Three Pricing Policies for a Multi-Product Multi-National Company

A price leader must formulate list prices every time he introduces a new product line (fairly frequently in a technologically developing industry). This is not easy. When the company is multi-national, pricing policy becomes further complicated by the issues of centralization versus autonomy of the national subsidiaries, and three pricing schemes are encountered in practice. Scheme 1. The price of an item is the same around the world, except that the customers absorb freight plus import duty. Very simple price coordination and auditing results from this policy. Scheme 2. National prices for the line equal an optimally determined national weighting factor multiplied by a set of benchmark prices. Scheme 3. The subsidiaries can take advantage of local competitive climates with no fixed requirement that prices be coordinated across the nations. For each pricing scheme the overall profit equals the model profit minus administrative costs. The three schemes are sequenced in order of their model profits, which is also their likely administrative cost sequence. We shall compute their comparative model profitabilities so as to have bonds against which to gauge administrative costs. A base case is presupposed. Adjustments to prices and to marketing budgets induce changes in the quantity sold, and hence in the production cost. The profit function is approximated as quadratic in the control variables of price and marketing budget, so that optimal adjustments can be calculated by little more than inverting a partitioned matrix.

Generalized Networks, Generalized Upper Bounding and Decomposition of the Convex Simplex Method

If the constraint matrix of a linear program has special structure it may be possible to speed computation. Techniques have been developed to take advantage of such special structures as generalized networks, generalized upper bounding, and decomposition. For these matrix structures, it is shown in this paper how to extend the techniques to Zangwill's mathematical programming algorithm, the convex simplex method.

Maneuvering Liquid Assets in a Multi-National Company: Formulation and Deterministic Solution Procedures

Over a finite horizon each national subsidiary of a multi-national company can be forecast to be a net source or sink of funds. Each of these subsidiaries in each year is considered to be the node of a network; funds flow along the directed arcs connecting the nodes. Liquid assets carried by the subsidiaries on the arcs between time periods earn interest minus adjustments for expected devaluations. In each time period a flow of funds between each pair of subsidiaries can be achieved by manipulating transfer prices and managerial fees, by making short term intersubsidiary loans, and by paying dividends up the intersubsidiary ownership tree. The costs and constraints on these flows are outlined with particular attention given to the IRC Subpart F regulations of the U.S. 1962 Revenue Act, and to the 1968 regulations of the Office of Foreign Direct Investment. It is shown to be extremely important that subsidiary dollar accounts count toward the compensating balance requirements of a U.S. bank, and it is also shown that there are benefits to a global tax consolidation under Subpart F. The problem can be solved as a generalized network (weighted distribution problem). This avoids the need to guess at the average discount rate if it is to be solved as an ordinary network.

Product Design: Subassemblies for Multiple Markets

A firm may cut costs by installing more parts than its products require. Each product or application requires a specified number of parts such as inductors, resistors and capacitors. For assembly and maintenance reasons, parts are grouped into subassembly modules. If there are economies of scale in manufacturing sub-assembly modules, it may be worthwhile to standardize on a few module designs that will be used in all products or applications even though a few more parts than needed are installed. The cost of giving away extra parts by using few standard modules must be balanced against the fixed costs of producing more types of standard modules. In the multi-market problem there is a fixed cost with the production of a module, and then another fixed cost when the module is used in a market. The paper presents a solution procedure and the time results of computer runs for the problem of finding the best standard modules for a multi-product, multi-market corporation.

Preempting an Alert Rival: Strategic Timing of the First Plant by Analysis of Sophisticated Rivalry

This paper examines the strategic rivalry in a duopoly where firms must correctly time the construction of the first plant in a growing market. We explicitly model rivalry for market share. Firms recognize the effect of the rival's actions on their profits; they behave noncooperatively to maximize discounted profits over the infinite horizon. For the timing problem we develop an appropriate solution concept. It is a Nash equilibrium in the space of sequential decision rules which specify each firm's correct action as a function of the state of the world. We then show how the equilibrium can be computed by backward induction dynamic programming. Numerical examples illustrate the sequential Nash solution and characterize the rivalry to be the first to build. Parametric analysis of the example enables us to explore the competitive dynamics of capacity choice in new markets.