Decreasing Marginal Costs Research Articles

Efficient public good provision by lotteries with nonlinear pricing

In this paper, we introduce nonlinear pricing of lottery tickets to the mechanism of Morgan (2000), in which a lottery is used to finance the public good. In a model with n symmetric agents, we find that incorporating this instrument fully achieves the efficient provision of public good when each agent’s initial wealth is sufficiently high. In a model with two asymmetric agents, there exists a nonlinear lottery mechanism that induces efficient public good provision provided that agents are not too heterogenous. Intuitively, the proposed nonlinear pricing rule leads to a decreasing marginal cost for ticket purchase, which provides stronger incentives for agents to make contributions, compared with Morgan (2000).

Location and two-echelon inventory network design with economies and diseconomies of scale in facility operating costs

Most existing facility location and network design models assume the facility cost as either a fixed cost term or a linear/concave function of the volume of demand assigned to a facility. In particular, a concave cost function implies decreasing marginal cost and exhibits economies of scale. However, when the assigned demand volume exceeds a certain level, diseconomies of scale may occur due to facility congestions, overuse of resources, increasing operational complexity, and so on, leading to a convex cost function with increasing marginal cost. This paper studies a warehouse–retailer network design problem, which simultaneously optimizes the warehouse locations, the warehouse–retailer assignment, and the multi-echelon inventory replenishment policy to minimize the total cost, including the warehouse location and operating costs, the inventory replenishment cost, and the transportation cost. In this paper, the warehouse operating cost is defined as a general function of the volume of demand assigned to a warehouse, which could be concave first due to economies of scale and then convex due to diseconomies of scale. We formulate this problem as a set-covering model and propose a column generation algorithm to solve its linear relaxation. The pricing problem of the column generation process, although formulated as a nonlinear mixed integer program, has nice structural properties and can be solved efficiently by a branch-and-bound method. To validate the effectiveness and efficiency of the proposed column generation algorithm, we conduct numerical studies based on randomly generated instances. Numerical results also demonstrate the impact of economies and diseconomies of scale on network design decisions and warehouse operating cost.

Observable Cyber Risk on Cournot Oligopoly Data Storage Markets

With the emergence of global digital service providers, concerns about digital oligopolies have increased, with a wide range of potentially harmful effects being discussed. One of these relates to cyber security, where it has been argued that market concentration can increase cyber risk. Such a state of affairs could have dire consequences for insurers and reinsurers, who underwrite cyber risk and are already very concerned about accumulation risk. Against this background, the paper develops some theory about how convex cyber risk affects Cournot oligopoly markets of data storage. It is demonstrated that with constant or increasing marginal production cost, the addition of increasing marginal cyber risk cost decreases the differences between the optimal numbers of records stored by the oligopolists, in effect offsetting the advantage of lower marginal production cost. Furthermore, based on the empirical literature on data breach cost, two possibilities are found: (i) that such cyber risk exhibits decreasing marginal cost in the number of records stored and (ii) the opposite possibility that such cyber risk instead exhibits increasing marginal cost in the number of records stored. The article is concluded with a discussion of the findings and some directions for future research.

Subjective equivalence scales using EU-SILC panel data for Poland, the Czech Republic, and Hungary

Equivalence scales are commonly employed in income analysis to compare the wealth of households of various compositions (e.g., 0-child, 1-child). The choice of weights for this type of analysis is not self-evident. In this paper, subjective equivalence scales for households in Poland, the Czech Republic, and Hungary are estimated. We use longitudinal EU-SILC data for 2005–2012 following the approach of Goedhart et al. (1977) as employed by Bishop et al. (2014). The use of longitudinal data shows that previous results on the subjective minimum income that were based on the OLS estimates for cross-section data overestimated the impact from current income and underestimated the role of economies of scale. Subjective equivalence scales imply a decreasing marginal cost of children in the three countries, which makes them distinct from the OECD scale. The marginal cost of a first child is similar to the values assumed in the OECD scale, but the cost of a second child is much lower.

Lying generators: manipulability of centralized payoff mechanisms in electrical energy trade

Optimal power flow (OPF) problems are focussing on the question how a power transmission network can be operated in the most economic way. The general aim in such scenarios is to optimize generator scheduling in order to meet consumption requirements, transmission constraints and to minimize the overall generation cost and transmission losses. We use a simple lossless DC load flow model for the description of the transmission network, and assume linearly decreasing marginal cost of generators with different parameters for each generator. We consider a scenario in which the generation values regarding the OPF are calculated by a central authority who is aware of the network parameters and production characteristics. Furthermore, we assume that a central mechanism is applied for the determination of generator payoffs in order to cover their generation costs and assign them with some profit. We analyze the situation when generators may provide false information about their production parameters and thus manipulate the OPF computation in order to potentially increase their resulting profit. We consider two central payoff mechanisms and compare their vulnerability for such manipulations and analyze their effect on the total social cost.

Pareto-improving tariff-tax reforms under imperfect competition

Constructing a duopoly model with non-constant marginal costs and a strict Pareto criterion, this paper examines welfare effects of world-price-fixing tariff reductions accompanied by adjustments of a domestic tax. If a destination-based consumption tax is used, this reform achieves a strict Pareto improvement under sufficiently decreasing marginal costs. If, in contrast, an origin-based production tax is employed, a strict Pareto improvement holds whether marginal cost is decreasing or not. Thus, we can conclude that tariff-tax reforms that improve the world welfare and are irrelevant of tax bases are possible if the targeted industry exhibits sufficiently decreasing marginal costs.

Sales Tax Competition and a Multinational with a Decreasing Marginal Cost

We examine a multinational firm which has a decreasing marginal cost, and the optimal sales tax policies of the regions where that firm operates. We show that the regions set higher sales taxes than those given by a cooperative equilibrium. Each region fails to fully internalize the effects of its tax level on another region's welfare and the incentives for that region's authority. Exponential cost functions which exhibit economies of scale (for example Cobb-Douglas) and linear demand functions satisfy our assumptions. Our results suggest the need to coordinate sales tax levels between countries and between smaller entities, like states in the United States. Smaller regions benefit more from such coordination. Lowering sales taxes in each region increases welfare for all regions, profits for firms, and consumer welfare.

Brand or Variety Choices and Periodic Sales as Substitute Instruments for Monopoly Price Discrimination

We study the puzzle that sellers often employ diverse strategies in terms of carrying multiple brands and holding periodic sales. These two selling tools can be substitute instruments to induce consumer self selection and implement price discrimination. We analyze the factors that affect a seller’s choice between the two pricing instruments and show how different combinations of the two instruments can be optimal under alternative market conditions. A seller may, surprisingly, increase her total number of offers when it becomes more costly to carry brands or hold sales if there are decreasing marginal costs of the alternative selling tool.

Sales Tax Competition and a Multinational with a Decreasing Marginal Cost

We examine a multinational firm which has a decreasing marginal cost, and the optimal sales tax policies of the regions where that firm operates. We show that the regions set higher sales taxes than those given by a cooperative equilibrium. Each region fails to fully internalize the effects of its tax level on another region's welfare and the incentives for that region's authority. Exponential cost functions which exhibit economies of scale (for example Cobb-Douglas) and linear demand functions satisfy our assumptions. Our results suggest the need to coordinate sales tax levels between countries and between smaller entities, like states in the United States. Smaller regions benefit more from such coordination. Lowering sales taxes in each region increases welfare for all regions, profits for firms, and consumer welfare.

The optimality of optimal punishments in Cournot supergames

The result of Colombo and Labrecciosa [Colombo, Luca and Labrecciosa, Paola (2006). ‘The suboptimality of optimal punishments in Cournot supergames’, Economics Letters 90, pp. 116–121.] that optimal punishments are inferior to Nash-reversion trigger strategies with decreasing marginal costs is shown to be due to the output when a firm deviates from the punishment path becoming negative.

Optimal investment in HIV prevention programs: more is not always better.

This paper develops a mathematical/economic framework to address the following question: Given a particular population, a specific HIV prevention program, and a fixed amount of funds that could be invested in the program, how much money should be invested? We consider the impact of investment in a prevention program on the HIV sufficient contact rate (defined via production functions that describe the change in the sufficient contact rate as a function of expenditure on a prevention program), and the impact of changes in the sufficient contact rate on the spread of HIV (via an epidemic model). In general, the cost per HIV infection averted is not constant as the level of investment changes, so the fact that some investment in a program is cost effective does not mean that more investment in the program is cost effective. Our framework provides a formal means for determining how the cost per infection averted changes with the level of expenditure. We can use this information as follows: When the program has decreasing marginal cost per infection averted (which occurs, for example, with a growing epidemic and a prevention program with increasing returns to scale), it is optimal either to spend nothing on the program or to spend the entire budget. When the program has increasing marginal cost per infection averted (which occurs, for example, with a shrinking epidemic and a prevention program with decreasing returns to scale), it may be optimal to spend some but not all of the budget. The amount that should be spent depends on both the rate of disease spread and the production function for the prevention program. We illustrate our ideas with two examples: that of a needle exchange program, and that of a methadone maintenance program.

The Life Cycle of the U. S. Tire Industry

1. Introduction A recent literature has emerged focusing on industry evolution, or the dynamic patterns that industries and firms follow as they systematically evolve over time. This literature is important because of the insights provided about how industries change, why they change, and the consequences of industrial change. year 1982 saw three fundamental contributions made to the research on the evolution of industry. Boyan Jovanovic published the first formal model of industry evolution, Richard Nelson and Sidney Winter presented their influential book on the causes and effects of this phenomenon, and Michael Gort and Steven Klepper published their careful analysis of the stages of the product life cycle. Knowledge concerning industry dynamics and industry evolution has expanded since then.' Despite this progress in the field of industry evolution, considerable gaps remain. For example, we lack an adequate empirical understanding of the evolutionary process at the single-industry level from the early to the late stages of its life cycle. Shakeouts have been identified in the literature as an integral component of this evolutionary process. sudden disappearance of large numbers of firms have been documented across a broad spectrum of industries, such as steel, airline carriers, financial intermediaries, automobiles, and tires. An important strand in the literature argues that the catalyst for these shakeouts is the introduction of a new dominant innovation. Confronted by a new technology introduced by a competitor, the inability of other firms to adopt this new dominant technology presumably forces them out of the market. Jovanovic and MacDonald (1994) made a pioneering and parsimonious contribution in this field of research by explaining patterns of number of firms, output, and prices of the U.S. tire industry. Despite the importance of their contribution, we argue that their model does not adequately describe the key historic developments that have taken place in this or many other industries that faced a shakeout of producers.2 domain of relevance of the Jovanovic-MacDonald model is limited. It assumes that one innovation followed by just one refinement is responsible for the nonmonotonicity in firm numbers. This implies that the model is applicable only for those industries having experienced just two technologies in their entire history: an initial low-tech and a subsequent high-tech phase. Most industries, including the automobile tire industry that was the testing ground of Jovanovic and MacDonald, have an ongoing history of significant improvements in product quality and productivity. It seldom occurs that one innovation is dominant. This is certainly true for the tire industry. Nelson (1987), in his study on the U.S. tire industry, observed that there was no single technical breakthrough that unlocked the industry's potential for highspeed production; nor was any individual or firm of overriding importance. advent of mass production was a cumulative process resulting from a vast number of successive small changes (pp. 331-2, italics added). Almost half a century ago, Reynolds (1938, p. 463) described a similar process: The great improvement in tire quality during the past 30 years is undoubtedly due to constant repetition of [the] cycle of invention and imitation. We take a different approach than Jovanovic and MacDonald and explain the nonmonitonicity in firm numbers as resulting from gradual unit cost reduction over time leading to declining profit margins. In the present paper, we relate this cumulative process to the concept of learning-by-doing. We will test the model using data of the American tire industry. We do this to facilitate the comparison between our model and that of Jovanovic and MacDonald and because this industry is one of the few for which data are available for a long time period. process of learning-by-doing leading to decreasing marginal costs over time has an important impact on the number of firms in the industry. …

Learning to play Cournot duopoly strategies

The paper reports results from experiments designed to determine whether subjects can learn to play Cournot duopoly strategies and whether their out-of-equilibrium play is consistent with the predictions of learning models. The experiments include duopolies with constant and with decreasing marginal costs, and with theoretically stable and unstable equilibria. After a few periods, subjects do play stable interior equilibria but they do not play stable boundary equilibria nor unstable interior equilibria. Subjects' out-of-equilibrium play is inconsistent with the predictions of the learning models.

Cost Sharing under Increasing Returns: A Comparison of Simple Mechanisms

A technology with decreasing marginal costs is used by agents with equal rights. Each agent demands a quantity of output and costs are divided by means of a fixed formula. Several such mechanisms are compared for the existence of Nash equilibrium demand profiles and for the equity properties of these equilibria. Among three mechanisms, average cost pricing, the Shapley–Shubik cost sharing, and serial cost-sharing, only the latter two possess at least one Nash equilibrium on a reasonable domain of individual preferences. Only the serial cost sharing equilibria pass the equity tests of No Envy and Stand Alone cost.Journal of Economic LiteratureClassification Numbers: C72, D63.

Cost Sharing Under Increasing Returns: A Comparison of Simple Mechanisms

A technology with decreasing marginal costs is used by agents with equal rights. Each agent demands a quantity of output and costs are divided by means of a fixed formula. Several such mechanisms are compared for the existence of Nash equilibrium demand profiles and for the equity properties of these equilibria. Among three mechanisms, average cost pricing, the Shapley-Shubik cost sharing and serial cost-sharing, only the latter two possess at least one Nash equilibrium on a reasonable domain of individual preferences. Only the serial cost sharing equilibria pass the equity tests of No Envy and Stand Alone cost.

Raising Children: Private Expenditure and Foregone Earnings*

Abstract. From the point of view of an individual household there are two major types of private cost of children, viz. direct household expenditure for the offspring plus (usually) mothers' foregone earnings. Both aspects have been studied theoretically and empirically, but thus far only separately. The joint empirical analysis of these main costs of children are the subject of this paper. Employing the Austrian Consumer Survey of 1984/85 and 1983's Microcensus, household expenditure on one, two and three children and mothers' foregone earnings are estimated for a comparable sample of households.In order to estimate household expenditure on children a modified Prais‐Houthakker model has been employed. Labour force participation functions as well as human‐capital wage equations were estimated using a multinomial logit model and allowing for both the impact of career interruptions and part‐time work. Through simulation on the basis of these estimates we arrive at comparable life‐time earnings of women with no, one, two or three children. We then add the relevant differences to the expenditure on children to obtain the “total” private cost of children.Being aware of the limitations of our analysis–not all monetary private outlays and no public expenditure are included, no consideration of children's benefits to parents, etc. ‐ we can nevertheless draw some tentative conclusions: there are decreasing marginal costs for the second child and rather constant costs for the third child, except for the case of “low attachment“ to the labour force, where marginal cost also declines for the third child. Assuming utility maximizing households, one could arrive at a policy prescription for raising birth rates: find a means to reduce foregone earnings which appear to be a major deterrent to having more than one child.

Transport Cost in Cournot Duopoly with Several Markets.

The effects of change in transport cost are investigated for homogeneous Cournot duopoly with several regional or international markets and with decreasing marginal costs. A new existence proof is given for the unique Cournot duopoly equilibrium based on an integration of mathematical and diagrammatical approaches. Two cases are analyzed, in one of which the marginal revenue of any firm is assumed to decrease with an increase in the other firm's output, and in the other it is an increasing function of the other firm's output. In both cases the firms are assumed to have decreasing marginal costs.

A comparison of user-optimum versus system-optimum traffic assignment in transportation network design

In this report, we compare the computational efficiency and results of solving two alternative models for the problem of determining improvements to an urban road network. Using a 1462 link, 584 node test network of the north Dallas area, we compare a model which assumes user-optimum behavior of travelers with a model which assumes system-optimum flows. Both of these models allow improvements to the road network to take on any nonnegative value, rather than requiring discrete improvement values. Investment costs are modeled by functions with decreasing marginal costs. Unfortunately, the user-optimum model, which is much more realistic than the system-optimum one, normally cannot be solved optimally. However, the simpler system-optimum model can be optimally solved, provided that investment costs are approximated by linear functions. Thus, for this network design problem we compare an accurate representation which can be solved only approximately with an approximate representation which can be solved optimally. Our computational testing showed that the system-optimum model produces solutions as good as those from the user-optimum model, and thus seems justified when favored by other considerations, such as ease of coding, availability of “canned” programs, etc.