paying down the environmental debt we reflect on scenarios of sustain able development constant utility paths in which the stock of pollution is drawn down by investments in environmental cleanup we also report on con stant utility as interest on the vector of capital stocks in our economy jel 02 the costs of cleaning up the environment involve multiyear programs for many sites and or problems and sums in the billions of dollars we have superfund activities in the united states in mind but obviously the site cleanup problems facing the people of eastern europe are also very large scale cleanup expenditures resemble programs of investment in infrastructure rather than once over disbursements for troubleshoot

investment incentives in procurement auctions this paper investigates firms incentives to invest in cost reduction in the first price sealed bid auction a format largely used for procurement two central features of the model are that we allow firms to be heterogeneous and that investment is observable we find that firms will tend to underinvest in cost reduction because they anticipate fiercer head on competition using the second price auction as a benchmark we also find that the first price auction will elicit less investment from market participants and that this is socially inefficient these results have implications for market design when investment is important different market institutions provide different incentives for firms to reduce costs acquire information expand and so on in short to undertake any activity that affects their competitive positions accordingly the performance of these market institutions should be judged not only from a static perspective taking firms competitive positions as given but also from a dynamic perspective auction markets are a natural competitive environment to study because there is a clear sense in which we can design such markets by choosing appropriate rules for competition in this paper we study how the first price auction fpa a format commonly used for procurement affects firms incentives to invest in cost reduction many procurement markets are characterized by a small number of participants heterogeneity among firms and low rates of turnover therefore it is interesting to investigate to what extent the format used for the auction contributes to these characteristics the basic ingredients of our model are as follows there are n firms and one of them has the opportunity prior to the auction to make an investment we model this investment as an improvement in the ex ante distribution of costs for this firm the main question we ask is what are the firm s incentives to invest given that this investment is observed by its competitors clearly the benefits of such investment depend on how the firm s competitors react in other words to determine the firm s incentive to invest we need to compare the equilibrium at the procurement stage if it makes this investment and if it does not in section 3 we derive new comparative statics results for the fpa we find that after the investment the investor s opponents will bid collectively more aggressively this result holds generally when there are only two bidders or when the investor s opponents are symmetric proposition 1 otherwise a sufficient condition is that investment changes market leadership proposition 2 in the language of industrial organization investment has a negative strategic effect in the fpa this erodes 1

constant consumption and the economic depreciation of natural capital the nonautonomous case we investigate economic depreciation of natural capital for cases of nonstationary output prices technology and interest rates for the former two cases exogenous movements in prices and technology constant consumption emerges under a strategy of investing to cover off economic depreciation the interest rate case requires a modified sinking fund strategy

efficiency and surplus bounds in cournot competition we derive bounds on the ratios of deadweight loss and consumer surplus to producer surplus under cournot competition to do so we introduce a parameterization of the degree of curvature of market demand using the parallel concepts of concavity and convexity the more concave is demand the larger the share of producer surplus in overall surplus the smaller is consumer surplus relative to producer surplus and the lower the ratio of deadweight loss to producer surplus deadweight loss over total potential surplus is at rst increasing with demand concavity then eventually

on the analysis of asymmetric first price auctions we provide a new set of tools for studying asymmetric rst price auctions connecting their equilibria to the concavity of the underlying type distributions and showing how one can use surplus expressions related to symmetric auctions to bound equilibrium behavior in asymmetric auctions we apply these tools to studying procurement auctions in which as is common in practice one seller is given an advantage re ecting for example better reliability or quality we show conditions under which for any given rst price handicap auction there is a second price auction with bonuses that outperforms it with most of our results involving ex post dominance

deforestation and development in a small open economy abstract our economy faces world prices and starts with a large endowment of land in forest and a small endowment of land in agriculture clearing of forested land yields marketable timber and a unit of land for agriculture early the high price of agricultural land drives the clearing process later the profit from marketing timber from the cleared land drives the process dates of phase transitions are endogenous we also set out a submodel of perpetual cyclic clearing and reforesting and show that it when cyclical harvesting regrowing is optimal the extent of clearing can be relatively large

aggregation and social choice a mean voter theorem a celebrated result of black 1948a demonstrates the existence of a simple majority winner when preferences are single peaked the social choice follows the preferences of the median voter the median voter s most preferred outcome beats any alternative however this conclusion does not extend to elections in which candidates differ in more than one dimension this paper provides a multi dimensional analog of the median voter result we provide conditions under which the mean voter s most preferred outcome is unbeatable according to a 64 majority rule the conditions supporting this result represent a significant generalization of caplin and nalebuff 1988 the proof of our mean voter result uses a mathematical aggregation theorem due to prekopa 1971 1973 and borell 1975 this theorem has broad applications in economics an application to the distribution of income is described at the end of this paper results on imperfect competition are presented in the companion paper caplin and nalebuff 1991

on the intergenerational allocation of natural resources it is known hartwick and others that under standard assumptions a society that invests in reproducible capital the competitive rents on its current extraction of exhaustible resources will enjoy a consumption stream constant in time it is shown here that this result can be interpreted as saying that an appropriately defined stock of capital including the initial endowment of resources is being maintained intact and that consumption can be interpreted as the interest on that patrimony this seems like a useful rule of thumb for policy

can affirmative action be cost effective an experimental examination of price preference auctions one of the most controversial questions facing our economy and society in recent years is the question of affirmative action the debate centers around an issue of minority representation in which the rights of the majority are depicted as being compromised by affirmative action programs set up to increase the welfare of minorities implicit in this discussion is the assumption that all affirmative action programs must be cost increasing this result it is claimed follows trivially from economic theory since any interference into the competitive process which prevents the most capable from being chosen must be wasteful and costly in this paper we challenge this claim with experimental results demonstrating that pricepreference auctions in which high cost minority firms are given preferential treatment in the awarding of contracts in such a way that it is possible for these firms to win a contract but not have submitted the lowest bid can be programs that both enhance minority representation and are cost effective in that they decrease the cost of government procurement in the theoretical literature on asymmetric auctions eric maskin and john riley 1995 and the optimal auction literature roger myerson 1981 it has been shown that in asymmetric auctions in which firms draw their costs from

design competition through multidimensional auctions this article studies design competition in government procurement by developing a model of two dimensional auctions wherefirms bid on both price and quality and bids are evaluated by a scoring rule designed by a buyer three auction schemes first score second score and second preferred offer are introduced and related to actual practices if the buyer can commit to a scoring rule in his best interest the resulting optimal scoring rule underrewards quality relative to the buyer s utility function and implements the optimal outcome for the buyer underfirst and second score auctions absent the commitment power the onlyfeasible scoring rule is the buyer s utility function under which 1 all three schemes yield the same expected utility to the buyer and 2 first and second score auctions induce the first best level of quality which turns out to be excessive from the buyer s point of view

government procurement and international trade abstract we model the bidding for a government contract in which there is imperfect competition each bidder is better informed about his own costs than either his rival bidders or the government and the distribution of the domestic firms costs differs from the distribution of foreign firms costs because of comparative advantage effects we find that the government minimizes its expected procurement cost by operating a price preference policy not necessarily purchasing from the lowest bidder

equilibrium in sealed high bid auctions there is a voluminous theoretical literature on sealed high bid auctions auctions in which bids are sealed and the high bidder pays his bid see for example vickrey 1961 myerson 1981 riley and samuelson 1981 milgrom and weber 1982 matthews 1983 maskin and riley 1984 holt 1980 cox smith and walker 1988 a critical property on which this literature relies is the existence of equilibrium in which buyers bidding strategies are monotonic in their types this enables the analyst to perform comparative statics as the distribution of types changes and to compare the welfare properties of the high bid auction with those of other auction institutions one case in which the existence of monotonic equilibrium is readily established is that in which buyers types are distributed smoothly independently and symmetrically in this case there exists a symmetric equilibrium one in which all bidders share the same bidding behaviour as a function of their valuations and this bid function is the solution to a first order differential equation

adjusting green nnp to measure sustainability weitzman provides a foundation for nnp as the stationary equivalent of a wealth maximizing path when there is a constant interest rate and no exogenous technological progress here the implications of weitzman s foundation are explored in a case encountered in resource models i e the case of non constant interest rates in a setting that allows for exogenous technological progress an expression for nnp is obtained that adjusts green nnp for anticipated capital gains and interest rate effects to produce a measure that indicates sustainability this result is important when measuring the relative sustainability of resource rich and resource poor countries i introduction how should net national product nnp be adjusted for the depletion of natural and environmental resources a prerequisite for examining this problem is to decide on an underlying notion of income at the personal level hicks 1946 defines income as the consumption that if kept constant would yield the same present value as a person s actual future receipts since market prices are not influenced by any single person this notion of income equals a person s maximal sustainable consumption at the national level national income can likewise be defined as the consumption that if kept constant would yield the same present value as the actual future consumption path unless the nation is a small open economy faced with given international prices this notion of national income will exceed

near optimality of second price mechanisms in a class of asymmetric auctions consider a setting with n sellers having i i d costs with log concave density f from cumulative f and a buyer who puts a premiumi on procuring from seller i we show how for any given 1 n a sim ple second price bonus auction can be chosen which comes surprisingly close to giving the auctioneer the same surplus as an optimal mecha nism the bonuses depend only on the magnitude and monotonicity of the slope of virtual costs given f we show that these in turn depend only on fairly coarse information about f we explore how this result generalizes to asymmetrically distributed costs abstract

first price auctions with general information structures implications for bidding and revenue we explore the impact of private information in sealed bid first price auctions for a given symmetric and arbitrarily correlated prior distribution over values we characterize the lowest winning bid distribution that can arise across all information structures and equilibria the information and equilibrium attaining this minimum leave bidders indifferent between their equilibrium bids and all higher bids our results provide lower bounds for bids and revenue with asymmetric distributions over values we also report further characterizations of revenue and bidder surplus including upper bounds on revenue our work has implications for the identification of value distributions from data on winning bids and for the informationally robust comparison of alternative auction mechanisms

resource depletion and sustainability in small open economies abstract exogenous price changes affect the amount that a small country exporting natural resource commodities must invest to sustain its consumption level the necessary amount is given by the difference between hotelling rent and the discounted sum of future terms of trade effects capital gains the latter term is found to be large relative to the former in the case of petroleum depletion in indonesia this suggests that resource rich countries will need to invest more than previously expected to sustain their consumption levels if natural resource prices continue their long term historical decline

are bid preferences benign the effect of small business subsidies in highway procurement auctions abstract bid preferences in procurement auctions allow firms from an identifiable group an advantage in bidding against unfavored firms while economic efficiency is expected to fall as a result of bid preferences government procurement costs may either increase or decrease depending on the competitive response of favored and unfavored firms this paper uses data from california auctions for road construction contracts where small businesses receive a 5 percent bid preference in auctions for projects using only state funds and no preferential treatment on projects using federal aid i show that while firms bidding behavior matches theoretical predictions procurement costs are 3 8 percent higher on auctions using preferences the higher procurement cost in preference auctions is attributed to reduced participation by lower cost large firms structural estimates of latent firm costs are then used to evaluate how efficiency and the division of surplus between firms and the government are impacted by bid preferences firm profits are 3 1 percent lower under bid preferences however this is overwhelmed by the efficiency loss due to reduced large firm participation the efficiency loss conditional on firm participation is estimated to represent around 0 1 percent of overall procurement costs including the adverse effect of preferences on the participation of large firms increases the estimated efficiency loss to 3 6 percent which represents 27 cents for each additional dollar awarded to small businesses through the program counterfactual simulations indicate that if participation were instead inelastic to bid preferences the 5 percent bid preference would be close to the optimal level

aggregation and imperfect competition on the existence of equilibrium we present a new approach to the theory of imperfect competition and apply it to study price competition among differentiated products the central result provides general conditions under which there exists a pure strategy price equilibrium for any number of firms producing any set of products this includes products with multi dimen sional attributes in addition to the proof of existence we provide conditions for uniqueness our analysis covers location models the characteristics approach and probabilistic choice together in a unified framework to prove existence we employ aggregation theorems due to prekopa 1971 and borell 1975 our companion paper caplin and nalebuff 1991 introduces these theorems and develops the application to super majority voting rules we present a new approach to the theory of imperfect competition and apply it to study price competition among differentiated products the central result is that there exists a pure strategy price equilibrium for any number of firms producing any set of products in addition to the proof of existence we provide conditions for uniqueness our model both unites diverse strands of the earlier literature and opens up uncharted areas for future analysis in particular we expand the traditional one dimensional framework to allow for multi dimen sional product differentiation our approach involves twin restrictions on consumer preferences one on individuals preferences the other on the distribution of preferences across society these are generalizations of the restrictions supporting 64 majority rule presented in caplin and nalebuff 1988 to prove existence we apply a new technique of aggregation this technique is valuable in a variety of other problems in the companion paper we use the aggregation result to generalize our earlier work on 64 majority rule and to characterize the relationship between the distribution of human capital and the distribution of income caplin and nalebuff 1991 there are additional applications in statistics and in search theory we begin with a brief review of the early literature on imperfect competition describing in more detail the existence problem and previous solutions section 3 presents our twin assumptions and shows that they cover many standard cases in section 4 we introduce the aggregation theorem and use it in the analysis of demand functions the proof of existence of equilibrium is in section

how costly is affirmative action government contracting and california s proposition 209 abstract this paper investigates the effect of disadvantaged business enterprise subcontractor goals on the winning bids for highway construction contracts using california s proposition 209 which prohibited the consideration of race or gender in awarding state funded contracts after proposition 209 prices on state funded contracts fell by 5 6 relative to federally funded projects for which preferences still applied most of the price decline after proposition 209 resulted from the mix of subcontractors employed which seems to arise from the higher costs of firms located in high minority areas finally short run barriers to entry and expansion may increase the cost of affirmative action