the learning path of the hidden economy the tax burden and tax evasion in new zealand this paper considers the learning curve relationship between the aggregate tax rate and the relative size of the hidden economy in new zealand some simple non linear models are estimated so that the effects of changes in the effective tax rate on the underground economy can be simulated this study finds that about half of the hidden activity in new zealand is a learned response to changing opportunities and constraints in fiscal policy but this amount varies over the business cycle simulating a zero tax rate permits us to discover the natural rate of underground and criminal activity some partial lessons are drawn for taxation policy in that country

pricing frills and customer ratings this paper explores whether and how a firm should adapt its strategy in view of consumer use of prior customer ratings specifically we consider optimal pricing and whether the firm should offer an unexpected frill to early customers to enhance their product experiences we show that if price history is unobserved by consumers a forward looking firm should always modify its strategy from single period optimal one but it may be optimal to do so by lowering price by lowering price and offering frills or by raising price and offering frills depending on the market growth rate specifically the last strategy becomes optimal when market growth rate is high enough the results are similar when the price history is observed by consumers except that no deviation from single period profit maximization choices is optimal when market growth is low enough we also analyze whether the firm should prefer that the price information be stated in or left out of consumer reviews in addition in considering the effects of consumer heterogeneity we conclude that the optimal firm s effort to affect ratings is higher when the idiosyncratic part of consumer uncertainty is larger

women s discrimination in developing countries a new data set for better policies summary based on a new data set this paper develops two innovative indicators to measure gender inequalities in developing countries the indicators measure different aspects of constraints imposed on women by social institutions that is laws norms traditions and codes of conduct that exist in societies for centuries the paper finds that social institutions are the most important single factor determining women s participation in economic activities outside the household

the effect of taxes on labor supply in the underground economy this paper uses micro data from a randomized survey carried out in the metropolitan area of quebec city canada to analyze the decision to evade taxes and work in the underground economy the results indicate that taxes distort labor market activities away from the regular sector to the underground sector but the distortion is small for the average worker the distortion is large however for particular groups of the population such as welfare claimants copyright 1994 by american economic association

an economic analysis of acting white this paper formalizes a widely discussed peer eect entitled acting white acting white is modeled as a two audience signaling quandary signals that induce high wages can be signals that induce peer group rejection without peer eects equilibria involve all ability types choosing dierent levels of education acting white alters the equilibrium dramatically the possibly empty set of lowest ability individuals and the set of highest ability individuals continue to reveal their type through investments in education ability types in the middle interval pool on a common education level only those in the lower intervals are accepted by the group the model s predictions t many stylized facts in the anthropology and sociology literatures regarding social interactions among minority group members

progressive income taxation and the underground economy abstract with a progressive income tax system decreasing absolute and nondecreasing relative risk aversion are sufficient conditions for either a rise in the tax rate or a revenue neutral increase in progressivity to cause growth in the underground economy

explaining fashion cycles imitators chasing innovators in product space abstract this paper considers the problem of a fashion trend setter confronting an imitator who can produce the same product at lower cost a one dimensional product space is considered which is an abstraction of the key attribute of some consumer good three broad strategies can be optimal for the fashion leader 1 never innovate which milk profits from the initially advantageous position but ultimately concede the market without a fight 2 innovate once but only once which just temporarily defers conceding the market 3 cycle infinitely around product space never letting the imitator catch up and capture the market sometimes the cycles start immediately sometimes the innovator should wait for a time before beginning the cycles the optimal solution exhibits strong state dependency with so called skiba curves separating regions in state space where various of these strategies are optimal there are even instances of intersecting skiba curves in most cases analytical expressions can be stated that characterize these skiba curves

an expository note on individual risk without aggregate uncertainty abstract in economies where agents bear some risk the analysis would often be facilitated by the assumption that the risks are i i d and disappear in the aggregate a formal appeal to the law of large numbers requires the consideration of a sequence of finite economies in an economy with a continuum of agents there are countable families of sets for which it is impossible for a law of large numbers to be valid with countably many agents and a finitely additive measure independence is compatible with the law of large numbers

street crime and street culture a model shows how reputation concerns can support widespread street crime a street culture where the direct incentives for such behavior are weak there are social benefits to street reputations but those benefits are dominated when reputation concerns draw into crime those who obtain no direct gain from it the model matches facts about violent crime that a standard model cannot easily explain including low monetary returns disproportionate victimization of the young and poor and high variance in rates across small distances the model generates novel implications for policy and social science including a negative effect of social capital

learning tastes through social interaction abstract this paper offers an information based model of social interaction and analyzes optimal investment and pricing of services that facilitate interaction in a duopoly agents have uncertainty over their preferences but are aware that they are correlated with others so there exists an incentive to communicate with others in the population when a firm s good can be bundled with a coordination mechanism for its consumers its value is endogenously determined due to a consumption externality although this mechanism increases total surplus it is underprovided and consumer surplus decreases

the costs of missing the millennium development goal on gender equity abstract at the millennium summit the world community pledged to promote gender equality and chose as a specific target the achievement of gender equity in primary and secondary education by the year 2005 in every country of the world based on the findings from a growing empirical literature that suggests that gender equity in education promotes economic growth reduced fertility child mortality and undernutrition we estimate what the costs in terms of growth and forgone fertility mortality and undernutrition reduction will be for the 45 countries that are on current projections unlikely to meet the target our estimates suggest that by 2005 the countries that are off track are likely to suffer 0 1 0 3 percentage points lower per capita growth rates as a result will have 0 1 0 4 more children per woman and by 2015 an average of 15 per 1 000 higher rates of under five mortality and 2 5 percentage points higher prevalence of underweight children under five sensitivity analyses suggest that the results are quite robust to using different specifications and approaches to estimating these losses

undp s gender related indices a critical review abstract this paper critically reviews the two gender related indices proposed by undp in the 1995 human development report the gender related development index gdi and the gender empowerment measure gem while supporting the need to develop indicators that reliably track women s empowerment gem as well as the impact of gender inequality on overall human development gdi we argue that the particular ways in which these indices were constructed and the assumptions made to overcome data gaps severely limit their usefulness and result in very misleading international comparisons wherever appropriate we suggest remedies for some of the shortcomings identified

why do people care about social status abstract this paper shows that complementary interaction can induce people to care about social status because it serves as a signal of non observable abilities there is a unique separating equilibrium in which everyone cares about social status in this equilibrium a person s social status perfectly reveals his abilities and everyone matches with a person of like ability the analysis shows that people s instrumental concern for social status has important welfare and policy implications indeed peoples efforts to keep up with the joneses may be welfare enhancing

macroeconomic implications of conspicuous consumption a sombartian dynamic model this chapter presents a dynamic general equilibrium model in which consumers have status preference i investigate the manner in which capital accumulation is impeded by conspicuous consumption a la corneo and jeanne j public econ 66 55 71 1997a following the literature social norms are given as either bandwagon type or snob type i then show that when the economy is characterized by a bandwagon type social norm capital accumulation exhibits interesting patterns those patterns include for example an oscillating convergence path the rise of the economy feeds its decay through conspicuous consumption and that decay suppresses conspicuous consumption and engenders prosperity as predicted by sombart liebe luxus und kapitalismus reprinted 1967 deutscher taschenbuch verlag munchen 1912

optimal income tax in the presence of status effects abstract the existence of distortions from individuals competing to attain social status by using consumption signals justifies some measure of income tax as a counter acting distortion the question posed here is whether it also constitutes a reason for a more progressive income tax schedule the answer is found to be broadly negative if progressiveness is interpreted as a more convex tax schedule unless the rich are more concerned with status seeking than the poor on the other hand status seeking makes the optimal tax schedule steeper so that redistribution is increased essentially the analysis of status seeking based on a signaling approach confirms and strengthens the existing view of an optimal tax schedule and can be incorporated into the diamond american economic review 88 1998 83 95 approach

globalisation women s economic rights and forced labour economy s penetration by foreign direct investment by and large has no sta tistically significant impact globalisation might weaken the general bargaining position of labour such that outcome related la bour standards might suffer however being more open toward trade is likely to promote rather than hinder the realisation of t wo labour rights considered as core or fundamental by the international labour organisation namely the elimination of economic discrimination and of forced labour

the canadian underground and measured economies granger causality results using new time series data for the size of the canadian underground economy the relationship between unreported and measured gdp in that country is examined granger causality tests are conducted with a proper allowance for the non stationarity of the data it is found that there is clear evidence of such causality from measured gdp to hidden output but only very mild evidence of granger causality in the reverse direction this result supports similar evidence for new zealand reported by the first author and has several interesting policy implications

pecuniary emulation inequality and growth abstract we study a two class growth model in which agents care about both consumption and the social perception of their wealth rank the latter determines the social status enjoyed by agents social perceptions are based upon noisy signals of wealth and in equilibrium there is incomplete separation of classes the steady growth rate of the economy increases with the full information status differential between classes and contrary to the growth model without status it is affected by the initial level of wealth inequality both too much equality and too much inequality are detrimental to economic growth

help or hindrance religion s impact on gender inequality in attitudes and outcomes summary this paper investigates the effect of religiosity on attitudes toward gender equality using world values survey data results indicate that religiosity is strongly correlated with gender inequitable attitudes across countries further ols tsls and 3sls regression estimates reveal that gender inequitable attitudes are associated with negative effects on seven measures of gender equality of well being and public policy no single religion stands out as more gender inequitable than others the impact of religiosity is likely transmitted via stealth effects on everyday behavior in economic transactions in labor markets household resource allocation and government spending

the growth tax in the united states by providing public goods including law and order national defense and income redistribution that expands the gains from exchange the scope and membership of the constitutional agreement government expenditures act as a positive externality on the growth rate beyond that level taxes act as a negative externality in this paper a simple model is formulated and the optimal growth maximizing tax rate found empirical estimation finds it to be in the range of 21 5 22 9 percent the effect of taxation beyond this level is a cumulative loss of about 30 trillion 1972 dollars in gnp over the period 1949 89

learning from neighbours when payoffs from different actions are unknown agents use their own past experience as well as the experience of their neighbours to guide their decision making in this paper we develop a general framework to study the relationship between the structure of these neighbourhoods and the process of social learning we show that in a connected society local learning ensures that all agents obtain the same payoffs in the long run thus if actions have different payoffs then all agents choose the same action and social conformism obtains we develop conditions on the distribution of prior beliefs the structure of neighbourhoods and the informativeness of actions under which this action is optimal in particular we identify a property of neighbourhood structures local independencewhich greatly facilitates social learning simulations of the model generate spatial and temporal patterns of adoption that are consistent with empirical work

word of mouth communication and social learning this paper studies the way that word of mouth communication aggregates the information of individual agents we find that the structure of the communication process determines whether all agents end up making identical choices with less communication making this conformity more likely despite the players naive decision rules and the stochastic decision environment word of mouth communication may lead all players to adopt the action that is on average superior these socially efficient outcomes tend to occur when each agent samples only a few others i introduction economic agents must often make decisions without knowing the costs and benefits of the possible choices given the frequency with which such situations arise it is understandable that agents often choose not to perform studies or experiments but instead rely on whatever information they have obtained via casual word of mouth communication reliance on this sort of easily obtained information appears to be common in circumstances ranging from consumers choosing restaurants or auto mechanics to business managers evaluating alternative organizational structures this paper studies two related environments in arguing that individuals reliance on word of mouth communication has interesting implications for their aggregate behavior first motivated by the diffusion of new technologies we consider a choice between two competing products with unequal qualities or payoffs and show that the structure of communication is important in determining whether the population as a whole is likely to learn to use the superior product second we consider a choice between two products or practices that are equally good and ask whether consumers are likely to herd onto a single choice or whether diversity will obtain even in the long run we explore the implications of word of mouth communication in a simple nonstrategic environment there is a large population of identical players each of whom repeatedly chooses between two possible actions each player s payoff is determined by his own

low schooling for girls slower growth for all cross country evidence on the effect of gender inequality in education on economic development using cross country and panel regressions this article investigates how gender inequality in education affects long term economic growth such inequality is found to have an effect on economic growth that is robust to changes in specifications and controls for potential endogeneities the results suggest that gender inequality in education directly affects economic growth by lowering the average level of human capital in addition growth is indirectly affected through the impact of gender inequality on investment and population growth some 0 4 0 9 percentage points of differences in annual per capita growth rates between east asia and sub saharan africa south asia and the middle east can be accounted for by differences in gender gaps in education between these regions

gender inequality and economic growth a cross country analysis abstract this paper investigates empirically the determinants of economic growth for a set of semi industrialized export oriented economies in which women provide the bulk of labor in the export sector the primary hypothesis tested is that gender inequality which contributes to women s relatively lower wages was a stimulus to growth via the effect on exports during 1975 95 empirical analysis shows that gdp growth is positively related to gender wage inequality in contrast to recent work which suggests that income inequality slows growth evidence also indicates that part of the impact of gender wage inequality on growth is transmitted through its positive effect on investment as a share of gdp

conspicuous consumption and race evidence from south africa abstract a century ago thorstein veblen introduced socially contingent consumption into the economic literature this paper complements the scarce empirical literature by testing his conjecture on south african household data and finds that black and coloured households spend relatively more on visible consumption than comparable white households following the approach of charles et al 2009 this paper explores whether the differences in visible expenditures can be explained with a signaling model of status seeking moreover it is assessed to which extent positional concerns motivate conspicuous consumption although the socially contingent share in visible consumption increases with income different incentives to consume conspicuously seem to explain that at every level of income black households spend relatively more on visible consumption than comparable white households in contrast to the findings of charles et al 2009 where differential spending on conspicuous consumption can be found also within each group separately the model s core hypothesis fails to hold within the group of white south africans

why the gender gap in wages narrowed in the 1980s since 1976 the gender gap in wages on average declined by about 1 per year this article focuses on identifying the factors underlying this trend three data sets are analyzed the current population survey the panel study of income dynamics and the national longitudinal survey we find that convergence in measurable work related characteristics schooling and work experience explains one third to one half the narrowing the remainder is attributable to a relative increase in women s returns to experience as well as to declining wages in blue collar work and other factors

income tax evasion an intersectoral analysis abstract this paper develops an intersectoral model of income tax evasion with general equilibrium effects key elements of the model are imperfectly substitutable outputs from the compliant and evading sectors and workers with heterogeneous evasion costs the model allows for biased public expenditures a wide range of behavioural responses and both legitimate and criminal activities evading tax as well as tax avoidance activities qualitative and quantitative assessments are undertaken for the effects of tax rate changes on evasion activity relative output prices and real tax revenues this approach offers useful findings for taxation policy and is amenable to further analytical extensions

learning from the behavior of others conformity fads and informational cascades learning by observing the past decisions of others can help explain some otherwise puzzling phenomena about human behavior for example why do people tend to converge on similar behavior why is mass behavior prone to error and fads the authors argue that the theory of observational learning and particularly of informational cascades has much to offer economics business strategy political science and the study of criminal behavior

on limiting the market for status signals abstract in many societies individuals care how others view them in their efforts to impress such individuals engage in consumption signals which attempt to establish higher levels of status than their true status type this leads to an inefficiency which offers the possibility of a pareto improving tax policy the impacts of tax policy and benefits on the signalling equilibrium are considered

pricing of conspicuous goods a competitive analysis of social effects abstract social needs play an important role in the purchase of conspicuous goods in this article the authors extend traditional economic models to accommodate social needs such as desire for uniqueness and conformism and examine their implications for pricing conspicuous goods first in the context of a duopoly the authors identify the conditions under which the desire for uniqueness can increase demand among some consumers as the price of a product increases second the authors show that though the desire for uniqueness leads to higher prices and firm profits a desire for conformity leads to lower prices and profits third the authors find that consumers purchase high quality products not because of their desire for uniqueness but despite it finally marketers of conspicuous goods may find it beneficial not to emphasize the functional differences among their products when the need for uniqueness is high in a laboratory test the authors find support for the claim that demand for a product amo

a distributional analysis of the gender wage gap in bangladesh this article empirically investigates the gender wage gap in bangladesh during the period 2005 2009 applying unconditional quantile regression models the article demonstrates that women are paid less than men throughout the wage distribution and the gap is higher at the lower end of the distribution discrimination against women is the primary determinant of the wage gap the article also demonstrates that the observed gender wage gap is likely to be underestimated if we ignore selection in full time employment a number of policy implications are discussed

design innovation and fashion cycles a model of fashion cycles is developed in which designs are used as a signaling device in a dating game a monopolist periodically creates a new design over time the price of the design falls as it spreads across the population once sufficiently many consumers own the design it is profitable to create a new design and thereby render the old design obsolete this paper gives conditions under which all consumers would be better off by banning the use of fashion competition among designers may lead to less frequent changes in fashion and to higher prices than monopoly copyright 1995 by american economic association

microfinance and gender empowerment in this paper we develop a theoretical model of household production bargaining and credit to analyse how access to microcredit affects intra household decision making and welfare and identify conditions under which female household members are most likely to benefit we show that consistent with ethnographic accounts of the impact of microcredit programmes on poor households access to loans can lead to a variety of outcomes for intra household decision making and welfare depending on initial conditions and that in some instances women borrowers may experience a decline in welfare we identify two instances in which a woman is most likely to benefit when there is scope for investing the loan profitably in a joint activity and when a large share of the household budget is devoted to household public goods

south south migration and discrimination against women in social institutions a two way relationship summary using the social institutions and gender index sigi from the oecd development centre this paper provides evidence on the two way relationship between discrimination against women in social institutions and south south migration on the one hand discriminatory social institutions in both origin and destination countries are an additional determinant of female migration on the other hand migration implies changes in discrimination against women according to the level of gender inequalities at destination specifically migration toward countries with low levels of discrimination promotes gender equality in social institutions at home while migration toward destinations with high levels of discrimination has the reverse effect

contests for ranks experimental evidence we use experiments to analyze multiple dimensions of the relationship between rank incentives and individual performance in our experiment i rank is defined as subjects relative position in their group based on their performance in a real effort task and ii subjects earnings are independent of their performance we find that any rank incentive improves mean performance than no rank incentive and this result is independent of the group size in the large group the mean performance increases strictly in all except at the highest rank incentive but in the small group the mean performance increases weakly in rank incentives finally the mean performance is significantly higher in the large than in the small group because of a higher prestige effect in additional treatments in which we do not reveal the identity of the statusprize winners we find that average performance is identical to that in the baseline treatment without any status prizes the last result signifies the important role that public revelation plays to enhance the strength of status the results are important for managerial practices

size and scope of the underground economy in germany the objective of this paper is to improve estimations of the size and scope of the underground economy by introducing a new approach that combines the advantages of the two most commonly used approaches i e currency demand and multiple indicators multiple causes mimic the new approach is applied to germany among other things it is shown that the approach yields improved estimation results some policy perspectives are discussed in the concluding section

an empirical test for tax evasion this paper develops a methodology that uses microeconomic data from individual tax returns to test for the presence of tax evasion the test is then applied to a large sample of taxpayers drawn from the u s treasury tax file for 1977 the frequency of evasion indicated by the test is significantly greater than zero and within the wide range that other evidence suggests is the extent of evasion the associations between evasion and characteristics of the taxpayer such as marginal tax rate income age and marital status are also investigated and compared to the findings of earlier studies

keeping it off the books an empirical investigation of firms that engage in tax evasion this article uses a unique dataset that contains detailed information on firms from around the world to investigate factors that affect under reporting behaviour the empirical strategy employed exploits the nature of the dependent variable which is interval coded and uses interval regression which provides an asymptotically efficient estimator provided that the classical linear model assumptions hold these assumptions are investigated using standard diagnostic tests that have been modified for the interval regression model evidence is presented that shows that the firms in all regions engage in under reporting regression results indicate that government corruption has the single largest causal effect on under reporting resulting in the percentage of sales not reported to the tax authority being 51 3 higher taxes have the second single largest causal effect on under reporting resulting in the percentage of sales not reported to the tax authority being 18 0 higher followed by access to financing

a strategic model of social and economic networks we study the stability and efficiency of social and economic networks when self interested individuals can form or sever links first for two stylized models we characterize the stable and efficient networks there does not always exist a stable network that is efficient next we show that this tension persists generally to assure that there exists a stable network that is efficient one is forced to allocate resources to nodes that are not responsible for any of the production we characterize one such allocation rule the equal split rule and another rule that arises naturally from bargaining of the players

conspicuous consumption snobbism and conformism abstract we develop a model in which consumers purchase a conspicuous good in order to signal high income and thereby achieve greater social status in equilibrium the signalling value of conspicuous consumption depends in an identifiable way on the number of consumers and consumer behaviour is characterized by either snobbism or conformism the market demand curve for the conspicuous good may exhibit a positive slope if consumers are conformist we derive some unconventional policy implications concerning the taxation of luxuries and the voluntary provision of public goods

horizontal and vertical differentiation the launhardt model we show how the spatial duopoly proposed by launhardt in 1885 where firms have access to different transportation technologies allows one to model in a simple and elegant way the two major types of product differentiation i e horizontal and vertical we consider the cases where firms are located near the market end points or near the market center launhardt s analysis of price determination is then extended by allowing firms to choose strategically their transportation rates subgame perfect nash equilibria involve minimum maximum vertical product differentiation when horizontal product differentiation is large small enough

gender inequality endogenous cultural norms and economic development this research focuses on the role played by cultural norms in the long run persistence of gender inequalities cultural norms about gender roles are considered to be endogenous and can generate gender inequality and low development traps indeed when the gender gap is internalized it leads to inegalitarian views about gender roles due to these inegalitarian beliefs boys receive more education and the initial gender gap is reinforced the existence of gender inequality traps is pointed out by the world bank as a major obstacle for economic development wdr 2006 the present article allows for a better understanding of the persistence of such traps and the means to escape

globalization and the empowerment of women an analysis of spatial dependence via trade and foreign direct investment summary this article tests the hypothesis that higher women s economic and social rights in foreign countries with which a country is connected via trade and foreign direct investment fdi spill over into higher rights among the laggards a phenomenon known as spatial dependence analyzing women s rights over the period 1981 2007 in a global sample and samples of countries at different stages of economic development we find consistent evidence for spill over effects via trade links with the exception of a sample of low income countries we also find some evidence for similar effects via fdi but only for economic rights and only in middle income countries

network competition i overview and nondiscriminatory pricing we develop a model of unregulated competition between interconnected networks and analyze the mature and transition phases of the industry in this deregulated environ ment networks pay negotiated or regulated access charges to each other and com pete in prices for customers we show that a competitive equilibrium may fail to exist for large access charges or for large network substitutability and that freely negotiated access charges may prevent effective competition in the mature phase of the industry and erect barriers to entry in the transition toward competition last we examine the meaning and impact of policies such as the efficient component pricing rule

veblen effects in a theory of conspicuous consumption the authors examine conditions under which veblen effects arise from the desire to achieve social status by signaling wealth through conspicuous consumption while veblen effects cannot ordinarily arise when preferences satisfy a single crossing property they may emerge when this property fails in that case budget brands are priced at marginal cost while luxury brands though not intrinsically superior are sold at higher prices to consumers seeking to advertise wealth luxury brands earn strictly positive profits under conditions that would with standard formulations of preferences yield marginal cost pricing the authors explore factors that induce veblen effects and they investigate policy implications copyright 1996 by american economic association

getting ahead of the joneses when equality increases conspicuous consumption among bottom tier consumers it is widely believed that increasing the equality of material possessions or income in a social group should lead people at the bottom of the distribution to consume less and save more however this prediction and its causal mechanism have never been studied experimentally five studies show that greater equality increases the satisfaction of those in the lowest tier of the distribution because it reduces the possession gap between what they have and what others have however greater equality also increases the position gains derived from status enhancing consumption since it allows low tier consumers to get ahead of the higher proportion of consumers clustered in the middle tiers as a result greater equality reduces consumption when consumers focus on the narrower possession gap but it increases consumption when they focus on the greater position gains i e when consumption is conspicuous social competition goals are primed and the environment is competitive

the size and development of the shadow economy an empirical investigation from states of india abstract using the state level data from india this paper investigates the size of the hidden economy in indian states over the period 1974 75 to 1995 96 our analysis has shown that after liberalization of the indian economy in 1991 92 the growth in the size of the hidden economy has decreased on an average our results show that the growth in the size of the hidden economy is approximately 4 less in scheduled election years than in all other years we also demonstrate that the growth is significantly lower in those states where the coalition government is in power an increased growth of newspapers and the literacy rates translate to cleaner governance e g to fewer amounts of shadow economy activities in the economy

on the informational role of quantities durable goods and consumers word of mouth communication a dynamic incomplete information game is set up to study the introduction of a durable good when consumers can learn its quality from previous buyers high sales today imply fewer potential buyers tomorrow but each buyer will have better information about the good consumers are fully rational and can update their beliefs even when they do not directly receive information in equilibrium no news is bad news a low quality firm follows a fly by night strategy randomizing over the timing of sales a high quality firm spreads out its sales more smoothly solving a stochastic dynamic programming problem copyright 1997 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association