Babu Nahata

Theory of Vertical Control with Variable Proportions

The effect of vertical integration by an input monopolist on the price of the final product and the derived demands are examined when the production is of CES and the demand for the final product is of constant elasticity. The results are proved by analytical methods. Specifically, when the elasticity of substitution is less than one, the price of the final product can decrease but, regardless of any conditions, the derived demand for the nonmonopolized input decreases. However, that of monopolized input decreases if and only if the elasticity of substitution exceeds the elasticity of demand.

Pay-What-You-Want Pricing: Can It Be Profitable?

Using a game theoretic framework, we show that not only can pay-what-you-want pricing generate positive profits, but it can also be more profitable than charging a fixed price to all consumers. Further, whenever it is more profitable, it is also Pareto-improving. We derive conditions in terms of two cost parameters, namely the marginal cost parameter for the seller, and the social preference parameter of a consumer to incorporate behavioral considerations for paying too little compared to her reference price.

Package Sizes, Tariffs, Quantity Discount and Premium

We analyze nonlinear pricing problem under monopoly using two hidden types of agents with linear demands and fully characterize all possible optimal solutions for both ordered and non-ordered demands. We show that both optimal packages can either contain Pareto-efficient quantities or one package can be undersized or oversized. All these effects are non- degenerate and are expected to hold for nonlinear demands. Surprisingly, the total output under nonlinear price discrimination with self- selection is neither unambigously realted to efficiency nor to the degree of monopoly power (demand elasticity). We also show that under limited range of parameters quantity premia can occur only when demands are ordered.

Price Discrimination using Linear and Nonlinear Pricing Simultaneously

Price discrimination practiced by using linear and nonlinear pricing simultaneously raises the average price for heterogenous consumers paying linear price but lowers for homogeneous group who pay nonlinear price. Discrimination lowers consumer surplus for both groups but increases total surplus.

The Degree of Distortions under Second-Degree Price Discrimination

Under second-degree price discrimination, both types of consumers get efficient quantities when the net-of-cost valuation functions intersect at least once at some positive quantity and the point of intersection lies between the two peaks. Distortions can be upward or downward.

Distortion in Screening and Spatial Preferences

We study a multidimensional screening problem with minimal restrictions on valuations. Our ?-relaxation of the constraints excludes bunching and cycles in the graph of active incentive-compatibility constraints. Therefore, the Lagrange multipliers do exist and enable us in characterizing distortion. In particular, under “spatial” preferences that include both the Hotelling and the Spence-Mirrlees cases, the solution has a simple planar graph. Consequently, the pattern of distortion is centrifugal, i.e., the points of service are biased towards the low-valuation market segments

Effects of Horizontal Merger on Price, Profits, and Market Power in a Dominant-Firm Oligopoly

Assuming that all firms have rising marginal costs, merger between a dominant firm and one of the firms in the competitive fringe is considered. The effects on market price and output, profits and market power are shown when the dominant firm operates as a two-plant firm after merger and output arises from both plants. It is proved that if merger offers no efficiency gain, then market price always rises; and if merger results in efficiency gain, then market price falls if and only if there are sufficiently large number of firms in the fringe. In any case, there is profit incentive for merger to take place. [611]

Pay-What-You-Want Pricing Under Competition: Breaking the Bertrand Trap

This paper investigates the viability of Pay-What-You-Want (PWYW) pricing when firms compete without restrictions of a minimum payment requirement. We show that the equilibrium outcomes are different when underpayers, consumers paying less than marginal cost, are present as opposed to when they are absent. In particular, when PWYW pricing is practiced without restricting the presence of underpayers or any minimum payment requirement, then the only two equilibrium structures are: either both firms use the posted price and earn zero profits, or one firm adopts PWYW pricing and the other uses the posted price. The asymmetric pricing equilibrium leads to a softening of price competition where both firms earn positive profits and the Bertrand Trap is broken.

Method of Digraphs for Multi-dimensional Screening

We study a general model of multi-dimensional screening for discrete types of consumers without the single-crossing condition or any other essential restrictions. Such generality motivates us to introduce graph theory into optimization by treating each combination of active constraints as a digraph. Our relaxation of the constraints (a slackness parameter) excludes bunching and cycles among the constraints. Then, the only possible solution structures are rivers, which are acyclic rooted digraphs, and the Lagrange multipliers can be used to characterize the solutions. Relying on these propositions, we propose and justify an optimization algorithm. In the experiments, its branch-and-bound version with a good starting plan shows fewer iterations than a complete search among all rivers.

Economies of Scope and Tying Agreements

This article broadens the concept of cost in tie-in agreements. It is shown that the relevant economic criterion to be used in evaluating the tie-in agreements is not the price of the tied goods. Instead, where multiproduct buying is involved, it is the total acquisition costs of tied-in products which should be used as the relevant economic criterion.