Customer poaching with differentiated products and switching costs.

We consider a dynamic two-period model where two firms offer products that are differentiated a la Hotelling. Consumers purchase products in a first period, and in a second period consumers are locked-in to their first-period choice of producer with a switching cost. In the second period firms are able to price discriminate based on consumers purcase history from period 1. We show that i) firms will approach their rival's customers by low prices in the second period (customer poaching) and that ineffcient switching will occur, ii) second-period prices are dependent on first-period market shares, a result in contrast to some of the received literature. Finally, iii) with high enough switching costs first-period prices is below the level in a static setting, and more so the higher the switching costs and the more differentiated the products are.Oligopoly and Other Imperfect Markets; Production; Pricing; and Market Structure; Size Distribution of Firms

An effective solution to the nonlinear, nonstationary Navier-Stokes equations for two dimensions

A sequence of approximate solutions for the nonlinear, nonstationary Navier-Stokes equations for a two-dimensional domain, from which explicit error estimates and rates of convergence are obtained, is described. This sequence of approximate solutions is based primarily on the Newton-Kantorovich method

A solution of one dimensional Fredholm integral equations of the second kind

Fredholm integral equations of the second kind of the one dimension are numerically solved. It is proven that the numerical solution converges to the exact solution of the integral equation. This is shown for periodic kernels and then extended to nonperiodic kernels. This development helps delineate a basic theory which has the potential of solving very complex problems

Slotting Allowances and Buy-Back Clauses

In this paper we investigate some of the most frequent arguments for the use of slotting allowances. It has been claimed that slotting allowances can be profitability used to increase retail profits at the cost of increasing consumer prices. A second argument is that slotting allowances can be used by producers of new product to signal the demand potential of their products. We find that in perfect information setting slotting allowances will never arise in equilibrium. Moreover, we question whether slotting allowances can serve as a signalling device. We argue that buy-back clauses are far better instruments to signal profitability of new product launches in the grocery sector.Demand and Price Analysis, L12, L40,

Measuring market liquidity: An introductory survey

Asset liquidity in modern financial markets is a key but elusive concept. A market is often said to be liquid when the prevailing structure of transactions provides a prompt and secure link between the demand and supply of assets, thus delivering low costs of transaction. Providing a rigorous and empirically relevant definition of market liquidity has, however, provided to be a difficult task. This paper provides a critical review of the frameworks currently available for modelling and estimating the market liquidity of assets. We consider definitions that stress the role of the bid-ask spread and the estimation of its components that arise from alternative sources of market friction. In this case, intra-daily measures of liquidity appear relevant for capturing the core features of a market, and for their ability to describe the arrival of new information to market participants

A solution for two-dimensional Fredholm integral equations of the second kind with periodic, semiperiodic, or nonperiodic kernels

A numerical scheme for solving two dimensional Fredholm integral equations of the second kind is developed. The proof of the convergence of the numerical scheme is shown for three cases: the case of periodic kernels, the case of semiperiodic kernels, and the case of nonperiodic kernels. Applications to the incompressible, stationary Navier-Stokes problem are of primary interest

A family of approximate solutions and explicit error estimates for the nonlinear stationary Navier-Stokes problem

An algorithm for solving the nonlinear stationary Navier-Stokes problem is developed. Explicit error estimates are given. This mathematical technique is potentially adaptable to the separation problem

A numerical solution for two-dimensional Fredholm integral equations of the second kind with kernels of the logarithmic potential form

Two dimensional Fredholm integral equations with logarithmic potential kernels are numerically solved. The explicit consequence of these solutions to their true solutions is demonstrated. The results are based on a previous work in which numerical solutions were obtained for Fredholm integral equations of the second kind with continuous kernels

Why is on-net traffic cheaper than off-net traffic? Access markup as a collusive device and a barrier to entry

Received literature have shown that if competing networks are restricted to linear and uniform pricing, high access charges can facilitate collusion; a result that breaks down if we allow for non-linear and discriminatory pricing, however. In this paper we add unbalanced calling pattern to the model and show that this may restore the use of high access charges. High access charges may make the firms collude on high prices. Moreover, when allowing for entry, we show that incumbents can profitably charge high access prices as a device to deter or soften entrants.Two-way access; non-linear pricing; competition; entry.

Consumer Heterogeneity and Pricing in a Duopoly with Switching Costs

It is well-known that switching costs may facilitate monopoly pricing in a market with price competition between two suppliers of a homogenous good, provided the switching cost is above some critical level. We show that introducing consumer heterogeneity tends to increase the critical switching cost and thereby reduce the stability of the collusive outcome. A testable implication is that widespread price discrimination should go hand in hand with efforts to create switching costs.