Abstract Surprisingly, formal proof on the optimality of a linear decision rule in the discrete time AK model with a CRRA utility function has not been established in the growth literature while that in the continuous time counterpart is well-established. This note fills such a gap: I provide a formal proof that consumption being linearly related to investment is a sufficient and necessary condition for Pareto optimality in the discrete time AK model.
{"title":"Optimality of a Linear Decision Rule in Discrete Time AK Model","authors":"Myungkyu Shim","doi":"10.1515/bejte-2021-0061","DOIUrl":"https://doi.org/10.1515/bejte-2021-0061","url":null,"abstract":"Abstract Surprisingly, formal proof on the optimality of a linear decision rule in the discrete time AK model with a CRRA utility function has not been established in the growth literature while that in the continuous time counterpart is well-established. This note fills such a gap: I provide a formal proof that consumption being linearly related to investment is a sufficient and necessary condition for Pareto optimality in the discrete time AK model.","PeriodicalId":44773,"journal":{"name":"B E Journal of Theoretical Economics","volume":"23 1","pages":"519 - 527"},"PeriodicalIF":0.4,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46646204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This paper studies the effects of “psychological momentum” on strategic behavior in single- and double-elimination tournaments. We show that in presence of both positive and negative momentum a single-elimination tournament elicits a higher total effort than that of a double-elimination tournament if and only if the positive momentum is insignificant and the negative momentum is significant. Regardless of momentum effects, a single-elimination tournament elicits a higher average effort per match than a double-elimination tournament does.
{"title":"Single- and Double-Elimination Tournaments under Psychological Momentum","authors":"Bo Chen, Xiandeng Jiang, Zijia Wang","doi":"10.1515/bejte-2019-0187","DOIUrl":"https://doi.org/10.1515/bejte-2019-0187","url":null,"abstract":"Abstract This paper studies the effects of “psychological momentum” on strategic behavior in single- and double-elimination tournaments. We show that in presence of both positive and negative momentum a single-elimination tournament elicits a higher total effort than that of a double-elimination tournament if and only if the positive momentum is insignificant and the negative momentum is significant. Regardless of momentum effects, a single-elimination tournament elicits a higher average effort per match than a double-elimination tournament does.","PeriodicalId":44773,"journal":{"name":"B E Journal of Theoretical Economics","volume":"22 1","pages":"509 - 525"},"PeriodicalIF":0.4,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49064794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We study Butters’s (1977. “Equilibrium Distributions of Sales and Advertising Prices.” The Review of Economic Studies 44 (3): 465–91) model under concave advertising costs, and determine a class of cost functions such that each seller sends the same finite number of ads in equilibrium. Then we consider the limit economy where the number of buyers and sellers grow indefinitely, and show that the equilibrium of the finite economy does not converge to an equilibrium in the limit economy.
{"title":"Equilibrium Pricing under Concave Advertising Costs","authors":"K. Kultti, Teemu Pekkarinen","doi":"10.2139/ssrn.3922689","DOIUrl":"https://doi.org/10.2139/ssrn.3922689","url":null,"abstract":"Abstract We study Butters’s (1977. “Equilibrium Distributions of Sales and Advertising Prices.” The Review of Economic Studies 44 (3): 465–91) model under concave advertising costs, and determine a class of cost functions such that each seller sends the same finite number of ads in equilibrium. Then we consider the limit economy where the number of buyers and sellers grow indefinitely, and show that the equilibrium of the finite economy does not converge to an equilibrium in the limit economy.","PeriodicalId":44773,"journal":{"name":"B E Journal of Theoretical Economics","volume":"23 1","pages":"529 - 535"},"PeriodicalIF":0.4,"publicationDate":"2021-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46543812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This paper considers contractual choice under imperfect legal systems, in particular, contracts with different timing of payment. Ex-ante payment contracts are risky for the buyer, because the seller may shirk. Ex-post payment contracts are risky for the seller, as the buyer may default. Optimal contract is solved for any given legal environment. Exchanges with lower gains from trade tend to adopt ex-post payment contracts. The seller is a better proposer than the buyer in terms of the efficiency of the proposed contract. Surprisingly, offering ex-ante payment contracts is not strictly better for the seller under any legal environment. Moreover, mixed payment contracts are also analyzed and shown to never be optimal.
{"title":"Legal Environment and Contractual Choice","authors":"Housi Cheng","doi":"10.1515/bejte-2020-0098","DOIUrl":"https://doi.org/10.1515/bejte-2020-0098","url":null,"abstract":"Abstract This paper considers contractual choice under imperfect legal systems, in particular, contracts with different timing of payment. Ex-ante payment contracts are risky for the buyer, because the seller may shirk. Ex-post payment contracts are risky for the seller, as the buyer may default. Optimal contract is solved for any given legal environment. Exchanges with lower gains from trade tend to adopt ex-post payment contracts. The seller is a better proposer than the buyer in terms of the efficiency of the proposed contract. Surprisingly, offering ex-ante payment contracts is not strictly better for the seller under any legal environment. Moreover, mixed payment contracts are also analyzed and shown to never be optimal.","PeriodicalId":44773,"journal":{"name":"B E Journal of Theoretical Economics","volume":"22 1","pages":"557 - 577"},"PeriodicalIF":0.4,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44966010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract A decision maker solicits information from two partially informed experts and then makes a choice under uncertainty. The experts can be either moderately or extremely biased relative to the decision maker, which is their private information. I investigate the incentives of the experts to share their private information with the decision maker and analyze the resulting effects on information transmission. I show that it may be optimal to consult a single expert rather than two experts if the decision maker is sufficiently concerned about taking advice from extremely biased experts. In contrast to what may be expected, this result suggests that getting a second opinion may not always be helpful for decision making.
{"title":"Cheap Talk with Multiple Experts and Uncertain Biases","authors":"Gülen Karakoç","doi":"10.1515/bejte-2020-0171","DOIUrl":"https://doi.org/10.1515/bejte-2020-0171","url":null,"abstract":"Abstract A decision maker solicits information from two partially informed experts and then makes a choice under uncertainty. The experts can be either moderately or extremely biased relative to the decision maker, which is their private information. I investigate the incentives of the experts to share their private information with the decision maker and analyze the resulting effects on information transmission. I show that it may be optimal to consult a single expert rather than two experts if the decision maker is sufficiently concerned about taking advice from extremely biased experts. In contrast to what may be expected, this result suggests that getting a second opinion may not always be helpful for decision making.","PeriodicalId":44773,"journal":{"name":"B E Journal of Theoretical Economics","volume":"22 1","pages":"527 - 556"},"PeriodicalIF":0.4,"publicationDate":"2021-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44323499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In their seminal paper, Grossman, G. M., and C. Shapiro. 1984. “Informative Advertising with Differentiated Products.” The Review of Economic Studies 51: 63–81 assume that it is not profitable for a firm to deviate to the supercompetitive price of Salop, S. C. 1979. “Monopolistic Competition with outside Goods.” The Bell Journal of Economics 10: 141–56. In this note, it is shown that this assumption is violated if, roughly, each firm reaches less than half of all consumers unless it is a duopoly. This implies that most of the simulations in Grossman, G. M., and C. Shapiro. 1984. “Informative Advertising with Differentiated Products.” The Review of Economic Studies 51: 63–81 are not actually equilibria. More importantly, this implies that for their equilibrium to exist nearly all consumers must receive at least one ad. For example, with just four firms in the market, at least 96% of the consumers must receive at least one ad, and this percentage increases with the number of firms in the market.
{"title":"A Note on the Existence of the Competitive Equilibrium in","authors":"Anthony Creane","doi":"10.1515/bejte-2021-0013","DOIUrl":"https://doi.org/10.1515/bejte-2021-0013","url":null,"abstract":"Abstract In their seminal paper, Grossman, G. M., and C. Shapiro. 1984. “Informative Advertising with Differentiated Products.” The Review of Economic Studies 51: 63–81 assume that it is not profitable for a firm to deviate to the supercompetitive price of Salop, S. C. 1979. “Monopolistic Competition with outside Goods.” The Bell Journal of Economics 10: 141–56. In this note, it is shown that this assumption is violated if, roughly, each firm reaches less than half of all consumers unless it is a duopoly. This implies that most of the simulations in Grossman, G. M., and C. Shapiro. 1984. “Informative Advertising with Differentiated Products.” The Review of Economic Studies 51: 63–81 are not actually equilibria. More importantly, this implies that for their equilibrium to exist nearly all consumers must receive at least one ad. For example, with just four firms in the market, at least 96% of the consumers must receive at least one ad, and this percentage increases with the number of firms in the market.","PeriodicalId":44773,"journal":{"name":"B E Journal of Theoretical Economics","volume":"22 1","pages":"629 - 647"},"PeriodicalIF":0.4,"publicationDate":"2021-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41792319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In their seminal 1954 paper on the existence of competitive equilibrium, Arrow and Debreu state what they call an “important principle”, namely that it is necessary for the existence of equilibrium that every consumer has some asset or can supply some labour service which has a positive price at equilibrium. It does not seem to have been noticed that this claim is incorrect. We provide a very simple model of a private ownership economy with three goods where a competitive equilibrium exists, but consumers who have nothing to sell but their labour end up with zero wealth in equilibrium. As zero wealth must be taken to mean non-survival, and the Arrow–Debreu model is frequently interpreted as assuming that all consumers can survive without trade, we also briefly discuss the issue of non-survival in equilibrium. We finally point out that our example illustrates the possibility that technological progress may result in a situation where the value of work becomes negligible.
{"title":"On an “Important Principle” of Arrow and Debreu","authors":"A. Vilks","doi":"10.1515/bejte-2021-0074","DOIUrl":"https://doi.org/10.1515/bejte-2021-0074","url":null,"abstract":"Abstract In their seminal 1954 paper on the existence of competitive equilibrium, Arrow and Debreu state what they call an “important principle”, namely that it is necessary for the existence of equilibrium that every consumer has some asset or can supply some labour service which has a positive price at equilibrium. It does not seem to have been noticed that this claim is incorrect. We provide a very simple model of a private ownership economy with three goods where a competitive equilibrium exists, but consumers who have nothing to sell but their labour end up with zero wealth in equilibrium. As zero wealth must be taken to mean non-survival, and the Arrow–Debreu model is frequently interpreted as assuming that all consumers can survive without trade, we also briefly discuss the issue of non-survival in equilibrium. We finally point out that our example illustrates the possibility that technological progress may result in a situation where the value of work becomes negligible.","PeriodicalId":44773,"journal":{"name":"B E Journal of Theoretical Economics","volume":"22 1","pages":"621 - 627"},"PeriodicalIF":0.4,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41953043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The model in which an individual maximizes his ordinal or cardinal total utility has long been the paradigm of individual choice theory. However, the two mainstream utility theories, the ordinal and cardinal total utility theories, have caused a dilemma, i.e. one has to sacrifice one of the following two: the good property of utility ordinality, or common-sense notions such as the law of diminishing marginal utility. Ordinal theory keeps the former but gives up the latter, while cardinal theory keeps the latter but sacrifices the former. We propose an ordinal marginal utility approach aiming to solve this dilemma by changing the very first assumption regarding individual choice.
{"title":"A Rehabilitation of the Law of Diminishing Marginal Utility: An Ordinal Marginal Utility Approach","authors":"Chung‐Cheng Lin, Shi‐Shu Peng","doi":"10.1515/bejte-2020-0158","DOIUrl":"https://doi.org/10.1515/bejte-2020-0158","url":null,"abstract":"Abstract The model in which an individual maximizes his ordinal or cardinal total utility has long been the paradigm of individual choice theory. However, the two mainstream utility theories, the ordinal and cardinal total utility theories, have caused a dilemma, i.e. one has to sacrifice one of the following two: the good property of utility ordinality, or common-sense notions such as the law of diminishing marginal utility. Ordinal theory keeps the former but gives up the latter, while cardinal theory keeps the latter but sacrifices the former. We propose an ordinal marginal utility approach aiming to solve this dilemma by changing the very first assumption regarding individual choice.","PeriodicalId":44773,"journal":{"name":"B E Journal of Theoretical Economics","volume":"22 1","pages":"453 - 481"},"PeriodicalIF":0.4,"publicationDate":"2021-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/bejte-2020-0158","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46783348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We show that bilateral cross-holding can be profitable for firms with symmetric technologies in a Stackelberg oligopoly. Furthermore, if firms involved in cross-holding obtain a strategic advantage to be the leaders (i.e. Stackelberg leadership through cross-holding), such cross-holding will improve both consumer surplus and social welfare. We also discuss robustness of our main results with respect to convex costs and product differentiation.
{"title":"Passive Cross-Holding in a Stackelberg Oligopoly","authors":"Hongkun Ma, Chenhang Zeng","doi":"10.1515/bejte-2020-0041","DOIUrl":"https://doi.org/10.1515/bejte-2020-0041","url":null,"abstract":"Abstract We show that bilateral cross-holding can be profitable for firms with symmetric technologies in a Stackelberg oligopoly. Furthermore, if firms involved in cross-holding obtain a strategic advantage to be the leaders (i.e. Stackelberg leadership through cross-holding), such cross-holding will improve both consumer surplus and social welfare. We also discuss robustness of our main results with respect to convex costs and product differentiation.","PeriodicalId":44773,"journal":{"name":"B E Journal of Theoretical Economics","volume":"22 1","pages":"431 - 452"},"PeriodicalIF":0.4,"publicationDate":"2021-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/bejte-2020-0041","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45162815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In a model of information disclosure with multiple experts we compare homogeneous panels and diverse panels. The distinguishing feature of our model is selective investigation: there are multiple aspects relevant to decision making and each expert can strategically choose some aspects to investigate. We show that homogeneous panels lead to unbalanced investigation and unbalanced action, while under diverse panels both investigations and actions are balanced. In most circumstances, diverse panels perform better than homogeneous panels.
{"title":"Expert Panels with Selective Investigation","authors":"Q. Gong, Huanxing Yang","doi":"10.1515/bejte-2021-0010","DOIUrl":"https://doi.org/10.1515/bejte-2021-0010","url":null,"abstract":"Abstract In a model of information disclosure with multiple experts we compare homogeneous panels and diverse panels. The distinguishing feature of our model is selective investigation: there are multiple aspects relevant to decision making and each expert can strategically choose some aspects to investigate. We show that homogeneous panels lead to unbalanced investigation and unbalanced action, while under diverse panels both investigations and actions are balanced. In most circumstances, diverse panels perform better than homogeneous panels.","PeriodicalId":44773,"journal":{"name":"B E Journal of Theoretical Economics","volume":"22 1","pages":"369 - 404"},"PeriodicalIF":0.4,"publicationDate":"2021-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/bejte-2021-0010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41480225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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