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We examine how endogenous product differentiation affects the behavior of a mixed duopoly market where a private firm competes with a partially privatized public firm under both Cournot and Bertrand competition. We also analytically derive the optimal degree of partial privatization of the public firm. Generally, privatizations increase the likelihood of no firm investing in equilibrium, resulting in markets with more homogenous goods. The public firm is more motivated to invest in product differentiation, particularly when prioritizing social welfare, while the private firm undertakes more investments when investments are not highly effective under Bertrand competition. We also demonstrate that a complete nationalization is not necessarily optimal in all contexts, and whether regulators privatize more or less depends on different market settings. Partial privatizations can enhance welfare when firms compete in quantities and investments in product differentiation are moderately effective. However, complete nationalization is socially optimal when firms compete in prices. JEL classification: D43, L13, L32, L33

We examine an environmental policy which may be revisited by a new administration. We allow for pollution to be persistent over time and for uncertainty in next period’s environmental policy. When pollution is non-persistent, we show that regulatory uncertainty is inconsequential for output, pollution, or emission fees. However, when pollution is persistent, we find that firms shift more output into the first period when facing a regulator with stronger environmental concerns. We also measure the ineffciencies stemming from ignoring pollution persistence and from policy uncertainty, identifying in which contexts they are severe or negligible. JEL classification: L13, L51, Q58.

This paper examines green alliances between environmental groups (EGs) and polluting firms, which have become more common in the last decades, and analyzes how they affect policy design. We first show that the activities of regulators and EGs are strategic substitutes, giving rise to free-riding incentives on both agents. Nonetheless, the presence of the EG yields smaller welfare benefits when firms are subject to regulation than when they are not. In addition, the introduction of environmental policy yields large welfare gains when the EG is absent but small benefits when the EG is already present.

We consider a common pool resource (CPR) where, in the first stage, every firm chooses an equity share on its rivalsiproOts (cross-ownership) and, in the second stage, firms compete for the resource. We identify equilibrium equity shares in this setting, and compare them against the socially optimal shares that maximize welfare. Our results show that equity shares are welfare improving under certain conditions, but can lead to a socially insufficient exploitation of the CPR if shares are large enough; as in a merger where firms equally share equity. We also found that, as the number of firms exploiting the resource increases, socially excessive exploitation occurs under larger parameter combinations. We analyze common policy tools, such as quotas and emission fees, evaluating how they are a§ected by equity shares; and then compare them against a novel policy tool: optimal equity taxes.

This paper examines how positive or negative perceptions about innovation affect firms' strategic behavior when certifying their products. In particular, we consider two types of firm (innovative and noninnovative) which choose between three signals: (a) certified claim, (b) uncertified claim, and (c) no claim. The consumer, either exhibiting positive or negative perceptions, is uninformed about the firm's type and only observes the firm's claim. We find that a separating equilibrium arises in which information about the innovation is revealed to consumers. We also identify a pooling equilibrium in which both types of firm choose the same claim, concealing information from consumers. We show that regulation requiring mandatory certification can hinder information transmission. Our results also indicate that changes in product perceptions do not necessarily facilitate information transmission.

We extend previous work on the role of politically motivated donors who contribute to candidates in an election with single dimension policy preferences. In a two-stage game wherein donors observe candidate policy positions and then allocate funding accordingly, we find that reducing the cost of donations incentivizes candidates to position closer to one another, reducing policy divergence. Furthermore, we find that as donations become more effective at influencing voter decisions, candidates respond less to voter preferences and more to those of donors. In addition, we analyze the presence of asymmetries in the model using numerical analysis techniques. We also extend our model by allowing for public funding from governments. By implementing stringent campaign contribution limits, candidate positions align with voter preferences at the cost of wider policy divergence. In contrast, unlimited campaign contributions lead to candidate positions moving away from voters to donors’ preferences, but increase policy convergence.

This paper examines the competition between organic and non-organic firms, their incentives to undertake a horizontal merger, and the effect of mergers on firms’ market shares. We also consider an alternative setting where one firm can acquire its rival. For generality, we allow for product differentiation, demand, and cost asymmetries. Our results show that both organic and non-organic firms, despite their cost asymmetries and demand differentials, have incentives to merge under large conditions. When demand and cost differentials are significant, we identify settings under which a firm (either organic or non-organic) purchases its rival, to subsequently shut it down, and yet increase its profits. We then study under which conditions the merger can be welfare improving, which is more likely when goods are highly differentiated and their production costs are relatively symmetric.

We study entry policies as an alternative form of environmental policy. Given the strong political opposition to standard output subsidies and taxes, several countries have recently used entry policies to promote renewable energy technology, such as solar panels and biofuels. We study a two-stage game in which two regulators choose an entry policy (i.e., tax, subsidy or permit) to maximize domestic welfare. Observing the policy, firms decide the region in which to enter and compete as Cournot oligopolists. We find that both domestic (uncoordinated) policies and internationally coordinated policies increase welfare relative to unregulated settings. However, the welfare gains from international policy coordination are only large when the product is extremely clean. These results indicate that the welfare gains of international policy coordination may only offset the costs of negotiation in relatively clean industries.

We consider a sequential-move game in which a polluting monopolist chooses whether to acquire a green technology, and a potential entrant responds deciding whether to join the market and, upon entry, whether to invest in clean technology. Our paper compares two models: one in which environmental regulation is strategically set before firms’ decisions; and another where regulation is selected after firms’ entry and investment decisions. We show that a proactive regulation that strategically anticipates firms’ behavior can implement different market structures. In particular, policy makers can choose emission fees to induce competition and/or investment in clean technology, giving rise to market structures that maximize social welfare.

This chapter applies the analysis of equilibrium bidding behavior in first-price auctions from Chap. 2 to answer different questions. In Exercise 3.1, we measure the seller’s expected revenue in this auction format when bidders draw their valuations from a generic distribution function and then evaluate this expected revenue in the case that bidders’ valuations are uniformly distributed.

This chapter considers similar industries as those we analyzed in Chap. 2, but assuming that firms compete in prices. In this setting, every firm simultaneously and independently chooses the price for its product. When firms sell a homogeneous good (such as the same cereal variety, cement, or other minerals), the firm setting the lowest price captures all sales while all other firms sell zero units. When firms sell heterogeneous goods (such as clothing), the firm setting the lowest price may attract more, but not all customers.

We start our analysis of auction formats with the second-price auction, where the winning bidder does not pay the bid he submitted but, instead, the second-highest bid. This auction format is relatively easy to analyze, requiring limited mathematical steps, and thus we believe that it can serve as a first approximation to bidding behavior for non-technical readers. Examples of this auction format include eBay sales, auctioning radio spectrums, and the pricing that search engines, such as Google, Bing, or Yahoo, use to sell keyword-based advertising.

In this chapter, we study all-pay auctions. As in the auction formats we examined in previous chapters, every bidder submits his bid and the bidder submitting the highest bid wins the object. However, as opposed to other auctions where only the winning bidder must pay for the object (either the highest or second-highest bid), in the all-pay auction every bidder must pay the bid that he submitted. As expected, this makes bidders less aggressive in their bids than in other auction formats, which we demonstrate to hold under different settings. Examples of all-pay auctions include contests, political campaigns, awarding of monopoly licenses, and R&D races where players (e.g., firms) cannot recover their participation costs upon losing. More recently, we can also find this type of auctions being used by internet sellers such as QuiBids.com, which requires bidders to purchase tokens/points before an auction starts, and then submit their token bids, which cannot be recovered regardless of the outcome of the auction.

This chapter examines auctions where all bidders share the same (common) value for the object, but none of them observe an accurate signal of the object’s true valuation. Instead, every bidder privately observes a noisy signal about the object’s value and, based on this signal, submits a bid. This model is typically used to analyze the auctioning of oil leases, as firms exploiting the oil reservoir would earn a similar profit if they win the auction, but they have imprecise and potentially different signals of the amount of oil barrels in the reservoir (as they receive different engineering reports) and, as a consequence, hold different estimates of the oil lease’s profitability.

This chapter takes a regulatory approach by considering some of the models of imperfect competition analyzed in previous chapters (monopoly and oligopolies with different numbers of firms) and examines different policy tools that can induce firms to produce the output level that maximizes the social welfare (we refer to this output level as the “socially optimal output”), such as subsidies and taxes for each unit of output that the firm produces.

In this chapter we introduce the reader to auctions where the seller offers more than one unit (multi-unit auctions).

This chapter studies the strategic interaction of firms in the presence of network effects, where the adoption of the same technology or standard by several firms allows each firm to benefit from larger market demand, lower production cost, or both. This can happen even when the technology that firms adopt is inferior to other technologies, such as the Blue-ray disk, often regarded as inferior to High-Definition DVDs.

In this chapter, we study firms’ incentives to invest in research and development (R&D) with the goal of lowering their production costs in subsequent periods. Exercise 6.1 starts analyzing these incentives in a stylized setting, a monopoly where a single firm operates in all periods. In this context, the monopolist anticipates that any R&D investment today will lower its production costs in the next period, when it still maintains a monopolistic position. In other words, the monopolist does not have incentives to invest in R&D to become more competitive in the future, relative to its rivals. In oligopoly models, however, every firm considers this incentive to improve its relative cost advantage. Exercises 6.2 and 6.3 examine this incentive, first in an oligopoly where firms compete in quantities (Exercise 6.2) and then in one where firms compete in prices (Exercise 6.3). In both exercises, we evaluate whether firms may have more or less incentives to invest in R&D than what they would under monopoly, which helps us identify whether the presence of more than one firm provides firm with an additional incentive to invest, relative to monopoly, or with less incentives. Exercise 6.4 then evaluates the welfare that arises in equilibrium, comparing whether that under monopoly is larger than under oligopoly, and Exercise 6.5 examines if R&D investments increase in oligopolistic markets that became more competitive (with more firms).

This chapter generalizes previous auction formats by allowing the winning bidder to pay the kth highest bid, while all losing bidders pay zero. This implies that in the first-price auction, we have that k = 1, as the winning bidder pays the highest bid; and in the second-price auction, k = 2, as he pays the second-highest bid. A similar argument applies to the third-price auction, where k = 3, as the winning bidder pays the third-highest bid, and, more generally, to any other auction format where k > 3.

In this chapter, we analyze first-price auctions, where every bidder privately observes his valuation for the object and submits his bid to the seller (e.g., in a sealed envelope). The seller ranks all bids, selects as a winner the bidder who submitted the highest bid to pay the bid he submitted. All other bidders pay zero and not receive the object.

In this chapter, we evaluate the seller’s expected revenue in different auction formats and show under which contexts this revenue is equivalent. First, Exercise 6.1 considers the first-price, second-price, third-price, and all-pay auctions from the previous chapters, evaluating the expected revenue that each of them generate, and showing that the expected revenue coincides.

This chapter analyzes strategic interaction of firms under incomplete information. Exercise 9.1 studies entry decisions when the incumbent’s cost is unobservable to the entrant. We show that the low-cost firm can strategically increase output relative to the complete information setting, to the level that the high-cost firm cannot profitably imitate, in order to deter entry. Exercise 9.2 examines the firm’s incentives to offer damaged goods at an extra cost. We find that consumers are better off since high-value consumers can buy the undamaged version of the good at a lower price while low-value consumers can buy the damaged good who are otherwise not served. Exercise 9.3 considers firms’ incentives to invest in corporate social responsibility (CSR) when consumers do not receive accurate signal on product quality. We report that the high-quality firm can invest in CSR to signal its product differentiation from low-quality rivals, and CSR investments are usually observed in market with noisy signals such as fashionable clothes, cosmetics, and electronics to distinguish from counterfeit or inferior products. Exercise 9.4 identifies firms’ intertemporal pricing decisions when they can advertise and poach consumers from one another. We find that in a symmetric setting, every firm obtains an equal share of the market in the first period, and sells to its rival’s consumers at a price half of that selling to its own consumers in the second period.

This chapter studies firms’ incentives to merge and collude in imperfectly competitive markets. Exercise 7.1 begins with the basic setting of mergers between two firms into a monopoly. Exercise 7.2 extends into the setting of N-firm mergers. We show that when the number of firms that merge is sufficiently high, mergers become profitable as the gain in market power more than offsets output increase of the firms that do not merge, and this is referred to as the “80% rule” after Salant et al. (1983). Exercise 7.3 suggests that when there are three or more firms merging together, the merger is unsustainable because every participating firm has incentives to leave and free ride on output reduction of the cartel to increase its own output and profit levels. Exercise 7.4 finds that firms have stronger incentives to merge when the merged firm benefits from cost-reduction effects. Exercise 7.5 analyzes mergers in a sequential-move game. We report that while a leader has incentives to acquire a follower, those incentives are weakened when the follower market becomes more competitive. To summarize, the existence of outsiders weakens firms’ incentives to merge, unless the merged firm gains significant market power, enjoys cost advantage, or maintains output leadership.

After studying markets with only one firm in Chap. 1, we now turn to industries with two or more firms (oligopolies) either compete in quantities (Chap. 2) or in prices (Chap. 3). In this chapter, we assume that every firm chooses independently and simultaneously its output level, yielding an equilibrium output for each firm and an equilibrium aggregate output for the industry. Given this aggregate output, the equilibrium price is determined by the demand function entailing equilibrium profits for each firm.

This paper considers firms’ incentives to merge under imperfect competition, where we allow for product differentiation, cost asymmetries, and pollution intensities (green and brown goods). We first analyze mergers in the absence of environmental regulation, showing that mergers induce an output shift towards the lowest cost firm. When emission fees are introduced, however, firms also consider their relative pollution intensities, potentially reverting the above output shift. We show that socially excessive mergers can arise when firms shift output to the more cost-efficient firm which may cause more pollution. In contrast, socially insufficient mergers can arise if output shifts reduce pollution.

This study analyzes a conservation procurement auction with bidirectional externalities, that is, conservation output can affect the costs of individuals dedicated to market production, and vice versa. The procurer does not observe bidders’ efficiency in conservation or market production. Each market failure alone (asymmetric information or the presence of externalities) deviates optimal output away from the first best. Their coexistence, however, rather than producing larger output inefficiencies, can move optimal output closer to the first best when negative conservation externalities are minor. In this setting, the benefit from acquiring information about bidders’ types is small. In contrast, when conservation externalities are substantial, the procurer would have strong incentives to acquire information before designing the auction.

Experimental methods have been widely used to elicit consumer preferences. However, the estimates are challenged because the existing literature indicates that individuals overstate their economic valuation in hypothetical settings, thus giving rise to the so-called “hypothetical bias.” Although many studies seek to experimentally test which factors emphasize or ameliorate the hypothetical bias, no studies analyze its theoretical foundations. Our results also provide empirically testable implications, such as that hypothetical bias increases in a commodity’s income elasticity of demand and budget share.

In this paper, we analyze a duopoly market with investment in abatement technology under environmental regulation. We use a three-stage game where firms invest in a green technology with spillover effects in the first stage, the regulator sets the emission fee in the second stage, and production of the polluting good occurs in the third stage. We analyze two different regulatory regimes: (1) each firm faces the same emission fee (uniform fee), and (2) each firm faces an emission fee dependent on the investment in green technology (type-dependent fee). Firms can differ through their costs of investing in the abatement technology (asymmetric efficiency). We obtain that social welfare is unambiguously higher under the type-dependent regime than otherwise. In addition, we find that the asymmetry in efficiency of investment affects firms’ profits, identifying that efficient (inefficient) firms favor type-dependent (uniform) policy regimes.

This paper analyzes a common property resource shared by two countries in the presence of two forms of bilateral externalities: the tragedy of the commons and the environmental damage resulting from the exploitation of the resource. We demonstrate that both cooperative and non-cooperative forms of regulation produce a negative effect on firms’ profits, as they increase firms’ unit production costs. However, regulation can also entail a positive effect on profits by mitigating industry overproduction. We show that the magnitude of these two effects depends not only on the type of regulatory instrument, but also on the rate of resource extraction and the environmental damage in each country. We identify conditions under which the positive effect of regulation dominates its negative effect, thus increasing firms’ profits and ultimately incentivizing them to support the introduction of regulation, either at the national or international level.

This paper examines a model of investment in abatement where polluting firms produce output while investing in RD (2) produce output alone; or (3) engage in both activities. We evaluate how the emergence of each result is affected by the market structure in which firms compete and by the severity of spillover effects. We then measure welfare levels in each equilibrium profile. Overall, we show that firms endogenously choose to focus on R&D only when the market is concentrated and spillover effects are small. In other type of industries, our findings indicate that firms may focus on output production or engage in both activities under relatively large conditions.

We analyze a two-stage sequential-move model of location and pricing to identify firm’s location, output, and welfare. We consider two pricing regimes (mill pricing and spatial price discrimination) and, unlike previous literature, allow in each of them for a non-uniform population density, non-constant location costs (i.e., the setup costs, such rental costs and land prices, differ by firm’s location), and endogenous market boundaries. Under constant location costs, our results show the firm locates at the city center under both mill and discriminatory pricing, and that output is larger under spatial price discrimination. Welfare comparisons are, however, ambiguous. Under non-constant location costs, we find the optimal location can move away from the city center, and does not coincide across pricing regimes. Compared with mill pricing, spatial price discrimination generates a higher level of output. We also find that welfare is higher (lower) under mill than under discriminatory pricing when transportation rates are low (high, respectively).

This paper studies an incomplete information model in which a preventable accident occurred. The judge determining punitive damages observes the firm's (defendant) investment decisions, but is uninformed about the firm's experience adopting safety measures. Our model allows firms to file an appeal if the judge's verdict is incorrect, which the judge may accept or reject. We identify under which conditions a separating equilibrium exists where the firm's investment decisions signal its type to the judge, who responds with a correct verdict, thus avoiding future appeals. Our paper also finds conditions under which a pooling equilibrium exists whereby the firm's investment in precaution conceals its type from the judge, who can respond with an incorrect verdict thus giving rise to appeals. Furthermore, we show that the separating equilibrium is more likely to arise if the percentage of revenue that defendants are required to pay in punitive damages decreases, if the punitive-to-compensatory ratio increases, and if the legal cost of filing an appeal increases.

This paper examines the effect of uniform and firm-specific environmental regulation on the production decisions, and profits, of polluting and green firms. While both types of regulation increase firms' costs and thus entail a negative effect on profits, firm-specific regulation can also yield a positive effect for relatively inefficient firms by alleviating their cost disadvantage. When such cost disadvantage is sufficiently large, we show that the positive effect of firm-specific regulation dominates its negative effect, leading inefficient (efficient) firms to support (oppose) socially optimal regulation. Furthermore, our findings indicate that such support for environmental policy can originate not only from the most common ally (the green firm) but also from polluting firms.

We consider a duopoly in which firms can strategically choose equity shares on their rival’s profits before competing in quantities. We identify equilibrium equity shares, and subsequently compare them against the optimal equity shares that maximize social welfare. Most previous studies assume that equity shares are exogenous, and those allowing for endogenous shares do not evaluate if equilibrium shares are socially excessive or insufficient. Our results also help us identify taxes on equity acquisition that induce firms to produce a socially optimal output without the need to directly tax output levels.