. Derivation With cross price elasticities equal to zero, the rule simplifies as follows.

  17. Why isn’t the entire social cost used as ‘true’ marginal cost? • When markup is applied, consumption decreases (relative to marginal cost pricing). The externality cost therefore also decreases.

  18. In fact, the fraction of externality costs that should be included in the markup depends on the deficit that would result under marginal (private) cost pricing. • Oum and Tretheway assert that the fraction of externality costs that should be included will decrease as markup increases.

  19. In addition, if lambda is large, it is more costly to satisfy the budget constraint. In this case, optimal regulator behavior puts less emphasis on the externality costs. • Finally, the optimal output combination is not necessarily the same as in the marginal cost pricing case.

  20. In conclusion: • This pricing rule can be applied in many cases. • I.E. Airports create noise, pollution, so landing fees can be determined to be quasi-optimal after consideration of the airport’s external social costs.

  21. Thank You

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