Many scarce public resources are allocated below market-clearing prices (and sometimes for free). Such "non-market" mechanisms necessarily sacrifice some surplus, yet they can potentially improve equity by increasing the rents enjoyed by agents with low willingness to pay. In this paper, we develop a model of mechanism design with redistributive concerns. Agents are characterized by a privately observed willingness to pay for quality, and a publicly observed label. A market designer controls allocation and pricing of a set of objects of heterogeneous quality, and maximizes a linear combination of revenue and total surplus| with Pareto weights that depend both on observed and unobserved agent characteristics. We derive structural insights about the form of the optimal mechanism and describe how social preferences influence the use of non-market mechanisms.
Tous Géographes ? Quel enseignement de la géographie dans un monde tout numér...Sophie TAN - EHRHARDT
Mémoire de Master 2 MEEF réalisé dans le cadre de la formation professionnelle au métier de professeur d'histoire-géographie, sous la direction d'Henri Desbois.
Ce mémoire analyse les bouleversements de l'enseignement de la géographie à l'ère du numérique et d'Internet.
Tous Géographes ? Quel enseignement de la géographie dans un monde tout numér...Sophie TAN - EHRHARDT
Mémoire de Master 2 MEEF réalisé dans le cadre de la formation professionnelle au métier de professeur d'histoire-géographie, sous la direction d'Henri Desbois.
Ce mémoire analyse les bouleversements de l'enseignement de la géographie à l'ère du numérique et d'Internet.
Social Cost Benefit Analysis: Concept of social cost benefit, significance of SCBA, Approach to SCBA,
UNIDO approach to SCBA, Shadow pricing of resource, the little miracle approach,
Project Implementation: Schedule of project implementation, Project Planning, Project Control, Human
aspects of project management, team building, high performance team.
Equity-efficiency trade-off in quasi-linear environmentsGRAPE
We study a simple equity-efficiency problem: a designer allocates a fixed amount of money to a population of agents differing in privately observed marginal values for money. She can only screen agents by asking them to burn utility (through some socially wasteful activity). We show that giving a lump-sum payment is outperformed by a mechanism with utility burning when the agent with the lowest money-denominated cost of engaging in the wasteful activity has an expected value for money that exceeds the average value by more than a factor of two.
This report is prepared for the Social Purpose Business course at Schulich School of Business as a practice to apply the social entrepreneurship business model planning methods.
Policymakers frequently use price regulations as a response to inequality in the markets they control. In this paper, we examine the optimal structure of such policies from the perspective of mechanism design. We study a buyer-seller market in which agents have private information about both their valuations for an indivisible object and their marginal utilities for money. The planner seeks a mechanism that maximizes agents’ total utilities, subject to incentive and market-clearing constraints. We uncover the constrained Pareto frontier by identifying the optimal trade-off between allocative efficiency and redistribution. We find that competitive-equilibrium allocation is not always optimal. Instead, when there is substantial inequality across sides of the market, the optimal design uses a tax-like mechanism, introducing a wedge between the buyer and seller prices, and redistributing the resulting surplus to the poorer side of the market via lump-sum payments. When there is significant same-side inequality, meanwhile, it may be optimal to impose price controls even though doing so induces rationing.
Seminar: Gender Board Diversity through Ownership NetworksGRAPE
Seminar on gender diversity spillovers through ownership networks at FAME|GRAPE. Presenting novel research. Studies in economics and management using econometrics methods.
The European Unemployment Puzzle: implications from population agingGRAPE
We study the link between the evolving age structure of the working population and unemployment. We build a large new Keynesian OLG model with a realistic age structure, labor market frictions, sticky prices, and aggregate shocks. Once calibrated to the European economy, we quantify the extent to which demographic changes over the last three decades have contributed to the decline of the unemployment rate. Our findings yield important implications for the future evolution of unemployment given the anticipated further aging of the working population in Europe. We also quantify the implications for optimal monetary policy: lowering inflation volatility becomes less costly in terms of GDP and unemployment volatility, which hints that optimal monetary policy may be more hawkish in an aging society. Finally, our results also propose a partial reversal of the European-US unemployment puzzle due to the fact that the share of young workers is expected to remain robust in the US.
Social Cost Benefit Analysis: Concept of social cost benefit, significance of SCBA, Approach to SCBA,
UNIDO approach to SCBA, Shadow pricing of resource, the little miracle approach,
Project Implementation: Schedule of project implementation, Project Planning, Project Control, Human
aspects of project management, team building, high performance team.
Equity-efficiency trade-off in quasi-linear environmentsGRAPE
We study a simple equity-efficiency problem: a designer allocates a fixed amount of money to a population of agents differing in privately observed marginal values for money. She can only screen agents by asking them to burn utility (through some socially wasteful activity). We show that giving a lump-sum payment is outperformed by a mechanism with utility burning when the agent with the lowest money-denominated cost of engaging in the wasteful activity has an expected value for money that exceeds the average value by more than a factor of two.
This report is prepared for the Social Purpose Business course at Schulich School of Business as a practice to apply the social entrepreneurship business model planning methods.
Policymakers frequently use price regulations as a response to inequality in the markets they control. In this paper, we examine the optimal structure of such policies from the perspective of mechanism design. We study a buyer-seller market in which agents have private information about both their valuations for an indivisible object and their marginal utilities for money. The planner seeks a mechanism that maximizes agents’ total utilities, subject to incentive and market-clearing constraints. We uncover the constrained Pareto frontier by identifying the optimal trade-off between allocative efficiency and redistribution. We find that competitive-equilibrium allocation is not always optimal. Instead, when there is substantial inequality across sides of the market, the optimal design uses a tax-like mechanism, introducing a wedge between the buyer and seller prices, and redistributing the resulting surplus to the poorer side of the market via lump-sum payments. When there is significant same-side inequality, meanwhile, it may be optimal to impose price controls even though doing so induces rationing.
Seminar: Gender Board Diversity through Ownership NetworksGRAPE
Seminar on gender diversity spillovers through ownership networks at FAME|GRAPE. Presenting novel research. Studies in economics and management using econometrics methods.
The European Unemployment Puzzle: implications from population agingGRAPE
We study the link between the evolving age structure of the working population and unemployment. We build a large new Keynesian OLG model with a realistic age structure, labor market frictions, sticky prices, and aggregate shocks. Once calibrated to the European economy, we quantify the extent to which demographic changes over the last three decades have contributed to the decline of the unemployment rate. Our findings yield important implications for the future evolution of unemployment given the anticipated further aging of the working population in Europe. We also quantify the implications for optimal monetary policy: lowering inflation volatility becomes less costly in terms of GDP and unemployment volatility, which hints that optimal monetary policy may be more hawkish in an aging society. Finally, our results also propose a partial reversal of the European-US unemployment puzzle due to the fact that the share of young workers is expected to remain robust in the US.
Revisiting gender board diversity and firm performanceGRAPE
Cel: oszacować wpływ inkluzywności władz spółek na ich wyniki.
Co wiemy?
• Większość firm nie ma równosci płci w organach (ILO, 2015)
• Większość firm nie ma w ogóle kobiet we władzach
Demographic transition and the rise of wealth inequalityGRAPE
We study the contribution of rising longevity to the rise of wealth inequality in the U.S. over the last seventy years. We construct an OLG model with multiple sources of inequality, closely calibrated to the data. Our main finding is that improvements in old-age longevity explain about 30% of the observed rise in wealth inequality. This magnitude is similar to previously emphasized channels associated with income inequality and the tax system. The contribution of demographics is bound to raise wealth inequality further in the decades to come.
(Gender) tone at the top: the effect of board diversity on gender inequalityGRAPE
The research explores to what extent the presence of women on board affects gender inequality downstream. We find that increasing presence reduces gender inequality. To avoid reverse causality, we propose a new instrument: the share of household consumption in total output. We extend the analysis to recover the effect of a single woman on board (tokenism(
Gender board diversity spillovers and the public eyeGRAPE
A range of policy recommendations mandating gender board quotas is based on the idea that "women help women". We analyze potential gender diversity spillovers from supervisory to top managerial positions over three decades in Europe. Contrary to previous studies which worked with stock listed firms or were region locked, we use a large data base of roughly 2 000 000 firms. We find evidence that women do not help women in corporate Europe, unless the firm is stock listed. Only within public firms, going from no woman to at least one woman on supervisory position is associated with a 10-15% higher probability of appointing at least one woman to the executive position. This pattern aligns with various managerial theories, suggesting that external visibility influences corporate gender diversity practices. The study implies that diversity policies, while impactful in public firms, have limited
effectiveness in promoting gender diversity in corporate Europe.
Tone at the top: the effects of gender board diversity on gender wage inequal...GRAPE
We address the gender wage gap in Europe, focusing on the impact of female representation in executive and non-executive boards. We use a novel dataset to identify gender board diversity across European firms, which covers a comprehensive sample of private firms in addition to publicly listed ones. Our study spans three waves of the Structure of Earnings Survey, covering 26 countries and multiple industries. Despite low prevalence of female representation and the complex nature of gender wage inequality, our findings reveal a robust causal link: increased gender diversity significantly decreases the adjusted gender wage gap. We also demonstrate that to meaningfully impact gender wage gaps, the presence of a single female representative in leadership is insufficient.
Gender board diversity spillovers and the public eyeGRAPE
A range of policy recommendations mandating gender board quotas is based on the idea that "women help women". We analyze potential gender diversity spillovers from supervisory to top managerial positions over three decades in Europe. Contrary to previous studies which worked with stock listed firms or were region locked, we use a large data base of roughly 2 000 000 firms. We find evidence that women do not help women in corporate Europe, unless the firm is stock listed. Only within public firms, going from no woman to at least one woman on supervisory position is associated with a 10-15\% higher probability of appointing at least one woman to the executive position. This pattern aligns with the Public Eye Managerial Theory, suggesting that external visibility influences corporate gender diversity practices. The study implies that diversity policies, while impactful in public firms, have limited effectiveness in promoting gender diversity in corporate Europe.
The European Unemployment Puzzle: implications from population agingGRAPE
We study the link between the evolving age structure of the working population and unemployment. We build a large New Keynesian OLG model with a realistic age structure, labor market frictions, sticky prices, and aggregate shocks. Once calibrated to the European economies, we use this model to provide comparative statics across past and contemporaneous age structures of the working population. Thus, we quantify the extent to which the response of labor markets to adverse TFP shocks and monetary policy shocks becomes muted with the aging of the working population. Our findings have important policy implications for European labor markets and beyond. For example, the working population is expected to further age in Europe, whereas the share of young workers will remain robust in the US. Our results suggest a partial reversal of the European-US unemployment puzzle. Furthermore, with the aging population, lowering inflation volatility is less costly in terms of higher unemployment volatility. It suggests that optimal monetary policy should be more hawkish in the older society.
Evidence concerning inequality in ability to realize aspirations is prevalent: overall, in specialized segments of the labor market, in self-employment and high-aspirations environments. Empirical literature and public debate are full of case studies and comprehensive empirical studies documenting the paramount gap between successful individuals (typically ethnic majority men) and those who are less likely to “make it” (typically ethnic minority and women). So far the drivers of these disparities and their consequences have been studied much less intensively, due to methodological constraints and shortage of appropriate data. This project proposes significant innovations to overcome both types of barriers and push the frontier of the research agenda on equality in reaching aspirations.
Overall, project is interdisciplinary, combining four fields: management, economics, quantitative methods and psychology. An important feature of this project is that it offers a diversified methodological perspective, combining applied microeconometrics, as well as experimental methods.
when will pi network coin be available on crypto exchange.DOT TECH
There is no set date for when Pi coins will enter the market.
However, the developers are working hard to get them released as soon as possible.
Once they are available, users will be able to exchange other cryptocurrencies for Pi coins on designated exchanges.
But for now the only way to sell your pi coins is through verified pi vendor.
Here is the what'sapp contact of my personal pi vendor
+12349014282
2. Elemental Economics - Mineral demand.pdfNeal Brewster
After this second you should be able to: Explain the main determinants of demand for any mineral product, and their relative importance; recognise and explain how demand for any product is likely to change with economic activity; recognise and explain the roles of technology and relative prices in influencing demand; be able to explain the differences between the rates of growth of demand for different products.
5 Tips for Creating Standard Financial ReportsEasyReports
Well-crafted financial reports serve as vital tools for decision-making and transparency within an organization. By following the undermentioned tips, you can create standardized financial reports that effectively communicate your company's financial health and performance to stakeholders.
What website can I sell pi coins securely.DOT TECH
Currently there are no website or exchange that allow buying or selling of pi coins..
But you can still easily sell pi coins, by reselling it to exchanges/crypto whales interested in holding thousands of pi coins before the mainnet launch.
Who is a pi merchant?
A pi merchant is someone who buys pi coins from miners and resell to these crypto whales and holders of pi..
This is because pi network is not doing any pre-sale. The only way exchanges can get pi is by buying from miners and pi merchants stands in between the miners and the exchanges.
How can I sell my pi coins?
Selling pi coins is really easy, but first you need to migrate to mainnet wallet before you can do that. I will leave the what'sapp contact of my personal pi merchant to trade with.
+12349014282
BONKMILLON Unleashes Its Bonkers Potential on Solana.pdfcoingabbar
Introducing BONKMILLON - The Most Bonkers Meme Coin Yet
Let's be real for a second – the world of meme coins can feel like a bit of a circus at times. Every other day, there's a new token promising to take you "to the moon" or offering some groundbreaking utility that'll change the game forever. But how many of them actually deliver on that hype?
Yes of course, you can easily start mining pi network coin today and sell to legit pi vendors in the United States.
Here the what'sapp contact of my personal vendor.
+12349014282
#pi network #pi coins #legit #passive income
#US
how to sell pi coins in South Korea profitably.DOT TECH
Yes. You can sell your pi network coins in South Korea or any other country, by finding a verified pi merchant
What is a verified pi merchant?
Since pi network is not launched yet on any exchange, the only way you can sell pi coins is by selling to a verified pi merchant, and this is because pi network is not launched yet on any exchange and no pre-sale or ico offerings Is done on pi.
Since there is no pre-sale, the only way exchanges can get pi is by buying from miners. So a pi merchant facilitates these transactions by acting as a bridge for both transactions.
How can i find a pi vendor/merchant?
Well for those who haven't traded with a pi merchant or who don't already have one. I will leave the what'sapp number of my personal pi merchant who i trade pi with.
Message: +12349014282 VIA Whatsapp.
#pi #sell #nigeria #pinetwork #picoins #sellpi #Nigerian #tradepi #pinetworkcoins #sellmypi
Abhay Bhutada Leads Poonawalla Fincorp To Record Low NPA And Unprecedented Gr...Vighnesh Shashtri
Under the leadership of Abhay Bhutada, Poonawalla Fincorp has achieved record-low Non-Performing Assets (NPA) and witnessed unprecedented growth. Bhutada's strategic vision and effective management have significantly enhanced the company's financial health, showcasing a robust performance in the financial sector. This achievement underscores the company's resilience and ability to thrive in a competitive market, setting a new benchmark for operational excellence in the industry.
how to sell pi coins effectively (from 50 - 100k pi)DOT TECH
Anywhere in the world, including Africa, America, and Europe, you can sell Pi Network Coins online and receive cash through online payment options.
Pi has not yet been launched on any exchange because we are currently using the confined Mainnet. The planned launch date for Pi is June 28, 2026.
Reselling to investors who want to hold until the mainnet launch in 2026 is currently the sole way to sell.
Consequently, right now. All you need to do is select the right pi network provider.
Who is a pi merchant?
An individual who buys coins from miners on the pi network and resells them to investors hoping to hang onto them until the mainnet is launched is known as a pi merchant.
debuts.
I'll provide you the what'sapp number.
+12349014282
Financial Assets: Debit vs Equity Securities.pptxWrito-Finance
financial assets represent claim for future benefit or cash. Financial assets are formed by establishing contracts between participants. These financial assets are used for collection of huge amounts of money for business purposes.
Two major Types: Debt Securities and Equity Securities.
Debt Securities are Also known as fixed-income securities or instruments. The type of assets is formed by establishing contracts between investor and issuer of the asset.
• The first type of Debit securities is BONDS. Bonds are issued by corporations and government (both local and national government).
• The second important type of Debit security is NOTES. Apart from similarities associated with notes and bonds, notes have shorter term maturity.
• The 3rd important type of Debit security is TRESURY BILLS. These securities have short-term ranging from three months, six months, and one year. Issuer of such securities are governments.
• Above discussed debit securities are mostly issued by governments and corporations. CERTIFICATE OF DEPOSITS CDs are issued by Banks and Financial Institutions. Risk factor associated with CDs gets reduced when issued by reputable institutions or Banks.
Following are the risk attached with debt securities: Credit risk, interest rate risk and currency risk
There are no fixed maturity dates in such securities, and asset’s value is determined by company’s performance. There are two major types of equity securities: common stock and preferred stock.
Common Stock: These are simple equity securities and bear no complexities which the preferred stock bears. Holders of such securities or instrument have the voting rights when it comes to select the company’s board of director or the business decisions to be made.
Preferred Stock: Preferred stocks are sometime referred to as hybrid securities, because it contains elements of both debit security and equity security. Preferred stock confers ownership rights to security holder that is why it is equity instrument
<a href="https://www.writofinance.com/equity-securities-features-types-risk/" >Equity securities </a> as a whole is used for capital funding for companies. Companies have multiple expenses to cover. Potential growth of company is required in competitive market. So, these securities are used for capital generation, and then uses it for company’s growth.
Concluding remarks
Both are employed in business. Businesses are often established through debit securities, then what is the need for equity securities. Companies have to cover multiple expenses and expansion of business. They can also use equity instruments for repayment of debits. So, there are multiple uses for securities. As an investor, you need tools for analysis. Investment decisions are made by carefully analyzing the market. For better analysis of the stock market, investors often employ financial analysis of companies.
1. Redistributive Allocation Mechanisms
(with an application to the potential European energy crisis)
Mohammad Akbarpour r
O Piotr Dworczak r
O Scott Duke Kominers*
(Stanford) (GRAPE & Northwestern) (Harvard)
22 November, 2022
European Central Bank, invited speaker seminar
Research sponsored by ERC grant IMD-101040122.
*Authors’ names are in certified random order.
2. Motivation
Many goods and services are allocated using non-market mechanisms,
even though monetary transfers are feasible:
Housing
3. Motivation
Many goods and services are allocated using non-market mechanisms,
even though monetary transfers are feasible:
Housing
Health care
4. Motivation
Many goods and services are allocated using non-market mechanisms,
even though monetary transfers are feasible:
Housing
Health care
Food
5. Motivation
Many goods and services are allocated using non-market mechanisms,
even though monetary transfers are feasible:
Housing
Health care
Food
Road access
6. Motivation
Many goods and services are allocated using non-market mechanisms,
even though monetary transfers are feasible:
Housing
Health care
Food
Road access
...
7. Motivation
Many goods and services are allocated using non-market mechanisms,
even though monetary transfers are feasible:
Housing
Health care
Food
Road access
...
Follow-up paper: Covid-19 vaccines
8. Motivation
Many goods and services are allocated using non-market mechanisms,
even though monetary transfers are feasible:
Housing
Health care
Food
Road access
...
Follow-up paper: Covid-19 vaccines
Focus today: Energy this winter in Europe
13. Motivation
Classical economic perspective: Distorting prices will lead to
inefficiency (I WT); if you want to redistribute, do so via lump-sum
payments (II WT)
▶ echoed in The Economist on 08/09/2022 and IMF WP/22/152
14. Motivation
Classical economic perspective: Distorting prices will lead to
inefficiency (I WT); if you want to redistribute, do so via lump-sum
payments (II WT)
▶ echoed in The Economist on 08/09/2022 and IMF WP/22/152
But: Welfare theorems ignore the issue of private information!
15. Motivation
Classical economic perspective: Distorting prices will lead to
inefficiency (I WT); if you want to redistribute, do so via lump-sum
payments (II WT)
▶ echoed in The Economist on 08/09/2022 and IMF WP/22/152
But: Welfare theorems ignore the issue of private information!
Governments do have some information... but far from perfect in
practice:
16. Motivation
Classical economic perspective: Distorting prices will lead to
inefficiency (I WT); if you want to redistribute, do so via lump-sum
payments (II WT)
▶ echoed in The Economist on 08/09/2022 and IMF WP/22/152
But: Welfare theorems ignore the issue of private information!
Governments do have some information... but far from perfect in
practice:
▶ Detailed financial situation?
17. Motivation
Classical economic perspective: Distorting prices will lead to
inefficiency (I WT); if you want to redistribute, do so via lump-sum
payments (II WT)
▶ echoed in The Economist on 08/09/2022 and IMF WP/22/152
But: Welfare theorems ignore the issue of private information!
Governments do have some information... but far from perfect in
practice:
▶ Detailed financial situation?
▶ Job market opportunities?
18. Motivation
Classical economic perspective: Distorting prices will lead to
inefficiency (I WT); if you want to redistribute, do so via lump-sum
payments (II WT)
▶ echoed in The Economist on 08/09/2022 and IMF WP/22/152
But: Welfare theorems ignore the issue of private information!
Governments do have some information... but far from perfect in
practice:
▶ Detailed financial situation?
▶ Job market opportunities?
▶ Exposure to interest rate hikes?
19. Motivation
Classical economic perspective: Distorting prices will lead to
inefficiency (I WT); if you want to redistribute, do so via lump-sum
payments (II WT)
▶ echoed in The Economist on 08/09/2022 and IMF WP/22/152
But: Welfare theorems ignore the issue of private information!
Governments do have some information... but far from perfect in
practice:
▶ Detailed financial situation?
▶ Job market opportunities?
▶ Exposure to interest rate hikes?
▶ Energy efficiency of housing?
20. Motivation
Classical economic perspective: Distorting prices will lead to
inefficiency (I WT); if you want to redistribute, do so via lump-sum
payments (II WT)
▶ echoed in The Economist on 08/09/2022 and IMF WP/22/152
But: Welfare theorems ignore the issue of private information!
Governments do have some information... but far from perfect in
practice:
▶ Detailed financial situation?
▶ Job market opportunities?
▶ Exposure to interest rate hikes?
▶ Energy efficiency of housing?
▶ Heating method?
21. Motivation
Classical economic perspective: Distorting prices will lead to
inefficiency (I WT); if you want to redistribute, do so via lump-sum
payments (II WT)
▶ echoed in The Economist on 08/09/2022 and IMF WP/22/152
But: Welfare theorems ignore the issue of private information!
Governments do have some information... but far from perfect in
practice:
▶ Detailed financial situation?
▶ Job market opportunities?
▶ Exposure to interest rate hikes?
▶ Energy efficiency of housing?
▶ Heating method?
▶ Family size?
22. Inequality-aware Market Design
Our approach: A market-design framework for determining the optimal
allocation under redistributive concerns
(Market-design perspective: the designer only controls a single market)
23. Inequality-aware Market Design
Our approach: A market-design framework for determining the optimal
allocation under redistributive concerns
(Market-design perspective: the designer only controls a single market)
Designer allocates a set of goods to agents differing in their observed
and unobserved characteristics.
24. Inequality-aware Market Design
Our approach: A market-design framework for determining the optimal
allocation under redistributive concerns
(Market-design perspective: the designer only controls a single market)
Designer allocates a set of goods to agents differing in their observed
and unobserved characteristics.
We derive the optimal mechanism under IC and IR constraints and
an objective that reflects redistributive concerns via welfare weights.
25. Inequality-aware Market Design
Our approach: A market-design framework for determining the optimal
allocation under redistributive concerns
(Market-design perspective: the designer only controls a single market)
Designer allocates a set of goods to agents differing in their observed
and unobserved characteristics.
We derive the optimal mechanism under IC and IR constraints and
an objective that reflects redistributive concerns via welfare weights.
Some key take-aways:
26. Inequality-aware Market Design
Our approach: A market-design framework for determining the optimal
allocation under redistributive concerns
(Market-design perspective: the designer only controls a single market)
Designer allocates a set of goods to agents differing in their observed
and unobserved characteristics.
We derive the optimal mechanism under IC and IR constraints and
an objective that reflects redistributive concerns via welfare weights.
Some key take-aways:
▶ Non-market mechanisms can be optimal!
27. Inequality-aware Market Design
Our approach: A market-design framework for determining the optimal
allocation under redistributive concerns
(Market-design perspective: the designer only controls a single market)
Designer allocates a set of goods to agents differing in their observed
and unobserved characteristics.
We derive the optimal mechanism under IC and IR constraints and
an objective that reflects redistributive concerns via welfare weights.
Some key take-aways:
▶ Non-market mechanisms can be optimal!
▶ If lump-sum payments are available, uniform price caps are never
optimal;
28. Inequality-aware Market Design
Our approach: A market-design framework for determining the optimal
allocation under redistributive concerns
(Market-design perspective: the designer only controls a single market)
Designer allocates a set of goods to agents differing in their observed
and unobserved characteristics.
We derive the optimal mechanism under IC and IR constraints and
an objective that reflects redistributive concerns via welfare weights.
Some key take-aways:
▶ Non-market mechanisms can be optimal!
▶ If lump-sum payments are available, uniform price caps are never
optimal;
▶ Instead, price caps should only be applied up to some threshold
consumption level;
29. Inequality-aware Market Design
Our approach: A market-design framework for determining the optimal
allocation under redistributive concerns
(Market-design perspective: the designer only controls a single market)
Designer allocates a set of goods to agents differing in their observed
and unobserved characteristics.
We derive the optimal mechanism under IC and IR constraints and
an objective that reflects redistributive concerns via welfare weights.
Some key take-aways:
▶ Non-market mechanisms can be optimal!
▶ If lump-sum payments are available, uniform price caps are never
optimal;
▶ Instead, price caps should only be applied up to some threshold
consumption level;
▶ Uniform price caps can be optimal when lump-sum payments are
costly;
30. Literature
Weitzman (1977): First paper to point out that random allocation
might be preferred to market pricing when agents’ “needs” are not
well expressed by willingness to pay.
Condorelli (2013): A full mechanism-design approach to Weitzman’s
problem
▶ On a technical level: We add heterogeneous quality of objects,
continuum of goods and agents, groups of agents with the same
observable characteristics, and designer’s preferences over revenue.
▶ On a conceptual level: We focus on a particular objective function
(weighted sum of utilities and revenue) and connect market
circumstances with practical conclusions about the optimal design.
Dworczak r
O Kominers r
O Akbarpour (2021): two-sided market
but “maximally simplified” (no heterogeneous quality, no observable
information, no restrictions on lump-sum transfers)
31. Literature
Price control, public provision of goods: Nichols and Zeckhauser (1982), Besley
and Coate (1991), Blackorby and Donaldson (1988), Viscusi, Harrington, and
Vernon (2005), Gahvari and Mattos (2007), Currie and Gahvari (2008)
Optimal taxation: Diamond and Mirrlees (1971), Atkinson and Stiglitz (1976),
Akerlof (1978), Saez and Stantcheva (2016)
Auctions with budget-constrained bidders: Che and Gale (1998), Fernandez and
Gali (1999); Che, Gale, and Kim (2012); Pai and Vohra (2014); Kotowski (2017)
Costly-screening/ money-burning literature: McAfee and McMillan (1992),
Damiano and Li (2007), Hartline and Roughgarden (2008), Hoppe, Moldovanu,
and Sela (2009), Condorelli (2012), Chakravarty and Kaplan (2013)
Methods (generalized ironing): Muir and Loertscher (2021), Ashlagi, Monachou,
and Nikzad (2021), Kleiner, Moldovanu, and Strack (2021), Z. Kang (2020a).
New threads in mechanism design with redistribution motives: Z. Kang
(2020b), M. Kang and Zheng (2020, 2021), Reuter and Groh (2021)
33. Model
A designer chooses a mechanism to allocate a unit mass of objects to
a unit mass of agents.
Each object has quality q ∈ [0, 1], q is distributed acc. to cdf F.
Each agent is characterized by a type (i, r, λ), where:
i is an observable label, i ∈ I (finite);
r is an unobserved willingness to pay (for quality), r ∈ R+;
λ is an unobserved social welfare weight, λ ∈ R+;
The type distribution is known to the designer.
If (i, r, λ) gets a good with quality q and pays t, her utility is qr − t,
while her contribution to social welfare is λ(qr − t)
34. Model
Comments for the energy context:
Quality normalized to 0 or 1, interpreted as quantity.
Then, q = 1 can be interpreted as the “normal consumption level.”
Instead of distribution of quality F, we just have total quantity S
available: F(q) = 1{q≥S}.
Throughout, assume that S < 1.
To the extent that some households have a higher “normal
consumption level,” we can (intuitively) fold it into the WTP r
r · qnormal = rqnormal
| {z }
r̃
· 1
35. Model
The designer has access to arbitrary (direct) allocation mechanisms
(Γ, T) where Γ(q|i, r, λ) is the probability that (i, r, λ) gets a good with
quality q or less, and T(i, r, λ) is the associated payment, subject to:
Feasibility: E(i,r,λ) [Γ(q|i, r, λ)] ≥ F(q), ∀q ∈ [0, 1];
IC constraint: Each agent (i, r, λ) reports (r, λ) truthfully;
IR constraint: U(i, r, λ) ≡ r
R
qdΓ(q|i, r, λ) − T(i, r, λ) ≥ 0;
Non-negative transfers: T(i, r, λ) ≥ 0, ∀(i, r, λ).
The designer maximizes, for some constant α ≥ 0, a weighted sum of
revenue and agents’ utilities:
E(i,r,λ) [αT(i, r, λ) + λU(i, r, λ)] .
36. Comments about the model
Lemma: It is without loss of optimality for the mechanism designer to
only elicit information about r through the mechanism—allocation and
transfers depend on (i, r) but not on λ directly.
37. Comments about the model
Lemma: It is without loss of optimality for the mechanism designer to
only elicit information about r through the mechanism—allocation and
transfers depend on (i, r) but not on λ directly.
This implies that the designer forms expectations over the unobserved
social welfare weights:
λi(r) ≡ E(i,r,λ) [λ| i, r] ;
we call these functions Pareto weights, and assume they are continuous.
38. Comments about the model
Lemma: It is without loss of optimality for the mechanism designer to
only elicit information about r through the mechanism—allocation and
transfers depend on (i, r) but not on λ directly.
This implies that the designer forms expectations over the unobserved
social welfare weights:
λi(r) ≡ E(i,r,λ) [λ| i, r] ;
we call these functions Pareto weights, and assume they are continuous.
Designer’s objective becomes:
E(i,r) [αTi(r) + λi(r)Ui(r)] .
39. Comments about the model
λi(r) ≡ E(i,r,λ) [λ| i, r]
Economic idea:
The designer assesses the “need” of agents by estimating the unobserved
welfare weights based on the observable (label i) and elicitable (wtp r)
information.
40. Comments about the model
λi(r) ≡ E(i,r,λ) [λ| i, r]
Economic idea:
The designer assesses the “need” of agents by estimating the unobserved
welfare weights based on the observable (label i) and elicitable (wtp r)
information.
Consequence:
The optimal allocation depends on the statistical correlation of labels
and willingness to pay with the unobserved social welfare weights.
41. Comments about the model
Correlation of labels with welfare weights:
If label i captures income brackets, then we may naturally think that
E[λ| i] ≡ λ̄i ≥ λ̄j ≡ E[λ| j]
if i corresponds to a lower income bracket than j;
42. Comments about the model
Correlation of labels with welfare weights:
If label i captures income brackets, then we may naturally think that
E[λ| i] ≡ λ̄i ≥ λ̄j ≡ E[λ| j]
if i corresponds to a lower income bracket than j;
Other possibilities (varies by country): Labels could capture family
size, energy efficiency of housing, heating method, exposure to
interest rate hikes.
43. Comments about the model
Correlation of WTP with welfare weights:
Suppose there is just one label I = {i}, but we elicit information
about willingness to pay of two patients for a treatment:
Agent A: e50,000
Agent B: e1,000
Naturally, we may presume that λi(r) is decreasing in r.
44. Comments about the model
Correlation of WTP with welfare weights:
Many labels, i captures low income, and we elicit information
about willingness to pay of two patients for a treatment:
Agent A: e 50,000
Agent B: e1,000
Naturally, we may presume that λi(r) is (“less”) decreasing in r.
45. Comments about the model
Correlation of WTP with welfare weights:
Suppose there is just one label I = {i}, but we elicit information
about WTP of two consumers for maintaining “normal” energy
consumption:
Agent A: $10,000
Agent B: $5,000
Naturally, we may presume that λi(r) is decreasing in r.
46. Comments about the model
Correlation of WTP with welfare weights:
Many labels, i captures family size and energy efficiency, but we
elicit information about WTP of two consumers for maintaining
“normal” energy consumption:
Agent A: $10,000
Agent B: $5,000
Naturally, we may presume that λi(r) is (“more”) decreasing in r.
47. Comments about the model
The role of revenue:
The weight α on revenue captures the value of a dollar in the
designer’s budget, spent on the most valuable “cause.”
48. Comments about the model
The role of revenue:
The weight α on revenue captures the value of a dollar in the
designer’s budget, spent on the most valuable “cause.”
When α = maxi λ̄i, then it is as if a lump-sum transfer to group i
were allowed; when α = averagei λ̄i, then it is as if lump-sum
transfers to all agents were allowed.
49. Comments about the model
The role of revenue:
The weight α on revenue captures the value of a dollar in the
designer’s budget, spent on the most valuable “cause.”
When α = maxi λ̄i, then it is as if a lump-sum transfer to group i
were allowed; when α = averagei λ̄i, then it is as if lump-sum
transfers to all agents were allowed.
When α > λ̄i for all i, there is an “outside cause”.
50. Comments about the model
The role of revenue:
The weight α on revenue captures the value of a dollar in the
designer’s budget, spent on the most valuable “cause.”
When α = maxi λ̄i, then it is as if a lump-sum transfer to group i
were allowed; when α = averagei λ̄i, then it is as if lump-sum
transfers to all agents were allowed.
When α > λ̄i for all i, there is an “outside cause”.
When α < λ̄i for some i, lump-sum payments to agents in group
i are prohibited or costly (insurance motive as in Gadenne et al.,
2022).
51. Comments about the model
The role of revenue:
The weight α on revenue captures the value of a dollar in the
designer’s budget, spent on the most valuable “cause.”
When α = maxi λ̄i, then it is as if a lump-sum transfer to group i
were allowed; when α = averagei λ̄i, then it is as if lump-sum
transfers to all agents were allowed.
When α > λ̄i for all i, there is an “outside cause”.
When α < λ̄i for some i, lump-sum payments to agents in group
i are prohibited or costly (insurance motive as in Gadenne et al.,
2022).
When α = 0, we are in the money-burning/costly-screening case.
53. Comments about the model
Universally desired goods
Let Gi(r) be the cdf of willingness to pay conditional on label i, and let
gi(r) be its continuous positive density on [ri, r̄i].
54. Comments about the model
Universally desired goods
Let Gi(r) be the cdf of willingness to pay conditional on label i, and let
gi(r) be its continuous positive density on [ri, r̄i].
We call the good universally desired (for group i) if ri > 0.
55. Comments about the model
Universally desired goods
Let Gi(r) be the cdf of willingness to pay conditional on label i, and let
gi(r) be its continuous positive density on [ri, r̄i].
We call the good universally desired (for group i) if ri > 0.
Interpretation: A vast majority of agents have a willingness to pay that is
bounded away from zero.
56. Comments about the model
Universally desired goods
Let Gi(r) be the cdf of willingness to pay conditional on label i, and let
gi(r) be its continuous positive density on [ri, r̄i].
We call the good universally desired (for group i) if ri > 0.
Interpretation: A vast majority of agents have a willingness to pay that is
bounded away from zero.
Examples:
“Essential” goods: housing, energy, food, basic health care;
57. Comments about the model
Universally desired goods
Let Gi(r) be the cdf of willingness to pay conditional on label i, and let
gi(r) be its continuous positive density on [ri, r̄i].
We call the good universally desired (for group i) if ri > 0.
Interpretation: A vast majority of agents have a willingness to pay that is
bounded away from zero.
Examples:
“Essential” goods: housing, energy, food, basic health care;
“Stores of value”: shares, currencies, commodities
59. Derivation of Optimal Mechanism
1 Objects are allocated “across” groups: F is split into I cdfs F⋆
i ;
60. Derivation of Optimal Mechanism
1 Objects are allocated “across” groups: F is split into I cdfs F⋆
i ;
2 Objects are allocated “within” groups: For each label i, the objects
F⋆
i are allocated optimally to agents in group i. Details
61. Derivation of Optimal Mechanism
1 Objects are allocated “across” groups: F is split into I cdfs F⋆
i ;
2 Objects are allocated “within” groups: For each label i, the objects
F⋆
i are allocated optimally to agents in group i. Details
62. Derivation of Optimal Mechanism
1 Objects are allocated “across” groups: F is split into I cdfs F⋆
i ;
2 Objects are allocated “within” groups: For each label i, the objects
F⋆
i are allocated optimally to agents in group i. Details
Observation: Only expected quality, Qi(r), matters for payoffs.
63. Derivation of Optimal Mechanism
1 Objects are allocated “across” groups: F is split into I cdfs F⋆
i ;
2 Objects are allocated “within” groups: For each label i, the objects
F⋆
i are allocated optimally to agents in group i. Details
Observation: Only expected quality, Qi(r), matters for payoffs.
Result: Within a group, agents are partitioned into intervals according to
WTP, with either the “market” or “non-market” allocation in each interval
64. Derivation of Optimal Mechanism
1 Objects are allocated “across” groups: F is split into I cdfs F⋆
i ;
2 Objects are allocated “within” groups: For each label i, the objects
F⋆
i are allocated optimally to agents in group i. Details
Observation: Only expected quality, Qi(r), matters for payoffs.
Result: Within a group, agents are partitioned into intervals according to
WTP, with either the “market” or “non-market” allocation in each interval
Market allocation: assortative matching between WTP and quality
Qi(r) = (F⋆
i )−1
(Gi(r)), ∀r ∈ [a, b];
65. Derivation of Optimal Mechanism
1 Objects are allocated “across” groups: F is split into I cdfs F⋆
i ;
2 Objects are allocated “within” groups: For each label i, the objects
F⋆
i are allocated optimally to agents in group i. Details
Observation: Only expected quality, Qi(r), matters for payoffs.
Result: Within a group, agents are partitioned into intervals according to
WTP, with either the “market” or “non-market” allocation in each interval
Market allocation: assortative matching between WTP and quality
Qi(r) = (F⋆
i )−1
(Gi(r)), ∀r ∈ [a, b];
Non-market allocation: random matching (rationing!) between
WTP and quality
Qi(r) = q̄, ∀r ∈ [a, b].
95. Economic Implications
Proposition 1 (WTP-revealed inequality )
Suppose that α ≥ λ̄i (lump-sum payments are available).
Then, it is optimal to ration agents with willingness to pay in some
(non-degenerate) interval if and only if the function αJi(r) + Λi(r)hi(r) is
not non-decreasing, where
hi(r) =
1 − Gi(r)
gi(r)
, Ji(r) = r − hi(r), Λi(r) = Ei
[λi(r̃) | r̃ ≥ r].
96. Economic Implications
Proposition 1 (WTP-revealed inequality )
Suppose that α ≥ λ̄i (lump-sum payments are available).
Then, it is optimal to ration agents with willingness to pay in some
(non-degenerate) interval if and only if the function αJi(r) + Λi(r)hi(r) is
not non-decreasing, where
hi(r) =
1 − Gi(r)
gi(r)
, Ji(r) = r − hi(r), Λi(r) = Ei
[λi(r̃) | r̃ ≥ r].
Assuming differentiability, the condition becomes
Λ′
i(r)hi(r) + α + (Λi(r) − α)h′
i(r) < 0.
97. Economic Implications
Proposition 1 (WTP-revealed inequality )
Suppose that α ≥ λ̄i (lump-sum payments are available).
Then, it is optimal to ration agents with willingness to pay in some
(non-degenerate) interval if and only if the function αJi(r) + Λi(r)hi(r) is
not non-decreasing, where
hi(r) =
1 − Gi(r)
gi(r)
, Ji(r) = r − hi(r), Λi(r) = Ei
[λi(r̃) | r̃ ≥ r].
Assuming differentiability, the condition becomes
Λ′
i(r)hi(r) + α + (Λi(r) − α)h′
i(r) < 0.
Some non-market allocation is optimal if willingness to pay is strongly
(negatively) correlated with the unobserved social welfare weights.
98. Economic Implications
Proposition 2 (Optimality of uniform rationing)
A necessary condition for uniform rationing (at a fixed low price) to be
optimal within group i is that
αr̄i ≤
Z r̄i
ri
rλi(r)dGi(r).
This condition becomes sufficient if αJi(r) + Λi(r)hi(r) is quasi-convex.
99. Economic Implications
Proposition 2 (Optimality of uniform rationing)
A necessary condition for uniform rationing (at a fixed low price) to be
optimal within group i is that
αr̄i ≤
Z r̄i
ri
rλi(r)dGi(r).
This condition becomes sufficient if αJi(r) + Λi(r)hi(r) is quasi-convex.
Key take-away: It is never optimal to use uniform rationing if a
lump-sum payment to group i is feasible.
100. Economic Implications
Proposition 2 (Optimality of uniform rationing)
A necessary condition for uniform rationing (at a fixed low price) to be
optimal within group i is that
αr̄i ≤
Z r̄i
ri
rλi(r)dGi(r).
This condition becomes sufficient if αJi(r) + Λi(r)hi(r) is quasi-convex.
Key take-away: It is never optimal to use uniform rationing if a
lump-sum payment to group i is feasible.
By an extension of the same argument: It is never optimal to have a
uniform price cap.
101. Economic Implications
Key idea behind optimality of rationing:
Offering a reduced-price option with rationing allows to screen for
vulnerable households.
102. Economic Implications
Key idea behind optimality of rationing:
Offering a reduced-price option with rationing allows to screen for
vulnerable households.
Each household chooses between a high per-unit price with no limit
on consumption or a lower per-unit price but up to a consumption
threshold q̄ < 1.
103. Economic Implications
Key idea behind optimality of rationing:
Offering a reduced-price option with rationing allows to screen for
vulnerable households.
Each household chooses between a high per-unit price with no limit
on consumption or a lower per-unit price but up to a consumption
threshold q̄ < 1.
Selection will be based on WTP.
104. Economic Implications
Key idea behind optimality of rationing:
Offering a reduced-price option with rationing allows to screen for
vulnerable households.
Each household chooses between a high per-unit price with no limit
on consumption or a lower per-unit price but up to a consumption
threshold q̄ < 1.
Selection will be based on WTP.
Key question: Do we get the “right” selection?
105. Economic Implications
Key idea behind optimality of rationing:
Offering a reduced-price option with rationing allows to screen for
vulnerable households.
Each household chooses between a high per-unit price with no limit
on consumption or a lower per-unit price but up to a consumption
threshold q̄ < 1.
Selection will be based on WTP.
Key question: Do we get the “right” selection?
If yes, subsidize (by reducing the per-unit price) the group that
self-identified as being in need.
106. Economic Implications
Key idea behind optimality of rationing:
Offering a reduced-price option with rationing allows to screen for
vulnerable households.
Each household chooses between a high per-unit price with no limit
on consumption or a lower per-unit price but up to a consumption
threshold q̄ < 1.
Selection will be based on WTP.
Key question: Do we get the “right” selection?
If yes, subsidize (by reducing the per-unit price) the group that
self-identified as being in need.
If no, then the rationing policy is pure allocative inefficiency.
107. Economic Implications
Key idea behind optimality of rationing:
The answer to the question largely depends on available labels!
108. Economic Implications
Key idea behind optimality of rationing:
The answer to the question largely depends on available labels!
Mathematically, we need strong negative correlation between WTP
and welfare weights (Λ′
i(r) < 0)
109. Economic Implications
Key idea behind optimality of rationing:
The answer to the question largely depends on available labels!
Mathematically, we need strong negative correlation between WTP
and welfare weights (Λ′
i(r) < 0)
This might hold when we control for confounding factors that wold
raise the WTP of poor households:
110. Economic Implications
Key idea behind optimality of rationing:
The answer to the question largely depends on available labels!
Mathematically, we need strong negative correlation between WTP
and welfare weights (Λ′
i(r) < 0)
This might hold when we control for confounding factors that wold
raise the WTP of poor households:
▶ Large family size;
111. Economic Implications
Key idea behind optimality of rationing:
The answer to the question largely depends on available labels!
Mathematically, we need strong negative correlation between WTP
and welfare weights (Λ′
i(r) < 0)
This might hold when we control for confounding factors that wold
raise the WTP of poor households:
▶ Large family size;
▶ Energy inefficiency of housing;
112. Economic Implications
Key idea behind optimality of rationing:
The answer to the question largely depends on available labels!
Mathematically, we need strong negative correlation between WTP
and welfare weights (Λ′
i(r) < 0)
This might hold when we control for confounding factors that wold
raise the WTP of poor households:
▶ Large family size;
▶ Energy inefficiency of housing;
▶ Electricity-based heating.
113. Economic Implications
Key idea behind optimality of rationing:
Advantage of consumption-capped price subsidy over lump-sum
payments: Additional screening!
114. Economic Implications
Key idea behind optimality of rationing:
Advantage of consumption-capped price subsidy over lump-sum
payments: Additional screening!
Market choices may reveal which households are really in need.
115. Economic Implications
Key idea behind optimality of rationing:
Advantage of consumption-capped price subsidy over lump-sum
payments: Additional screening!
Market choices may reveal which households are really in need.
Then, clear why uniform price and quantity caps can’t work!
116. Economic Implications
Key idea behind optimality of rationing:
Advantage of consumption-capped price subsidy over lump-sum
payments: Additional screening!
Market choices may reveal which households are really in need.
Then, clear why uniform price and quantity caps can’t work!
They distort economic efficiency without offering the screening
benefit.
117. Economic Implications
Key idea behind optimality of rationing:
Advantage of consumption-capped price subsidy over lump-sum
payments: Additional screening!
Market choices may reveal which households are really in need.
Then, clear why uniform price and quantity caps can’t work!
They distort economic efficiency without offering the screening
benefit.
Thus, they are dominated by lump-sum payments (here, we agree
with the Economist and the IMF paper)
118. Economic Implications
Key idea behind optimality of rationing:
Advantage of consumption-capped price subsidy over lump-sum
payments: Additional screening!
Market choices may reveal which households are really in need.
Then, clear why uniform price and quantity caps can’t work!
They distort economic efficiency without offering the screening
benefit.
Thus, they are dominated by lump-sum payments (here, we agree
with the Economist and the IMF paper)
What if lump-sum payments are costly? (administration costs,
insurance motive, behavioral aspects, etc.)
119. Economic Implications
Proposition 3 (Label-revealed inequality )
Suppose that
the average Pareto weight λ̄i for group i is strictly larger than the
weight on revenue α;
the good is universally desired (ri > 0).
Then, there exists r⋆
i > ri such that the optimal allocation is to ration (at
a price of 0) all types r ≤ r⋆
i .
120. Economic Implications
Proposition 3 (Label-revealed inequality )
Suppose that
the average Pareto weight λ̄i for group i is strictly larger than the
weight on revenue α;
the good is universally desired (ri > 0).
Then, there exists r⋆
i > ri such that the optimal allocation is to ration (at
a price of 0) all types r ≤ r⋆
i .
Interpretation: If the designer would like to redistribute to group i but
cannot give agents in that group a direct cash transfer, then it is optimal
to provide small quantities of universally desired goods for free.
121. Economic Implications
Proposition 3 (Label-revealed inequality )
Suppose that
the average Pareto weight λ̄i for group i is strictly larger than the
weight on revenue α;
the good is universally desired (ri > 0).
Then, there exists r⋆
i > ri such that the optimal allocation is to ration (at
a price of 0) all types r ≤ r⋆
i .
Interpretation: If the designer would like to redistribute to group i but
cannot give agents in that group a direct cash transfer, then it is optimal
to provide small quantities of universally desired goods for free.
Note: There might still be a price gradient for higher quantities (the exact
condition is the one we have seen before)
122. Economic Implications
Proposition 1 (Label-revealed inequality )
Suppose that
the average Pareto weight λ̄i for group i is strictly larger than the
weight on revenue α;
the good is universally desired (ri > 0).
Then, there exists r⋆
i > ri such that the optimal allocation is to ration (at
a price of 0) all types r ≤ r⋆
i .
“Wrong” intuition: A random allocation for free increases the welfare of
agents with lowest willingness to pay
123. Economic Implications
Proposition 1 (Label-revealed inequality )
Suppose that
the average Pareto weight λ̄i for group i is strictly larger than the
weight on revenue α;
the good is universally desired (ri > 0).
Then, there exists r⋆
i > ri such that the optimal allocation is to ration (at
a price of 0) all types r ≤ r⋆
i .
“Wrong” intuition: A random allocation for free increases the welfare of
agents with lowest willingness to pay
Correct Intuition: A random allocation for free enables the designer to
lower prices for all agents Picture
125. Conclusions
When to use in-kind redistribution? (provision of goods at a
below-market-clearing prices)
126. Conclusions
When to use in-kind redistribution? (provision of goods at a
below-market-clearing prices)
Roughly: When observable variables uncover inequality in the unobserved
welfare weights.
127. Conclusions
When to use in-kind redistribution? (provision of goods at a
below-market-clearing prices)
Roughly: When observable variables uncover inequality in the unobserved
welfare weights.
1 Label-revealed inequality:
128. Conclusions
When to use in-kind redistribution? (provision of goods at a
below-market-clearing prices)
Roughly: When observable variables uncover inequality in the unobserved
welfare weights.
1 Label-revealed inequality: When lump-sum payments are costly and
some groups can be identified as vulnerable, it is optimal to use some
in-kind redistribution for universally desired goods.
129. Conclusions
When to use in-kind redistribution? (provision of goods at a
below-market-clearing prices)
Roughly: When observable variables uncover inequality in the unobserved
welfare weights.
1 Label-revealed inequality: When lump-sum payments are costly and
some groups can be identified as vulnerable, it is optimal to use some
in-kind redistribution for universally desired goods.
▶ Energy context: Controlling electricity bills for poorest households may
be easier/ cheaper than direct cash transfers.
130. Conclusions
When to use in-kind redistribution? (provision of goods at a
below-market-clearing prices)
Roughly: When observable variables uncover inequality in the unobserved
welfare weights.
1 Label-revealed inequality: When lump-sum payments are costly and
some groups can be identified as vulnerable, it is optimal to use some
in-kind redistribution for universally desired goods.
▶ Energy context: Controlling electricity bills for poorest households may
be easier/ cheaper than direct cash transfers.
2 WTP-revealed inequality: When welfare weights are strongly and
negatively correlated with willingness to pay conditional on labels.
131. Conclusions
When to use in-kind redistribution? (provision of goods at a
below-market-clearing prices)
Roughly: When observable variables uncover inequality in the unobserved
welfare weights.
1 Label-revealed inequality: When lump-sum payments are costly and
some groups can be identified as vulnerable, it is optimal to use some
in-kind redistribution for universally desired goods.
▶ Energy context: Controlling electricity bills for poorest households may
be easier/ cheaper than direct cash transfers.
2 WTP-revealed inequality: When welfare weights are strongly and
negatively correlated with willingness to pay conditional on labels.
▶ Energy context: A well-designed subsidy system can screen for most
vulnerable households, better than a cash transfer scheme could.
133. Conclusions
We proposed a model of Inequality-aware Market Design.
Our analysis uncovers the importance of three factors:
134. Conclusions
We proposed a model of Inequality-aware Market Design.
Our analysis uncovers the importance of three factors:
1 Correlation between the unobserved welfare weights and the
information that the designer can elicit or observe directly;
135. Conclusions
We proposed a model of Inequality-aware Market Design.
Our analysis uncovers the importance of three factors:
1 Correlation between the unobserved welfare weights and the
information that the designer can elicit or observe directly;
2 Importance of availability of lump-sum transfers;
136. Conclusions
We proposed a model of Inequality-aware Market Design.
Our analysis uncovers the importance of three factors:
1 Correlation between the unobserved welfare weights and the
information that the designer can elicit or observe directly;
2 Importance of availability of lump-sum transfers;
3 Whether the good is universally desired or not.
137. Conclusions
We proposed a model of Inequality-aware Market Design.
Our analysis uncovers the importance of three factors:
1 Correlation between the unobserved welfare weights and the
information that the designer can elicit or observe directly;
2 Importance of availability of lump-sum transfers;
3 Whether the good is universally desired or not.
More work is needed on market design with redistributive
concerns:
138. Conclusions
We proposed a model of Inequality-aware Market Design.
Our analysis uncovers the importance of three factors:
1 Correlation between the unobserved welfare weights and the
information that the designer can elicit or observe directly;
2 Importance of availability of lump-sum transfers;
3 Whether the good is universally desired or not.
More work is needed on market design with redistributive
concerns:
1 There are hundreds (thousands?) of theory papers focusing on how to
maximize revenue or efficiency when allocating resources...
139. Conclusions
We proposed a model of Inequality-aware Market Design.
Our analysis uncovers the importance of three factors:
1 Correlation between the unobserved welfare weights and the
information that the designer can elicit or observe directly;
2 Importance of availability of lump-sum transfers;
3 Whether the good is universally desired or not.
More work is needed on market design with redistributive
concerns:
1 There are hundreds (thousands?) of theory papers focusing on how to
maximize revenue or efficiency when allocating resources...
2 ... but only a handful on how to achieve optimal redistribution.
140. Conclusions
We proposed a model of Inequality-aware Market Design.
Our analysis uncovers the importance of three factors:
1 Correlation between the unobserved welfare weights and the
information that the designer can elicit or observe directly;
2 Importance of availability of lump-sum transfers;
3 Whether the good is universally desired or not.
More work is needed on market design with redistributive
concerns:
1 There are hundreds (thousands?) of theory papers focusing on how to
maximize revenue or efficiency when allocating resources...
2 ... but only a handful on how to achieve optimal redistribution.
3 Much more work remains to be done... (many stylized assumptions in
our model!)
148. Derivation of the optimal “within-group” mechanism
The “within-group” problem:
Fixing a group of agents i, and a distribution of quality Fi available for
group i, what is the optimal way to allocate quality subject to IC and IR
constraints?
149. Derivation of the optimal “within-group” mechanism
The designer’s problem: (Qi(r) denotes expected quality)
max
Qi(r), Ui(ri)
Z r̄i
ri
Vi(r)Qi(r)dGi(r) + (λ̄i − α)Ui(ri)
150. Derivation of the optimal “within-group” mechanism
The designer’s problem: (Qi(r) denotes expected quality)
max
Qi(r)
Z r̄i
ri
Vi(r)Qi(r)dGi(r) + max{0, λ̄i − α}riQi(ri).
151. Derivation of the optimal “within-group” mechanism
The designer’s problem: (Qi(r) denotes expected quality)
max
Qi(r)
Z r̄i
ri
Vi(r)Qi(r)dGi(r) + max{0, λ̄i − α}riQi(ri).
In the above, Vi(r) = αJi(r) + Λi(r)hi(r), where
hi(r) =
1 − Gi(r)
gi(r)
, Ji(r) = r − hi(r), Λi(r) = Ei
[λi(r̃) | r̃ ≥ r].
152. Derivation of the optimal “within-group” mechanism
The designer’s problem: (Qi(r) denotes expected quality)
max
Qi(r)
Z r̄i
ri
Vi(r)Qi(r)dGi(r) + max{0, λ̄i − α}riQi(ri).
In the above, Vi(r) = αJi(r) + Λi(r)hi(r), where
hi(r) =
1 − Gi(r)
gi(r)
, Ji(r) = r − hi(r), Λi(r) = Ei
[λi(r̃) | r̃ ≥ r].
Feasible distribution of expected quality: CDF Φi such that
Fi ≻MPS Φi.
153. Derivation of the optimal “within-group” mechanism
The designer’s problem: (Qi(r) denotes expected quality)
max
Qi(r)
Z r̄i
ri
Vi(r)Qi(r)dGi(r) + max{0, λ̄i − α}riQi(ri).
In the above, Vi(r) = αJi(r) + Λi(r)hi(r), where
hi(r) =
1 − Gi(r)
gi(r)
, Ji(r) = r − hi(r), Λi(r) = Ei
[λi(r̃) | r̃ ≥ r].
Feasible distribution of expected quality: CDF Φi such that
Fi ≻MPS Φi.
Incentive-compatibility =⇒ Gi(r) = Φi(q)
154. Derivation of the optimal “within-group” mechanism
The designer’s problem: (Qi(r) denotes expected quality)
max
Qi(r)
Z r̄i
ri
Vi(r)Qi(r)dGi(r) + max{0, λ̄i − α}riQi(ri).
In the above, Vi(r) = αJi(r) + Λi(r)hi(r), where
hi(r) =
1 − Gi(r)
gi(r)
, Ji(r) = r − hi(r), Λi(r) = Ei
[λi(r̃) | r̃ ≥ r].
Feasible distribution of expected quality: CDF Φi such that
Fi ≻MPS Φi.
Incentive-compatibility =⇒ Qi(r) = Φ−1
i (Gi(r))
155. Derivation of the optimal “within-group” mechanism
The designer’s problem: (Qi(r) denotes expected quality)
max
Qi(r)
Z r̄i
ri
Vi(r)Qi(r)dGi(r) + max{0, λ̄i − α}riQi(ri).
In the above, Vi(r) = αJi(r) + Λi(r)hi(r), where
hi(r) =
1 − Gi(r)
gi(r)
, Ji(r) = r − hi(r), Λi(r) = Ei
[λi(r̃) | r̃ ≥ r].
Feasible distribution of expected quality: CDF Φi such that
Φ−1
i ≻MPS F−1
i .
Incentive-compatibility =⇒ Qi(r) = Φ−1
i (Gi(r))
156. Derivation of the optimal “within-group” mechanism
The designer’s problem is
max
Ψi
Z r̄i
ri
Vi(r)Ψi(Gi(r))dGi(r) + max{0, λ̄i − α}riΨi(0)
s.t. Ψi ≻MPS
F−1
i
Back
157. Derivation of the optimal “within-group” mechanism
The designer’s problem is
max
Ψi
Z 1
0
Vi(t)
z }| {
Z 1
t
Vi(G−1
i (x))dx + max{0, λ̄i − α}ri1{t=0}
dΨi(t)
s.t. Ψi ≻MPS
F−1
i
Back
158. Derivation of the optimal “within-group” mechanism
The designer’s problem is
max
Ψi
Z 1
0
Vi(t)
z }| {
Z 1
t
Vi(G−1
i (x))dx + max{0, λ̄i − α}ri1{t=0}
dΨi(t)
s.t. Ψi ≻MPS
F−1
i
Agents are partitioned into intervals according to WTP:
Back
159. Derivation of the optimal “within-group” mechanism
The designer’s problem is
max
Ψi
Z 1
0
Vi(t)
z }| {
Z 1
t
Vi(G−1
i (x))dx + max{0, λ̄i − α}ri1{t=0}
dΨi(t)
s.t. Ψi ≻MPS
F−1
i
Agents are partitioned into intervals according to WTP:
▶ Market allocation: assortative matching between WTP and quality
Qi(r) = F−1
i (Gi(r)), ∀r ∈ [a, b];
Back
160. Derivation of the optimal “within-group” mechanism
The designer’s problem is
max
Ψi
Z 1
0
Vi(t)
z }| {
Z 1
t
Vi(G−1
i (x))dx + max{0, λ̄i − α}ri1{t=0}
dΨi(t)
s.t. Ψi ≻MPS
F−1
i
Agents are partitioned into intervals according to WTP:
▶ Market allocation: assortative matching between WTP and quality
Qi(r) = F−1
i (Gi(r)), ∀r ∈ [a, b];
▶ Non-market allocation: random matching between WTP and quality
Qi(r) = q̄, ∀r ∈ [a, b].
Back
161. Derivation of the optimal “within-group” mechanism
The designer’s problem is
max
Ψi, F̃i
Z 1
0
Vi(t)
z }| {
Z 1
t
Vi(G−1
i (x))dx + max{0, λ̄i − α}ri1{t=0}
dΨi(t)
s.t. Ψi ≻MPS
F̃−1
i ≻FOSD
F−1
i
Agents are partitioned into intervals according to WTP:
▶ Market allocation: assortative matching between WTP and quality
Qi(r) = F−1
i (Gi(r)), ∀r ∈ [a, b];
▶ Non-market allocation: random matching between WTP and quality
Qi(r) = q̄, ∀r ∈ [a, b].
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