Group size and the private supply of a best-shot public good

This paper examines the relationship between group size and the likelihood that a best-shot public good is voluntarily provided. Holding fixed each member's individual probability of supplying the public good, the likelihood of supply increases as the group grows. This is the size effect. However, as group size increases, the probability that each individual member supplies decreases. This is the strategic effect. The net effect of group size on the likelihood is thus ambiguous. As group size increases without bounds, the two effects are offset—the likelihood approaches a finite limit.     

Allocation of Prizes in Contests with Size Effects

We examine the allocation of prizes in contests in which the number of contenders affects the prizes and costs. We assume that there are two groups of contenders. The government allocates a prize to the two groups, and the contenders in each group respectively compete for the prize. Examining the prize allocation in such contests, we obtain the following results. The aggregate effort increases in the prize share of the larger group. In contests with size effects through costs, the aggregate resource expended in the contests and the aggregate payoffs are independent of group size distribution if the prize is allocated in proportion to group size. The integration of contests with size effects through prizes can yield higher aggregate effort and payoffs than the decentralized contests.     

Efficiency and group size in the voluntary provision of public goods with threshold preference

What is the optimal group size in the voluntary provision of public goods in a purely altruistic economy? The popular consensus on this fundamental question is that the free-rider problem worsens as the group size increases. This study provides a counterexample of the consensus by featuring plausible threshold preferences for certain typical public goods. Under these preferences, marginal utility hardly diminishes below a threshold level, but declines significantly in close proximity to the threshold and nearly drops to zero above the threshold. We find that threshold preferences significantly reduce inefficiency. We also show that if marginal costs increase, then the threshold preferences lead to a partly positive relationship between efficiency and group size, which allows us to detect the locally efficient group size. Moreover, the locally efficient group size is proportional to the slope of the marginal costs as well as the threshold of marginal utility.     

How does the effect of pre-play suggestions vary with group size? Experimental evidence from a threshold public-good game

Numerous studies have examined factors influencing the likelihood of cooperative outcomes in nonzero-sum games, but there has been little study of the interaction between two of the most important: group size and pre-play cheap talk. We report results from an experiment in which groups of size between 2 and 15 play a one-shot multi-player threshold public-good game. In our random leader treatment, all group members select a suggestion (e.g., “Everyone should choose X”), with one randomly chosen to be broadcast to the group. In a choice only treatment, subjects choose suggestions but none is sent, and in a baseline treatment, there are no suggestions at all. We find a negative interaction between group size and this kind of communication: the beneficial effect of both suggestions overall and cooperative suggestions on cooperation, cooperative outcomes, and payoffs decreases sharply as the group size increases. We find a similar negative interaction in a follow-up treatment in which all group members’ suggestions are broadcast to the group. Our results suggest that care should be taken in generalising conclusions from small-group experiments to large groups.     

Effectiveness of Weighted Majority Rules with Random Decision Power Distribution

There is a large body of research studying the conditions under which majority decisions are best. In particular, in many circumstances, the probability of a group to decide correctly is higher than that of a random subgroup. Moreover, the latter probability increases as the subgroup size grows. Here we generalize those results by showing that, in the same setup, the simple majority rule is the most effective of all weighted majority rules when weights are distributed randomly between group members. For special families of weighted majority rules, rule effectiveness increases as we get “closer” to the simple majority rule.     

Conflict technology in cooperation: The group size paradox revisited

This paper studies the implications of punishment‐induced conflict in a public goods game. It shows, under plausible assumptions, how larger group size sometimes enhances punishing behavior in social dilemmas and hence supports higher levels of cooperation. Unlike existing approaches that focus on uncoordinated punishment, I consider punishment as a coordinated activity that may be resisted by those being punished and study the implications of punishment‐induced conflict situations. Developing a conflict model of punishment and combining it with a standard public good game, I show that coordinated punishment can yield the concentration effect of punishment, leading to a larger group advantage; that is, the larger the group, the easier it becomes to organize cooperation. The key idea is that when punishers coordinate their punishment, punishers as a coalition successfully divide defectors and punish each defector one by one. Surprisingly, even when coordination among punishers decays as group size increases, as long as the rate of decaying remains relatively slow the larger group advantage still obtains.     

The Scope of Anonymous Voluntary Bargaining Under Asymmetric Information

We present a model of anonymous collective bargaining where individuals'preferences and information may be significantly interdependent. We showthat the bargaining outcome becomes independent of individuals'preferences and information as the bargaining group increases in size. As acorollary, we show that anonymous voluntary bargaining completely fails inlarge groups. Either the difference between the bargaining outcome and thestatus quo vanishes as the size of the group becomes larger, or, thebargaining becomes coercive and results in a violation of at least someindividuals' rights. The result provides a rationale for the inherentdifficulty of reform in the presence of asymmetric information.
"There is nothing more difficult to carry out, nor more doubtful ofsuccess, nor more dangerous to handle, than to initiate a new order ofthings."
Niccolò Machiavelli, The Prince (1532)     

Tuition fees and equality of university enrolment

Abstract .  The relationship between tuition fee changes and the university enrolment of youth by parental income group in Canada is investigated. Comparisons between youth from Canadian provinces that increased tuition fees sharply in the 1990s and youth from provinces that instituted fee freezes were integral to identifying the relationship. Tuition fee increases coincided with reductions in the university enrolment of low-income youth, but with significantly smaller changes in the university enrolment of other youth. The relationships between government funding of universities and cohort size and university enrolments are also analyzed.     

Intra-Industry specialization: A cross-country analysis

This paper tests various hypotheses as to the determinants of intra-industry trade in thirty-eight developed and developing countries exporting manufactured goods. The econometric estimates for the entire group of countries show that the extent of intra-industry trade increases with the level of economic development (GNP per head), the size of domestic markets (GNP), and the openness of national economies. The existence of trading partners with common borders and geographical proximity further contributes to intra-industry trade.These hypotheses have also been confirmed for the developing country group. And while similarities in regard to trade orientation and the existence of border trade, as well as intercorrelation between the gross national product and per capita GNP, have reduced the statistical significance of the regression coefficients for these variables for the developed country group, this equation also has a high explanatory power.     

Measuring worker flows

The study explores differences between two measurement concepts of worker flows widely used in the literature referred to as the turnover and reallocation concepts. It is found that measuring worker flows by the turnover concept leads to substantially (about 5% of total employment) higher worker flow estimates and slightly increases age, size and industry group effects on firm level worker flows as well as differences between growing and declining firms relative to the reallocation concept.     

Welfare and the family size decision of low-income,two-parent families

This study determines the increase in family size given an increase in the per child welfare benefit for a family with children in the US. The family size decision was modeled as a discrete choice decision. Data were obtained from the 1980-91 March Current Population Surveys of the US Census Bureau on 13,516 low-income, nonmilitary, non-farm, two-parent families with at least one dependent child. Low income was any amount under twice the official poverty level. Parents were limited to ages 18-40 years. Alaska and Hawaii were excluded. The data sets for 1979-90 were pooled. The sample included 10% Blacks and 27% receiving some amount of welfare. Average ages were 28.9 years for mothers and 30.8 years for fathers. The average number of children was 2.43. Findings from the ordered probit model indicate that education had a negative impact on family size, and age and race had positive impacts. Wages did not have a significant effect. The state unemployment rate and the average state income had negative effects. Unearned income had a small but significant effect on family size. The marginal welfare benefit had a positive impact. Findings reinforce the wealth hypothesis, that wealthier societies have smaller family sizes. Family size declines with increases in wages and education, which reflect increases in opportunity costs for time. Family size increases with age, as rearing children is labor-intensive. Family size increases with unearned income and welfare benefits that make childbearing affordable. It is argued that poor people in developed societies behave more consistently like poor people in developing countries. A 100% increase in the per child welfare benefit resulted in a 2% increase in the number of children. The policy implication is that a considerable increase in welfare benefits will have only trivial behavioral impacts for the poor on family size decisions.     

Investment decisions and coordination problems in a market with network externalities: An experimental study

We study decision-making and the associated coordination problems in an experimental setting with network externalities. Subjects decide simultaneously in every round how much to invest out of a fixed endowment; the gain from an investment increases with total investment, so that an investment is profitable iff total investment exceeds a critical mass. The game has multiple, Pareto-ranked equilibria; we find that whether first-round total investment reaches critical mass predicts convergence towards the Pareto optimal full-investment equilibrium. Moreover, first-round investments and equilibrium convergence vary with critical mass and group size in a complex way that is explicable by subtle effects of strategic uncertainty on decision making.     

The Role of Market Size in the Formation of Jurisdictions

Administrative and political reorganization is being actively debated even in the mature, stable economies of Western Europe. This paper investigates the possibility that such a reorganization is tied to the integration of economic markets. The paper describes a model where heterogeneous individuals form coalitions for the provision of a public good and shows that the number and composition of these jurisdictions depend on the overall size of the market. The range of economic activities engaged in by jurisdiction members increases when the size of the market increases, and so does the range of their preferences over the public good. The result is a change in the endogenous borders of the jurisdictions, and a reorganization of all coalitions. The optimal number of jurisdictions is unique and increases with market size. In the absence of compensating transfers, however, the decentralized equilibrium need not be optimal and is not unique, although     

Collective Risk Control and Group Security: The Unexpected Consequences of Differential Risk Aversion

We provide an analysis of odds‐improving self‐protection for when it yields collective benefits to groups, such as alliances of nations, for whom risks of loss are public bads and prevention of loss is a public good. Our analysis of common risk reduction shows how diminishing returns in risk improvement can be folded into income effects. These income effects then imply that whether protection is inferior or normal depends on the risk aversion characteristics of underlying utility functions, and on the interaction between these, the level of risk, and marginal effectiveness of risk abatement. We demonstrate how public good inferiority is highly likely when the good is “group risk reduction.” In fact, we discover a natural or endogenous limit on the size of a group and of the amount of risk controlling outlay it will provide under Nash behavior. We call this limit an “Inferior Goods Barrier” to voluntary risk reduction. For the paradigm case of declining risk aversion, increases in group size(wealth) will cause provision of more safety to change from a normal to an inferior good thereby creating such a barrier.     

The sensitivity of partially regulated second-best prices to intercommodity cross elasticities of demand

Ramsey prices for multiproduct monopolists with competitive fringe are shown to be sensitive to cross elasticities of demand. The sensitivity increases with size of cross elasticities, and with size of difference between ratios of cross elasticities and of own-price elasticities.     

Auditing and competitive bidding in the public sector

This paper investigates the impact of a ministry's budget size on the choice between auditing a (Niskanen)bureau and employing competitive bidding in the provision of a publicly funded good. The ministry's marginal expected payoff increases fastest with budget size for auctioning as opposed to auditing. However, the ministry is shown to switch from a purely public provision to a competitive provision as the budget size increases even if expected fixed costs favor the audit. The study contributes to the literature by extending the Niskanen framework and by endogenizing the institutional arrangements for the provision of public sector goods.     

EDUCATIONAL VOUCHERS WHEN THERE ARE PEER GROUP EFFECTS—SIZE MATTERS*

In this article, I study the effects various educational voucher policies have on the sorting of children across schools and the per‐student expenditure levels at these schools, when a child's peer group matters and students differ over income and ability. I find that, depending on the magnitude of the voucher, switching from a public system to a voucher system could entail either welfare gains or losses. All voucher policies under consideration lead to greater inequality than the public system; however, these increases are not monotone in the voucher size.     

The Role of Human Capital in Manufacturing Plant Growth: Evidence from Taiwan

In this study, we set out to investigate the potential relationships between plant growth and size, age and human capital using a unique employer–employee matched data set for the Taiwanese manufacturing industry from 1998 to 2005. The general assumption of a reduction in plant growth with increases in plant size and plant age is confirmed by our manufacturing industry data set, while plant growth increases with the stock of human capital, albeit at a diminishing rate, thereby implying a positive concave relationship between plant growth and human capital. Moreover, we find that for plants with higher levels of human capital, the reduction in plant growth is more moderate with regard to size than with regard to age, indicating that differences in the stock of human capital within plants will tend to lead to differences in the patterns of age and size impacts on such plants' growth. Finally, substantial differences were observed among the influences of the various characteristics on plants with high, moderate and low growth in size.     

The Error-in-Rejection Probability of meta-analytic panel tests

The puzzling Monte Carlo finding that the size distortion of meta-analytic panel unit root tests increases with the number of panel series is explained as the cumulative effect of arbitrarily small size distortions in the time series tests composing the panel test.     

Immigration-induced effects of changes in size and skill distribution of the labor force on wages in the U.S.

We isolate the effect of immigration-induced changes in the size and skill distribution of the labor force on labor market outcomes using a model in which firms endogenously respond to these changes. We analytically show that while the immigration-induced increase in the size increases the relative wages, employment and output shares of the skill intensive sector, changes in the skill distribution lead to analytically ambiguous effects. We derive quantitative results for the US economy under different counter-factual scenarios with respect to immigration-induced changes in size and skill distribution of the labor force, where these changes resemble those of U.S. as a whole, New York, California and Canada, and reflect different immigration policy regimes. For example, immigration increases the mass of workers at the lower range of the skill distribution in the U.S., and the upper range in Canada. Regardless of these differences across scenarios, our quantitative results indicate that immigration increases the relative average wages of the skill intensive sector. Further, real wages of all workers increase due to reduced prices caused by the increased size of the labor force.