Ramsey Pricing in The Presence of Externality Costs

Authors: Tae Hoon Oum and Michael W. Thretheway

Lecturer: Chaowei Fan

A. Brief Review of Simplest Version of Ramsey Prices

Why do we need Ramsey Price? 1. First-best prices are nonviable. 2. Welfare-maximizing regulator must find an optimum set of prices subject to these constraints.

How do we start? 1. Requiring firm to adopt prices that deviate from marginal costs in order to reach the target profit level. 2. Assumptions: 1). There is only one strong natural monopolist, who faces no completion 2). The demands of products manufactured by this natural monopolist are independent of one another

What do we obtain?

( ) ( ) 1

( ) 1

( )where 0, the elasticity of demand in market

( )

i i i

i i i

i ii

i i i

p q MC q

p q e

p qe i

q p q

B. What problems does Ramsey Pricing have?

1. Independent Demands There should not exist only one multiproduct firm; there

should exist many other multiproduct firms, thereby the goods are interdependent.

2. Private Cost Ramsey only considers private costs But, we have to consider Social Cost Social Cost=Private Costs + External Costs 1). Private Cost: the costs that the buyer of a good or

service pays the seller. This can also be described as the costs internal to

the firm’s production function 2). External Costs: The costs that people other than buyer

are forced to pay as a result of the transaction. The bearers of such

costs can be either particular individuals or society at large Note: External costs are often both non-monetary

and problematic

C. What do Tae Hoon Oum and Michael W. Tretheway want to do? Examining the Ramsey pricing rule Where there are potential externality costs for all goods, And where all demands can be interdependent

D. How do they proceed?

Two sets of first order conditions must be satisfied to maximize the Lagrangian function

Bad! Bad! Really Bad!!! Even if SW is Maximum.

Another Big Finding

D. What conclusion do we get? When externality costs are present, the Ramsey rule is computed on the basis of the sum of marginal private cost and a fraction of marginal externality costs. It is not computed on the basis of social marginal costs.

The quantity shares under the first best social marginal cost pricing would not be preserved under Ramsey pricing.