Calem and Spulber, 1984 Presentation by Collin Philipps

 In this article, Calem and Spulber compare the implications of two part pricing in two different models.

Differences in market structure seriously affect the expected outcome.

 What can be determined?

Optimal pricing is related to the elasticity of demand, as in the simple Ramsey case As expected, it can be shown that competition lowers prices.

 The consumer will purchase both goods if the following is true:

 How do we know if goods are substitutes or complements?

 First, we will look at the case of a monopoly that sells differentiated goods to homogeneous consumers. The firm will maximize the following:

 If goods are complements, and consumers consume the goods together, then the monopolist can charge a total entry fee equal to the consumer’s surplus. Therefore, the pricing problem can be written as:

 The first order conditions of the profit function can be written as:

 The authors assert that this can be solved to produce:  If products are complements, then prices are equal to marginal costs. Tariffs are equal to the consumer’s total surplus.

 If goods are substitutes, then the profit function will become:

 And the first order conditions will be:

 And the first order conditions will be:

 Most importantly:

 Therefore, the monopolist sets prices above marginal costs. The optimal markup is a function of the price elasticity of demand.

 If multiple firms are engaged in production, then the first will maximize the following profit function

 The ideal entry fee is equal to: If goods are complements, firms will divide the entire consumer surplus between them.

 Prices will maximize the following:

 But, if goods are substitutes, then

 But, if goods are substitutes, then  The pricing rule is the same.

 For oligopoly, optimal prices are equal to marginal costs regardless of the relation between the goods. Effectively, the price is the only strategic variable.

 If consumers are not identical, the results will change.

The firm maximizes:  Where Na and Nb are the numbers of consumers of each type.

 Entry fees are set relative to the consumers with lower demand (to keep everyone in the market).

Therefore, the firm maximizes:

 FOC’s will be the following:   And this can be solved for a Ramsey-type markup rule. Monopoly prices will exceed marginal costs when products are substitutes.

 In the oligopoly case, equilibrium entry fees are similar to the multiproduct monopoly.

 Prices are optimal by the following equations:

 The price rule can be rewritten:  This suggests that nash equilibrium prices will exceed marginal cost if consumers are heterogenous.

 The price rule can be rewritten:  This suggests that nash equilibrium prices will exceed marginal cost if consumers are heterogenous.

 In the homogenous consumers case, oligopoly equilibrium prices equal marginal costs. The monopoly sets unit prices above marginal costs only when products are substitutes.

Entry fees are set equal to the consumer’s gains from trade or, in the case of complements, equal to the entire consumer surplus.

 Results from the heterogenous consumer model are quite different.

Oligopolistic Equilibrium prices will exceed marginal costs. If the goods are substitutes, the monopolist will also charge more than marginal cost.

The context of market structure can seriously change the expected outcome in a model. Real consumers are heterogeneous, and most firms have rivals. Therefore, the competitive oligopoly example is the most likely to resemble real markets.