Asymptotic behavior of market shares for a stochastic growth model

Consider a market with finitely many firms, each enjoying an uncertain growth. We assume the (random) growth rates of these firms are independent and identically distributed. We show that the asymptotic probability distribution of the market shares gives each firm an equal probability of dominating the market (while all other firms are almost extinguished). In particular, these conclusions are independent of the initial market shares of the firms. We conclude that sample paths fluctuate between almost domination and almost extinction. We also demonstrate that these fluctuations may be very slow. Extensions to situations where the total demand is restricted are discussed.     

Agency Costs in Apartment Property Management Contracts

Because fees for property management services are based on gross rental collections rather than on net operating incomes, property managers may not always act in the best interest of property owners. This study is an examination of the agency costs that result from the conflict of interests between owners and managers. A nationwide proprietary sample of 242 apartment properties is analyzed to compare agency costs of four distinct types of ownership structures. Agency costs, measured as operating expenses per square foot, are found to be significantly higher for institutional owners than for noninstitutional owners, but not significantly higher in cases where no competition for property management services exists. We conclude that agency costs of property management contracts are significant and the fee provisions of standard property management contracts should be changed to better align the interests of managers and owners.     

The co‐evolution of capabilities and transaction costs: explaining the institutional structure of production

This paper proposes that transaction costs and capabilities are fundamentally intertwined in the determination of vertical scope, and identifies the key mechanisms of their co‐evolution. Specifically, we argue that capability differences are a necessary condition for vertical specialization; and that transaction cost reductions only lead to specialization when capabilities along the value chain are heterogeneous. Furthermore, we argue that there are four evolutionary mechanisms that shape vertical scope over time. First, the selection process, itself driven by capability differences, dynamically shapes vertical scope; second, transaction costs are endogenously changed by firms that try to reshape the transactional environment to increase their profit and market share; third, changes in vertical scope affect the nature of the capability development process, i.e., the way in which firms improve their operations over time; and finally, the changes in the capability development process reshape the capability pool in the industry, changing the roster of qualified participants. These dynamics of capability and transaction cost co‐evolution are illustrated through two contrasting examples: the mortgage banking industry in the United States, which shows the shift from integrated to disintegrated production; and the Swiss watch‐manufacturing industry, which went from disintegration to integration. Copyright © 2005 John Wiley & Sons, Ltd.     

Optimal maintenance center inventories for fault-tolerant repairable systems

In many military and commercial contexts, complex equipment which is expected to perform very reliably is often designed to be fault-tolerant, that is, able to function although some of the parts have failed. A popular fault-tolerant design is the m-out-of-n system, where there are n identical parts, at least m of which must be functional for machine operation. Complex equipment of this type often undergoes scheduled maintenance overhauls at regular intervals during which all failed components are replaced. Failure to have replacements on hand for failed parts requires emergency measures at premium cost. When repairable parts are highly reliable and expensive, both holding and shortage costs are high. A reasonable objective is to choose initial spares inventory to minimize the sum of holding costs and expected shortage costs.We first develop a model to determine the optimal repairable parts inventory for a maintenance center servicing machines containing a single m-out-of-n system. The model is then extended to handle a related problem, finding optimal maintenance center inventories for machines containing several m-out-of-n systems of different parts, minimizing total expected costs subject to a constraint on total inventory investment.We assume that there is a fleet of machines, which experience identical workloads. There is a cycle time of T days between overhauls for an individual machine. A machine arrives at the maintenance center for overhaul each day. At the overhaul, all failed parts are removed and sent to a repair shop, from which they eventually return to the maintenance center to be used again as spares. The total number of spares undergoing repair and on hand is a constant. There are no backorders; if the number on-hand spares is insufficient to meet demand at an overhaul, a shortage penalty is assessed which depends on the number and type of spares required.While computing holding costs is straightforward, computing expected shortage costs is more complex. Expected shortage costs are dependent upon several factors, including component failure rates, the values of m and n, part repair rates, and the initial number of spares on hand. We assume that the system of interest is well specified, so that the parameters of the model are known except for the number of initial spares of each type, which are the decision variables. We model the on-hand inventory of each type of part as a Markov chain with the number of spares on hand at the end of each day as the states, under the assumptions that failure rates are constant and repair times follow independent exponential distributions. We then calculate the steady-state probabilities of stockout of various numbers of spares, as a function of the initial spares inventory. The expected shortage costs for a given type of spare may then be calculated by finding the product of the penalty cost for lacking p spares and the probability of lacking p spares and summing over all possible p values.Solutions to the problem of finding optimal initial inventory level for a machine containing a single m-out-of-n system may be found easily by enumeration. Solutions to the constrained problem where the machine contains several independent m-out-of-n systems, may be found by dynamic programming. Sensitivity analysis of costs to changes in the inventory investment constraint is clear, and computational effort is reasonable. A simple example is included to illustrate the solution method for both problems.