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Producter

producter

Before , I worked on over 10 products. I designed many of them from scratch. Producter Reviewing a new product every day has created my design perspective. Analyzing a product’s design system and values helps me to understand its strategy and purpose. I wanted to build a product-led startup, and create the best design system ever because I know how important this issue is for PLG companies. (It is obviously not just about building a design system. Let’s get to the bottom of it together.) , the founder of , emphasizes its importance on podcast ( ): Ed Sim Boldstart Ventures Build with Blake Barlett OpenView “I want to know where the designer/UX/UI person comes in. It’s really important in a PLG company for the product to be beautiful and the experience to be frictionless. I want to hear that language from a founder, and see support for that in the hiring. If there’s no designer on board by employee number ten, that’s a big red flag for me.” Three main pillars to achieve PLG using design: Embrace an attitude that puts the user first empathetic Cultivate a in your team design mindset Use and as a path to innovation with design change disruption Empathy with User-Centricity Every business that adopts a product-led growth model needs to deeply understand its users and customer journey. Knowing your users allows you to see what they see, feel what they feel, and experience things as they do, which builds empathy towards them and leads to better products. We interviewed people from diverse backgrounds from multiple companies at the beginning of the road. And, we threw away many designs to create a design system that would relieve their pain. Here is one of them :D But the important thing was that we put the user in the heart of our product from day one. And that is the essence of Producter’s mission. Customers/Users provide designers with insights such as context, using situations, actions, areas, topics, and motivations. By making all these pieces meaningful, designers try to complete the puzzle. To sum up, when creating a shared organizational vision, it is critical to place users’ needs at the forefront. Everyone Should Be a Designer It is critical to ask “ ” before even beginning to create a design system in a product-led company. (What level of experience do the founders have with product design?) Don’t worry; my partner and I are design-obsessed people. 😄 who will design But it’s not enough! All team members should have a design perspective even if they do not design as they should empathize with your users. After building our design system, we designed all modules together with Merve based on user feedback and needs. In this way, team members had the opportunity to analyze designs and evaluate flows that hadn’t yet been coded. Our first engineering intern who joined our team was the best example of this. Our team explained the importance of design in a product-driven company and how it is the key to success. As a result, he now gives opinions about which design might be the most user-friendly. And as we get closer to our users, the quality of their recommendations improves. Change & Disruption Today, product-led growth is key because of the needs and expectations of users, which has been demonstrated by a indicating that three out of four B2B buyers would prefer to educate themselves as opposed to learning about products from salespeople. statistic Before, you may not have imagined that design could replace a salesperson. A user-centered design system is the best onboarding method. And don’t just think of it for a first-time visitor to your product. In addition, if you add a new feature to your product, consider notifying your current users. You will present your user with a design for each of these possible scenarios. Do not believe that it is the best. That is just the version you are releasing today. You should not be afraid to break and modify your version to take it to the next level. Of course, many disruptions will occur while you are in this process. Don’t give up; keep reviewing data, collecting user feedback, and improving designs to reach the best version. Clayton Christensen sums up what the trap is for some companies: “The reason why it is so difficult for existing firms to capitalize on disruptive innovations is that their processes and their business model that make them good at the existing business actually make them bad at competing for the disruption.” We believe that design is crucial to creating a product-led growth strategy. Throughout the organization and with customers, your product team creates an extensive web of interactions and conversations about your product, where it can grow, and how it should grow. You can turn your business into a product-led growth company by investing in design. Also published on: https://blog.producter.co/why-is-design-so-critical-for-product-led-companies-ceb7d31a85db

3 Main Pillars to Achieve Product-Led Growth Through Design

Subscription software monetization is clearly popular today. I use a number of subscriptions and I’m sure you do, too. So each of us can recognize how reliance on subscription is growing. Approximately 9 out of 10 (89%) of software suppliers use subscription monetization models at least moderately, as detailed in Revenera’s Software Monetization Models and Strategies report, up from 82% just a year ago. And 61% anticipate that subscription is set to grow as a percentage of overall software license revenue in the coming 12–18 months. But hot on the heels of subscription are usage-based monetization models. This approach is being embraced widely, with 59% saying that usage-based are set to grow as a percentage of their overall software license revenue between now and 2026. Neither subscription nor usage-based models exist in a vacuum. Today’s approach to software is largely hybrid, blending approaches to both monetization and deployment models. Subscription and usage-based monetization can—and should—coexist to help software producers and IoT device manufacturers take a comprehensive approach to software monetization that helps drive annual recurring revenue (ARR) and optimize sales strategies. While it isn’t quite time for usage-based monetization models to overtake subscription in terms of revenue, it’s definitely time to realize the complementary nature of these models. Why Subscription and Usage-Based Models Are Good Together A user might need both subscription and usage-based access to products in your portfolio. They’re looking for the right tool at the right time at the right price. They’re facing ‘subscription fatigue’, craving a customized user experience, with access that’s easy and affordable. Software that’s monetized via subscription provides a recurring revenue model, with a customer paying for access on a monthly or annual basis. Some of its many upsides contribute to its popularity. The software supplier has financial stability and predictable revenues. The buyers benefit by gaining access with expenses that are OpEx, rather than CapEx; subscriptions are often somewhat flexible, meaning that the customer isn’t locked in to perpetual licenses. But the flexibility of subscription also has limits. Say I want to try a new feature in a product for which I only have a basic subscription. I may not be able to access that new or premium feature. Or if I want to use a different application in a suite of products, I might be locked out—and therefore look at a competitor’s product. A usage-based model, offered in tandem with subscription, helps alleviate the hurdles that can lead to customer churn. Usage-based monetization models are defined by usage metrics, such as consumption, pay-per-use, credit-based tokens, elastic access, or metered access. Software buyers appreciate usage-based models because they deliver on-demand access to a product, streamline procurement (which can help avoid project delays), allow allocation of costs to specific business units, and deliver an improved user experience. Usage-based models permit the user to gain access to a product just when they need it—maybe to test out a new feature, use it for a seasonal project, or to work outside of their primary job tasks on an occasional basis, for example. Today, among the software producers who are planning to change monetization models in the coming two years, 37% will be doing so to offer usage-based models to align with customer value. They recognize that by offering usage-based models, they sell software in the ways customers want to buy it, remove barriers for small- and mid-size enterprises, are able to make rapid changes, lower risk of software misuse, and are able to identify upsell and cross-sell opportunities. Integrating Monetization Models Requires Usage Data All of this is well and good, unless the software supplier gets hung up on how to actually implement usage-based pricing alongside other monetization models. Despite the high number of companies that plan to implement usage-based models, many of these same producers lack the insights they need to make their goals actionable: 44% say that a top hurdle for aligning price and value is that they “lack insights to monetize the most valuable features.” Improved usage data is essential for getting products to market quickly—and to monetize the features that are most in demand. Implementing usage-based models is only possible with accurate usage data. Though valuable for all monetization models, it’s essential for usage-based pricing. It can help teams from across the organization—marketing, product management, software engineering, sales, customer service, and compliance—with everything from feature prioritization or roadmap development to pricing decisions, billing, software version decisions, piracy tracking and more. How do you get from where you are—offering pure subscription or even a mix of subscription and perpetual licensing—to the point where you have a healthy blend of subscription with consumption opportunities for your end customers? Begin by taking two key steps: Step #1: Identify Potential Begin with a data-gathering period. Get the telemetry data that will provide a sense of the utilization—the appetite—for occasional use of your software. Close to ⅓ (29%) of software producers surveyed collect telemetry data, but don’t use it. Whether you’re collecting data and letting it go to waste or don’t yet have robust software usage analytics initiatives in place, now’s the time to let telemetry data give you insight into potential. By gathering data, you’ll have a sense of what products your customers may want to try. With an approach like elastic access, you can offer customers some product tryouts. Provide free tokens to see what products or features they adopt. Use this period of fact-gathering to work out the average cost and utilization of product or feature utilization for each customer persona. This will provide a valuable sense of what they’d use if they have access to the entire portfolio. It will also help provide answers to considerations such as what products to include in your price list and how many tokens you should charge for a software product. Step #2: Refine Your Offering and Pricing As you get used to looking at this data while it accumulates, you’ll be able to refine the offering and the pricing. As customers get accustomed to easy access to your software, you’ll be able to make the shift from free tokens to paid tokens. Roll out an initial cost rate table, based on the trial data, telemetry, and usage feedback. You’ll then be ready to iterate, using a progressive cycle to refine your offering and the pricing, arriving at a cost that accurately reflects the value that customers derive from your software. The feedback you receive during this time can also help drive new initiatives and promotions. Your Customers Benefit. You Benefit. Whether you consider it as part of the overall customer experience, a key to smart marketing, or an approach that eases your sales team’s work, the bottom line is that integrating usage-based monetization is good business. Gathering the usage data to make it happen will pay off–for you and for your clients, alike. Subscription software monetization is clearly popular today. I use a number of subscriptions and I’m sure you do, too. So each of us can recognize how reliance on subscription is growing. Approximately 9 out of 10 (89%) of software suppliers use subscription monetization models at least moderately, as detailed in Revenera’s Software Monetization Models and Strategies report , up from 82% just a year ago. And 61% anticipate that subscription is set to grow as a percentage of overall software license revenue in the coming 12–18 months. Software Monetization Models and Strategies report But hot on the heels of subscription are usage-based monetization models. This approach is being embraced widely, with 59% saying that usage-based are set to grow as a percentage of their overall software license revenue between now and 2026. Neither subscription nor usage-based models exist in a vacuum. Today’s approach to software is largely hybrid, blending approaches to both monetization and deployment models. Subscription and usage-based monetization can—and should—coexist to help software producers and IoT device manufacturers take a comprehensive approach to software monetization that helps drive annual recurring revenue (ARR) and optimize sales strategies. While it isn’t quite time for usage-based monetization models to overtake subscription in terms of revenue, it’s definitely time to realize the complementary nature of these models. Why Subscription and Usage-Based Models Are Good Together A user might need both subscription and usage-based access to products in your portfolio. They’re looking for the right tool at the right time at the right price. They’re facing ‘subscription fatigue’, craving a customized user experience, with access that’s easy and affordable. Software that’s monetized via subscription provides a recurring revenue model, with a customer paying for access on a monthly or annual basis. Some of its many upsides contribute to its popularity. The software supplier has financial stability and predictable revenues. The buyers benefit by gaining access with expenses that are OpEx, rather than CapEx; subscriptions are often somewhat flexible, meaning that the customer isn’t locked in to perpetual licenses. But the flexibility of subscription also has limits. Say I want to try a new feature in a product for which I only have a basic subscription. I may not be able to access that new or premium feature. Or if I want to use a different application in a suite of products, I might be locked out—and therefore look at a competitor’s product. A usage-based model, offered in tandem with subscription, helps alleviate the hurdles that can lead to customer churn. Usage-based monetization models are defined by usage metrics, such as consumption, pay-per-use, credit-based tokens, elastic access, or metered access. Software buyers appreciate usage-based models because they deliver on-demand access to a product, streamline procurement (which can help avoid project delays), allow allocation of costs to specific business units, and deliver an improved user experience. Usage-based models permit the user to gain access to a product just when they need it—maybe to test out a new feature, use it for a seasonal project, or to work outside of their primary job tasks on an occasional basis, for example. Today, among the software producers who are planning to change monetization models in the coming two years, 37% will be doing so to offer usage-based models to align with customer value. They recognize that by offering usage-based models, they sell software in the ways customers want to buy it, remove barriers for small- and mid-size enterprises, are able to make rapid changes, lower risk of software misuse, and are able to identify upsell and cross-sell opportunities. Integrating Monetization Models Requires Usage Data All of this is well and good, unless the software supplier gets hung up on how to actually implement usage-based pricing alongside other monetization models. Despite the high number of companies that plan to implement usage-based models, many of these same producers lack the insights they need to make their goals actionable: 44% say that a top hurdle for aligning price and value is that they “lack insights to monetize the most valuable features.” Improved usage data is essential for getting products to market quickly—and to monetize the features that are most in demand. Implementing usage-based models is only possible with accurate usage data. Though valuable for all monetization models, it’s essential for usage-based pricing. It can help teams from across the organization—marketing, product management, software engineering, sales, customer service, and compliance—with everything from feature prioritization or roadmap development to pricing decisions, billing, software version decisions, piracy tracking and more. How do you get from where you are—offering pure subscription or even a mix of subscription and perpetual licensing—to the point where you have a healthy blend of subscription with consumption opportunities for your end customers? Begin by taking two key steps: Step #1: Identify Potential Begin with a data-gathering period. Get the telemetry data that will provide a sense of the utilization—the appetite—for occasional use of your software. Close to ⅓ (29%) of software producers surveyed collect telemetry data, but don’t use it. Whether you’re collecting data and letting it go to waste or don’t yet have robust software usage analytics initiatives in place, now’s the time to let telemetry data give you insight into potential. By gathering data, you’ll have a sense of what products your customers may want to try. With an approach like elastic access , you can offer customers some product tryouts. Provide free tokens to see what products or features they adopt. Use this period of fact-gathering to work out the average cost and utilization of product or feature utilization for each customer persona. This will provide a valuable sense of what they’d use if they have access to the entire portfolio. It will also help provide answers to considerations such as what products to include in your price list and how many tokens you should charge for a software product. elastic access Step #2: Refine Your Offering and Pricing As you get used to looking at this data while it accumulates, you’ll be able to refine the offering and the pricing. As customers get accustomed to easy access to your software, you’ll be able to make the shift from free tokens to paid tokens. Roll out an initial cost rate table, based on the trial data, telemetry, and usage feedback. You’ll then be ready to iterate, using a progressive cycle to refine your offering and the pricing, arriving at a cost that accurately reflects the value that customers derive from your software. The feedback you receive during this time can also help drive new initiatives and promotions. Your Customers Benefit. You Benefit. Whether you consider it as part of the overall customer experience, a key to smart marketing, or an approach that eases your sales team’s work, the bottom line is that integrating usage-based monetization is good business. Gathering the usage data to make it happen will pay off–for you and for your clients, alike.

This Monetization Approach Is Becoming More Prominent in Software Sales

Hierdie monetiseringsbenadering word meer prominent in sagtewareverkope

أصبح هذا النهج الربحي أكثر بروزًا في مبيعات البرمجيات

Bu pul qazanma yanaşması proqram təminatının satışında daha çox önə çıxır

Este enfoque de monetización está adquiriendo cada vez mayor importancia en las ventas de software

Ez a bevételszerzési megközelítés egyre hangsúlyosabbá válik a szoftverértékesítésben

この収益化アプローチはソフトウェア販売においてますます顕著になってきている

វិធីសាស្រ្តរកប្រាក់នេះកាន់តែមានភាពលេចធ្លោក្នុងការលក់កម្មវិធី

이러한 수익화 접근 방식은 소프트웨어 판매에서 더욱 두드러지고 있습니다.

Approche oyo ya Monetisation Ezali Kokoma Plus Prominent na Vente ya Logiciel

Овој пристап за монетизација станува поистакнат во продажбата на софтвер

د پیسو مینځلو دا طریقه د سافټویر پلور کې خورا مشهور کیږي

Этот подход к монетизации становится все более заметным в продажах программного обеспечения

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Author:
(1) David Staines. Table of Links Abstract 1 Introduction 2 Mathematical Arguments 3 Outline and Preview 4 Calvo Framework and 4.1 Household’s Problem 4.2 Preferences 4.3 Household Equilibrium Conditions 4.4 Price-Setting Problem 4.5 Nominal Equilibrium Conditions 4.6 Real Equilibrium Conditions and 4.7 Shocks 4.8 Recursive Equilibrium 5 Existing Solutions 5.1 Singular Phillips Curve 5.2 Persistence and Policy Puzzles 5.3 Two Comparison Models 5.4 Lucas Critique 6 Stochastic Equilibrium and 6.1 Ergodic Theory and Random Dynamical Systems 6.2 Equilibrium Construction 6.3 Literature Comparison 6.4 Equilibrium Analysis 7 General Linearized Phillips Curve 7.1 Slope Coefficients 7.2 Error Coefficients 8 Existence Results and 8.1 Main Results 8.2 Key Proofs 8.3 Discussion 9 Bifurcation Analysis 9.1 Analytic Aspects 9.2 Algebraic Aspects (I) Singularities and Covers 9.3 Algebraic Aspects (II) Homology 9.4 Algebraic Aspects (III) Schemes 9.5 Wider Economic Interpretations 10 Econometric and Theoretical Implications and 10.1 Identification and Trade-offs 10.2 Econometric Duality 10.3 Coefficient Properties 10.4 Microeconomic Interpretation 11 Policy Rule 12 Conclusions and References Appendices A Proof of Theorem 2 and A.1 Proof of Part (i) A.2 Behaviour of ∆ A.3 Proof Part (iii) B Proofs from Section 4 and B.1 Individual Product Demand (4.2) B.2 Flexible Price Equilibrium and ZINSS (4.4) B.3 Price Dispersion (4.5) B.4 Cost Minimization (4.6) and (10.4) B.5 Consolidation (4.8) C Proofs from Section 5, and C.1 Puzzles, Policy and Persistence C.2 Extending No Persistence D Stochastic Equilibrium and D.1 Non-Stochastic Equilibrium D.2 Profits and Long-Run Growth E Slopes and Eigenvalues and E.1 Slope Coefficients E.2 Linearized DSGE Solution E.3 Eigenvalue Conditions E.4 Rouche’s Theorem Conditions F Abstract Algebra and F.1 Homology Groups F.2 Basic Categories F.3 De Rham Cohomology F.4 Marginal Costs and Inflation G Further Keynesian Models and G.1 Taylor Pricing G.2 Calvo Wage Phillips Curve G.3 Unconventional Policy Settings H Empirical Robustness and H.1 Parameter Selection H.2 Phillips Curve I Additional Evidence and I.1 Other Structural Parameters I.2 Lucas Critique I.3 Trend Inflation Volatility 10.4 Microeconomic Interpretation The stability property of the model can be repurposed to give a new window on the traditional microeconomic theory of general equilibrium. One of the central claims of this paper is that when there is no trend inflation and small noise, the economy does not need systematic central bank intervention to maintain economic stability. This may be surprising to modern Keynesian macroeconomists but not to those specialising in general equilibrium theory, where there has been a great deal of work on equilibrium stability. The model has to be re-imagined with idiosyncratic rather than aggregate risk (common noise). The aggregate economy will be in non-stochastic equilibrium thanks to any suitable law of large numbers. Therefore interest rates will be independent of individual shocks, which is isomorphic to having an inactive policy setting (ay = aπ = 0). In the small noise √ ε limit, the aggregate dynamics will be repeated at the idiosyncratic level so long as there is firm-specific labor.[99] The result assumes market incompleteness; with complete markets firms would fully insure against idiosyncratic risk. The focus on small noise may seem unusual given that idiosyncratic shocks are typically large relative to aggregate shocks. Nevertheless, it seems plausible in the case of nominal rigidity where there a substantial body of evidence favouring flexible adjustment in response to large shocks, consistent with the predictions of state-dependent pricing models (see for example Boivin et al. [2009]). Finally, an intriguing alternative explanation is that producers facing large shocks insure on a near competitive market, selecting allocations that are √ ε away from full insurance.[100] Thus, I have demonstrated that a natural benchmark free market equilibrium is stable under staggered optimization, in response to small noise. I feel this is a great improvement upon previous attempts to incorporate dynamics into general equilibrium microeconomics. These focused on tatonnement processes, based on unrealistically flexible out of equilibrium adjustment.[101] Staggered optimization should feature more prominently in microeconomic theory in future. This paper is available on arxiv under CC 4.0 license. [99] For simplicity throughout the main text, I have assumed there is perfect competition in the labor market. This is probably unrealistic but alternative flexible wage arrangements, like bargaining solutions or additional mark-downs, could be accommodated into θ and would therefore not appear. [100] It would be natural to think of √ ε as the approximate size of the excess. It is possible to have |ε| equilibria with ∆ adjusted to reflect demand heterogeniety. I will leave this to others. However, it would not impact first order dynamics, under the assumption here of firm-specific labor (recalling Footnote 9). [101] The idea originated with Walras [2014]. The framework struggles to generate clear or intuitive empirical predictions (see Sonnenschein [1972], Sonnenschein [1973], Mantel [1974] and Debreu [1974]). For further perspective consult Weintraub [1993]. Author: (1) David Staines. Author: Author: (1) David Staines. Table of Links Abstract Abstract 1 Introduction 1 Introduction 2 Mathematical Arguments 2 Mathematical Arguments 3 Outline and Preview 3 Outline and Preview 4 Calvo Framework and 4.1 Household’s Problem 4 Calvo Framework and 4.1 Household’s Problem 4.2 Preferences 4.2 Preferences 4.3 Household Equilibrium Conditions 4.3 Household Equilibrium Conditions 4.4 Price-Setting Problem 4.4 Price-Setting Problem 4.5 Nominal Equilibrium Conditions 4.5 Nominal Equilibrium Conditions 4.6 Real Equilibrium Conditions and 4.7 Shocks 4.6 Real Equilibrium Conditions and 4.7 Shocks 4.8 Recursive Equilibrium 4.8 Recursive Equilibrium 5 Existing Solutions 5 Existing Solutions 5.1 Singular Phillips Curve 5.1 Singular Phillips Curve 5.2 Persistence and Policy Puzzles 5.2 Persistence and Policy Puzzles 5.3 Two Comparison Models 5.3 Two Comparison Models 5.4 Lucas Critique 5.4 Lucas Critique 6 Stochastic Equilibrium and 6.1 Ergodic Theory and Random Dynamical Systems 6 Stochastic Equilibrium and 6.1 Ergodic Theory and Random Dynamical Systems 6.2 Equilibrium Construction 6.2 Equilibrium Construction 6.3 Literature Comparison 6.3 Literature Comparison 6.4 Equilibrium Analysis 6.4 Equilibrium Analysis 7 General Linearized Phillips Curve 7 General Linearized Phillips Curve 7.1 Slope Coefficients 7.1 Slope Coefficients 7.2 Error Coefficients 7.2 Error Coefficients 8 Existence Results and 8.1 Main Results 8 Existence Results and 8.1 Main Results 8.2 Key Proofs 8.2 Key Proofs 8.3 Discussion 8.3 Discussion 9 Bifurcation Analysis 9 Bifurcation Analysis 9.1 Analytic Aspects 9.1 Analytic Aspects 9.2 Algebraic Aspects (I) Singularities and Covers 9.2 Algebraic Aspects (I) Singularities and Covers 9.3 Algebraic Aspects (II) Homology 9.3 Algebraic Aspects (II) Homology 9.4 Algebraic Aspects (III) Schemes 9.4 Algebraic Aspects (III) Schemes 9.5 Wider Economic Interpretations 9.5 Wider Economic Interpretations 10 Econometric and Theoretical Implications and 10.1 Identification and Trade-offs 10 Econometric and Theoretical Implications and 10.1 Identification and Trade-offs 10.2 Econometric Duality 10.2 Econometric Duality 10.3 Coefficient Properties 10.3 Coefficient Properties 10.4 Microeconomic Interpretation 10.4 Microeconomic Interpretation 11 Policy Rule 11 Policy Rule 12 Conclusions and References 12 Conclusions and References Appendices Appendices A Proof of Theorem 2 and A.1 Proof of Part (i) A Proof of Theorem 2 and A.1 Proof of Part (i) A.2 Behaviour of ∆ A.2 Behaviour of ∆ A.3 Proof Part (iii) A.3 Proof Part (iii) B Proofs from Section 4 and B.1 Individual Product Demand (4.2) B Proofs from Section 4 and B.1 Individual Product Demand (4.2) B.2 Flexible Price Equilibrium and ZINSS (4.4) B.2 Flexible Price Equilibrium and ZINSS (4.4) B.3 Price Dispersion (4.5) B.3 Price Dispersion (4.5) B.4 Cost Minimization (4.6) and (10.4) B.4 Cost Minimization (4.6) and (10.4) B.5 Consolidation (4.8) B.5 Consolidation (4.8) C Proofs from Section 5, and C.1 Puzzles, Policy and Persistence C Proofs from Section 5, and C.1 Puzzles, Policy and Persistence C.2 Extending No Persistence C.2 Extending No Persistence D Stochastic Equilibrium and D.1 Non-Stochastic Equilibrium D Stochastic Equilibrium and D.1 Non-Stochastic Equilibrium D.2 Profits and Long-Run Growth D.2 Profits and Long-Run Growth E Slopes and Eigenvalues and E.1 Slope Coefficients E Slopes and Eigenvalues and E.1 Slope Coefficients E.2 Linearized DSGE Solution E.2 Linearized DSGE Solution E.3 Eigenvalue Conditions E.3 Eigenvalue Conditions E.4 Rouche’s Theorem Conditions E.4 Rouche’s Theorem Conditions F Abstract Algebra and F.1 Homology Groups F Abstract Algebra and F.1 Homology Groups F.2 Basic Categories F.2 Basic Categories F.3 De Rham Cohomology F.3 De Rham Cohomology F.4 Marginal Costs and Inflation F.4 Marginal Costs and Inflation G Further Keynesian Models and G.1 Taylor Pricing G Further Keynesian Models and G.1 Taylor Pricing G.2 Calvo Wage Phillips Curve G.2 Calvo Wage Phillips Curve G.3 Unconventional Policy Settings G.3 Unconventional Policy Settings H Empirical Robustness and H.1 Parameter Selection H Empirical Robustness and H.1 Parameter Selection H.2 Phillips Curve H.2 Phillips Curve I Additional Evidence and I.1 Other Structural Parameters I Additional Evidence and I.1 Other Structural Parameters I.2 Lucas Critique I.2 Lucas Critique I.3 Trend Inflation Volatility I.3 Trend Inflation Volatility 10.4 Microeconomic Interpretation The stability property of the model can be repurposed to give a new window on the traditional microeconomic theory of general equilibrium. One of the central claims of this paper is that when there is no trend inflation and small noise, the economy does not need systematic central bank intervention to maintain economic stability. This may be surprising to modern Keynesian macroeconomists but not to those specialising in general equilibrium theory, where there has been a great deal of work on equilibrium stability. The model has to be re-imagined with idiosyncratic rather than aggregate risk (common noise). The aggregate economy will be in non-stochastic equilibrium thanks to any suitable law of large numbers. Therefore interest rates will be independent of individual shocks, which is isomorphic to having an inactive policy setting (ay = aπ = 0). In the small noise √ ε limit, the aggregate dynamics will be repeated at the idiosyncratic level so long as there is firm-specific labor.[99] The result assumes market incompleteness; with complete markets firms would fully insure against idiosyncratic risk. The focus on small noise may seem unusual given that idiosyncratic shocks are typically large relative to aggregate shocks. Nevertheless, it seems plausible in the case of nominal rigidity where there a substantial body of evidence favouring flexible adjustment in response to large shocks, consistent with the predictions of state-dependent pricing models (see for example Boivin et al. [2009]). Finally, an intriguing alternative explanation is that producers facing large shocks insure on a near competitive market, selecting allocations that are √ ε away from full insurance.[100] Thus, I have demonstrated that a natural benchmark free market equilibrium is stable under staggered optimization, in response to small noise. I feel this is a great improvement upon previous attempts to incorporate dynamics into general equilibrium microeconomics. These focused on tatonnement processes, based on unrealistically flexible out of equilibrium adjustment.[101] Staggered optimization should feature more prominently in microeconomic theory in future. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv [99] For simplicity throughout the main text, I have assumed there is perfect competition in the labor market. This is probably unrealistic but alternative flexible wage arrangements, like bargaining solutions or additional mark-downs, could be accommodated into θ and would therefore not appear. [100] It would be natural to think of √ ε as the approximate size of the excess. It is possible to have |ε| equilibria with ∆ adjusted to reflect demand heterogeniety. I will leave this to others. However, it would not impact first order dynamics, under the assumption here of firm-specific labor (recalling Footnote 9). [101] The idea originated with Walras [2014]. The framework struggles to generate clear or intuitive empirical predictions (see Sonnenschein [1972], Sonnenschein [1973], Mantel [1974] and Debreu [1974]). For further perspective consult Weintraub [1993].

Microeconomic Stability Through Staggered Optimization

Author:
(1) David Staines. Table of Links Abstract 1 Introduction 2 Mathematical Arguments 3 Outline and Preview 4 Calvo Framework and 4.1 Household’s Problem 4.2 Preferences 4.3 Household Equilibrium Conditions 4.4 Price-Setting Problem 4.5 Nominal Equilibrium Conditions 4.6 Real Equilibrium Conditions and 4.7 Shocks 4.8 Recursive Equilibrium 5 Existing Solutions 5.1 Singular Phillips Curve 5.2 Persistence and Policy Puzzles 5.3 Two Comparison Models 5.4 Lucas Critique 6 Stochastic Equilibrium and 6.1 Ergodic Theory and Random Dynamical Systems 6.2 Equilibrium Construction 6.3 Literature Comparison 6.4 Equilibrium Analysis 7 General Linearized Phillips Curve 7.1 Slope Coefficients 7.2 Error Coefficients 8 Existence Results and 8.1 Main Results 8.2 Key Proofs 8.3 Discussion 9 Bifurcation Analysis 9.1 Analytic Aspects 9.2 Algebraic Aspects (I) Singularities and Covers 9.3 Algebraic Aspects (II) Homology 9.4 Algebraic Aspects (III) Schemes 9.5 Wider Economic Interpretations 10 Econometric and Theoretical Implications and 10.1 Identification and Trade-offs 10.2 Econometric Duality 10.3 Coefficient Properties 10.4 Microeconomic Interpretation 11 Policy Rule 12 Conclusions and References Appendices A Proof of Theorem 2 and A.1 Proof of Part (i) A.2 Behaviour of ∆ A.3 Proof Part (iii) B Proofs from Section 4 and B.1 Individual Product Demand (4.2) B.2 Flexible Price Equilibrium and ZINSS (4.4) B.3 Price Dispersion (4.5) B.4 Cost Minimization (4.6) and (10.4) B.5 Consolidation (4.8) C Proofs from Section 5, and C.1 Puzzles, Policy and Persistence C.2 Extending No Persistence D Stochastic Equilibrium and D.1 Non-Stochastic Equilibrium D.2 Profits and Long-Run Growth E Slopes and Eigenvalues and E.1 Slope Coefficients E.2 Linearized DSGE Solution E.3 Eigenvalue Conditions E.4 Rouche’s Theorem Conditions F Abstract Algebra and F.1 Homology Groups F.2 Basic Categories F.3 De Rham Cohomology F.4 Marginal Costs and Inflation G Further Keynesian Models and G.1 Taylor Pricing G.2 Calvo Wage Phillips Curve G.3 Unconventional Policy Settings H Empirical Robustness and H.1 Parameter Selection H.2 Phillips Curve I Additional Evidence and I.1 Other Structural Parameters I.2 Lucas Critique I.3 Trend Inflation Volatility 5.3 Two Comparison Models This subsection introduces two alternative models featuring monetary Non neutrality. They will be used in the next section and throughout the paper as a point of comparison with solutions of the Calvo model. The first model is classical, in the sense that it features perfectly flexible prices. The second is Keynesian because prices are not able to adjust fully to inflation. Along with the menu cost model discussed in Section 8, it is an example of a state-dependent pricing model. Crucially, it does not feature staggered optimization. Prices will typically change in every period. I layout the equivalence between the existing solution of Calvo and the Rotemberg model, I extend this equivalence to the original Lucas model, allowing me to view it as part of the observational equivalence claim of Lucas Jr [1976]. Finally, I briefly review the rest of the critique. 5.3.1 Lucas Model Lucas Jr [1972] is the original rational expectations monetary model. Markets are perfectly competitive and anticipated monetary shocks are impotent. Monetary non-neutrality arises because of imperfect information rather than sticky prices. Nevertheless, by adding a money demand function, I am able to derive surprising similarity to New Keynesian models with price rigidity. There are a collection of price-taking households.[34] Each produces a single good, using just its own labor.[35] The choice problem simplifies to a static labor-leisure trade-of The first order condition balances marginal revenue and marginal cost so Solving and log-linearizing gives an expression for an individual firm’s supply curve For parsimony, a reduced form aggregate demand curve replaces the Euler equation (18). Idiosyncratic taste shocks, reflected by the disturbance zt(i) in the individual firms demand schedule, are essential to the Lucas model. I assume they are independent and identically distributed across producers and time, with tail restrictions such that they will cancel out in aggregate almost surely. Here is the log-linear form There is linear aggregation so whilst Monetary non-neutrality is entirely driven by unexpected shocks. There is no role for price dispersion here, since the firms are price-takers and the distribution of relative price is unaffected by inflation. Unlike its Keynesian counterparts, the Lucas model would be unaffected by trend inflation. Using the individual supply curve (62), demand curve (64), steady state deviation (68) and the Lucas supply curve, (71) and (72) implies the expression for relative price deviation and from (69) and (70) This allows me to derive the following implicit formulation final form for the slope of the Lucas surprise Phillips curve 5.3.2 Rotemberg Pricing This model Rotemberg [1982] is perhaps the simplest formulation of state dependent pricing and the one most commonly compared to Calvo. The idea is that firms face a convex cost of changing prices and therefore they do not adjust immediately to their optimal flexible price. The problem is that convex costs of price changing imply firms change their prices every period through small adjustments. This runs contrary to an overwhelming body of evidence of infrequent large adjustment discussed in Appendix H.1.3. Therefore the first order conditions simplify to Finally, the resource constraint reflecting a wedge between production and consumption caused by the cost of price changing replaces (20) Author:
(1) David Staines. This paper is available on arxiv under CC 4.0 license. [34] It is not common to have differentiated products and price-taking behavior. For motivation imagine there were actually multiple households producing the same good and therefore competition between them or the possibility to set-up firms with a consequent free entry condition. Recall the Bertrand paradox that two competing firms can implement a competitive equilibrium. [35] This formulation comes from Romer [2012]. The idea is to avoid the households using the economy-wide labor market to deduce the aggregate price level. In the original paper, Lucas used an overlapping generations structure where households produced in one period then sold output in the next. Recent literature has developed more sophisticated stories about dispersed private information and strategic interaction. I do not pursue this approach as I am looking for a benchmark model. Author: (1) David Staines. Author: Author: (1) David Staines. Table of Links Abstract Abstract 1 Introduction 1 Introduction 2 Mathematical Arguments 2 Mathematical Arguments 3 Outline and Preview 3 Outline and Preview 4 Calvo Framework and 4.1 Household’s Problem 4 Calvo Framework and 4.1 Household’s Problem 4.2 Preferences 4.2 Preferences 4.3 Household Equilibrium Conditions 4.3 Household Equilibrium Conditions 4.4 Price-Setting Problem 4.4 Price-Setting Problem 4.5 Nominal Equilibrium Conditions 4.5 Nominal Equilibrium Conditions 4.6 Real Equilibrium Conditions and 4.7 Shocks 4.6 Real Equilibrium Conditions and 4.7 Shocks 4.8 Recursive Equilibrium 4.8 Recursive Equilibrium 5 Existing Solutions 5 Existing Solutions 5.1 Singular Phillips Curve 5.1 Singular Phillips Curve 5.2 Persistence and Policy Puzzles 5.2 Persistence and Policy Puzzles 5.3 Two Comparison Models 5.3 Two Comparison Models 5.4 Lucas Critique 5.4 Lucas Critique 6 Stochastic Equilibrium and 6.1 Ergodic Theory and Random Dynamical Systems 6 Stochastic Equilibrium and 6.1 Ergodic Theory and Random Dynamical Systems 6.2 Equilibrium Construction 6.2 Equilibrium Construction 6.3 Literature Comparison 6.3 Literature Comparison 6.4 Equilibrium Analysis 6.4 Equilibrium Analysis 7 General Linearized Phillips Curve 7 General Linearized Phillips Curve 7.1 Slope Coefficients 7.1 Slope Coefficients 7.2 Error Coefficients 7.2 Error Coefficients 8 Existence Results and 8.1 Main Results 8 Existence Results and 8.1 Main Results 8.2 Key Proofs 8.2 Key Proofs 8.3 Discussion 8.3 Discussion 9 Bifurcation Analysis 9 Bifurcation Analysis 9.1 Analytic Aspects 9.1 Analytic Aspects 9.2 Algebraic Aspects (I) Singularities and Covers 9.2 Algebraic Aspects (I) Singularities and Covers 9.3 Algebraic Aspects (II) Homology 9.3 Algebraic Aspects (II) Homology 9.4 Algebraic Aspects (III) Schemes 9.4 Algebraic Aspects (III) Schemes 9.5 Wider Economic Interpretations 9.5 Wider Economic Interpretations 10 Econometric and Theoretical Implications and 10.1 Identification and Trade-offs 10 Econometric and Theoretical Implications and 10.1 Identification and Trade-offs 10.2 Econometric Duality 10.2 Econometric Duality 10.3 Coefficient Properties 10.3 Coefficient Properties 10.4 Microeconomic Interpretation 10.4 Microeconomic Interpretation 11 Policy Rule 11 Policy Rule 12 Conclusions and References 12 Conclusions and References Appendices Appendices A Proof of Theorem 2 and A.1 Proof of Part (i) A Proof of Theorem 2 and A.1 Proof of Part (i) A.2 Behaviour of ∆ A.2 Behaviour of ∆ A.3 Proof Part (iii) A.3 Proof Part (iii) B Proofs from Section 4 and B.1 Individual Product Demand (4.2) B Proofs from Section 4 and B.1 Individual Product Demand (4.2) B.2 Flexible Price Equilibrium and ZINSS (4.4) B.2 Flexible Price Equilibrium and ZINSS (4.4) B.3 Price Dispersion (4.5) B.3 Price Dispersion (4.5) B.4 Cost Minimization (4.6) and (10.4) B.4 Cost Minimization (4.6) and (10.4) B.5 Consolidation (4.8) B.5 Consolidation (4.8) C Proofs from Section 5, and C.1 Puzzles, Policy and Persistence C Proofs from Section 5, and C.1 Puzzles, Policy and Persistence C.2 Extending No Persistence C.2 Extending No Persistence D Stochastic Equilibrium and D.1 Non-Stochastic Equilibrium D Stochastic Equilibrium and D.1 Non-Stochastic Equilibrium D.2 Profits and Long-Run Growth D.2 Profits and Long-Run Growth E Slopes and Eigenvalues and E.1 Slope Coefficients E Slopes and Eigenvalues and E.1 Slope Coefficients E.2 Linearized DSGE Solution E.2 Linearized DSGE Solution E.3 Eigenvalue Conditions E.3 Eigenvalue Conditions E.4 Rouche’s Theorem Conditions E.4 Rouche’s Theorem Conditions F Abstract Algebra and F.1 Homology Groups F Abstract Algebra and F.1 Homology Groups F.2 Basic Categories F.2 Basic Categories F.3 De Rham Cohomology F.3 De Rham Cohomology F.4 Marginal Costs and Inflation F.4 Marginal Costs and Inflation G Further Keynesian Models and G.1 Taylor Pricing G Further Keynesian Models and G.1 Taylor Pricing G.2 Calvo Wage Phillips Curve G.2 Calvo Wage Phillips Curve G.3 Unconventional Policy Settings G.3 Unconventional Policy Settings H Empirical Robustness and H.1 Parameter Selection H Empirical Robustness and H.1 Parameter Selection H.2 Phillips Curve H.2 Phillips Curve I Additional Evidence and I.1 Other Structural Parameters I Additional Evidence and I.1 Other Structural Parameters I.2 Lucas Critique I.2 Lucas Critique I.3 Trend Inflation Volatility I.3 Trend Inflation Volatility 5.3 Two Comparison Models This subsection introduces two alternative models featuring monetary Non neutrality. They will be used in the next section and throughout the paper as a point of comparison with solutions of the Calvo model. The first model is classical, in the sense that it features perfectly flexible prices. The second is Keynesian because prices are not able to adjust fully to inflation. Along with the menu cost model discussed in Section 8, it is an example of a state-dependent pricing model. Crucially, it does not feature staggered optimization. Prices will typically change in every period. I layout the equivalence between the existing solution of Calvo and the Rotemberg model, I extend this equivalence to the original Lucas model, allowing me to view it as part of the observational equivalence claim of Lucas Jr [1976]. Finally, I briefly review the rest of the critique. 5.3.1 Lucas Model Lucas Jr [1972] is the original rational expectations monetary model. Markets are perfectly competitive and anticipated monetary shocks are impotent. Monetary non-neutrality arises because of imperfect information rather than sticky prices. Nevertheless, by adding a money demand function, I am able to derive surprising similarity to New Keynesian models with price rigidity. There are a collection of price-taking households.[34] Each produces a single good, using just its own labor.[35] The choice problem simplifies to a static labor-leisure trade-of The first order condition balances marginal revenue and marginal cost so Solving and log-linearizing gives an expression for an individual firm’s supply curve For parsimony, a reduced form aggregate demand curve replaces the Euler equation (18). Idiosyncratic taste shocks, reflected by the disturbance zt(i) in the individual firms demand schedule, are essential to the Lucas model. I assume they are independent and identically distributed across producers and time, with tail restrictions such that they will cancel out in aggregate almost surely. Here is the log-linear form There is linear aggregation so whilst Monetary non-neutrality is entirely driven by unexpected shocks. There is no role for price dispersion here, since the firms are price-takers and the distribution of relative price is unaffected by inflation. Unlike its Keynesian counterparts, the Lucas model would be unaffected by trend inflation. Using the individual supply curve (62), demand curve (64), steady state deviation (68) and the Lucas supply curve, (71) and (72) implies the expression for relative price deviation and from (69) and (70) This allows me to derive the following implicit formulation final form for the slope of the Lucas surprise Phillips curve 5.3.2 Rotemberg Pricing This model Rotemberg [1982] is perhaps the simplest formulation of state dependent pricing and the one most commonly compared to Calvo. The idea is that firms face a convex cost of changing prices and therefore they do not adjust immediately to their optimal flexible price. The problem is that convex costs of price changing imply firms change their prices every period through small adjustments. This runs contrary to an overwhelming body of evidence of infrequent large adjustment discussed in Appendix H.1.3. Therefore the first order conditions simplify to Finally, the resource constraint reflecting a wedge between production and consumption caused by the cost of price changing replaces (20) Author: (1) David Staines. Author: Author: (1) David Staines. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv [34] It is not common to have differentiated products and price-taking behavior. For motivation imagine there were actually multiple households producing the same good and therefore competition between them or the possibility to set-up firms with a consequent free entry condition. Recall the Bertrand paradox that two competing firms can implement a competitive equilibrium. [35] This formulation comes from Romer [2012]. The idea is to avoid the households using the economy-wide labor market to deduce the aggregate price level. In the original paper, Lucas used an overlapping generations structure where households produced in one period then sold output in the next. Recent literature has developed more sophisticated stories about dispersed private information and strategic interaction. I do not pursue this approach as I am looking for a benchmark model.

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“If someone teaches it to you, they can teach someone else [or robot] and replace you.” — Naval Ravikant The traditional education system is suboptimal. It teaches memorization over understanding, conformity over curiosity, and compartmentalization over synthesis. It prepares us for a world that no longer exists while punishing the very skills life demands. Here’s the good news: You don’t need to follow that broken script. The key to success lies in designing your own curriculum. A learning system tailored to your unique goals and interests. This is how you become irreplaceable. The Flaws of Traditional Education Schools reward conformity, obedience, and rote memorization. The real world doesn’t. Here’s how traditional education sets us up for failure: 1. One Correct Answer Schools teach convergent thinking: one problem, one solution. Real life demands divergent thinking: one problem, infinite solutions. Creativity thrives not in finding the "correct" answer but in exploring new possibilities. For example, convergent thinking insists 1 + 1 = 2, and there’s only one method to solve it. If you solve it another way, you’re “wrong.” This rigidity is absurd. Alex Hormozi, in his book $100M Offers, asks, “How many ways can you use a brick?” You could build a wall, create a paperweight, design art, or even invent something new. These are abundant examples of divergent thinking. There are several “right” answers, and some are more right than others. That's how the real world works. When solutions are convergent, they’re easier to teach and easier to replace. If someone can teach you, they can teach someone else—or program a computer or robot to do the same thing. Divergent thinking happens with creativity, making it irreplaceable. 2. No Shortcuts Have you ever solved a math problem your way, only to fail because it wasn’t the way your teacher wanted? Me too. Traditional schools discourage shortcuts. They insist on “doing it the hard way” under the false pretense that you’ll learn more. But you don’t need to learn everything—you only need to learn what’s useful. The truth is, no one succeeds alone. A pencil is the product of thousands of people working together. Woodcutters, miners, rubber producers, and manufacturers who’ve never met. Schools lament that younger generations use calculators, computers, and now AI tools. But isn’t that the point of progress? Every generation should make life easier for the next. I don’t want to memorize faster or calculate quicker than a computer. That’s a race I’ll never win. Instead, I want to improve my creativity, the one skill computers can’t replicate. Tools like AI aren’t competition—they’re collaborators. They free us to think bigger and focus on what matters most: creating solutions that didn’t exist before. 3. Punishes for Copying Smart People. Copying isn’t only natural—it’s essential. You learned to speak, walk, and survive by imitating others. Copying smart people is how you speed up success. Want what someone has? Repeat their habits. Avoid what others regret? Study their mistakes and do the opposite. Copying with intelligence saves you decades of trial and error. There’s no point in wasting 40 years of your life trying to do the same things others have done before you. Copy what they’ve figured out
Get the outcomes faster
Figure new stuff out and make things easier for the next generations. Simple. If you don’t seek to create your own curriculum, you will receive one. You’ll be living a life that has been lived millions of times by millions of people. 4. Questioning Authority. In school, asking “Why?” can land you in detention. In life, it’s how you innovate. Questioning assumptions saves time, money, and energy. Rushing through tasks without asking why can cause rework and wasted effort. Take time to pause, reflect, and question the process for better, faster outcomes. 5. Effort Isn’t Rewarded; Results Are. School rewards effort—turn in your homework, and you’ll get points. Life doesn’t care how hard you try. If you miss the one crucial detail, your entire effort wastes. The market rewards outcomes, not inputs. Grind doesn’t matter; results do. 6. Memorization Is Useless. “School rewards you for what you can remember. The market rewards you for what you can predict. The latter pays more.” — Alex Hormozi Memorizing is storing data. Understanding is seeing how the data connects. It’s the difference between repeating a script and improvising a masterpiece. Think about it: Memorization is fragile. Forget one step in a process, and you’re stuck. Understanding is robust—it adapts and improvises.
Memorization is limited. Your brain has finite storage. Understanding compounds, connecting concepts across disciplines.
Memorization is replaceable. Why memorize the periodic table when Google can recall it in seconds? Understanding makes you irreplaceable.
Memorization feels like progress, but it’s fragile. Remember math class? Everything clicked until the pace picked up. You were suddenly memorizing formulas instead of understanding them. That didn’t end well. School rewards what you can remember. The real world pays for what you can predict. What Schools Got Right While the flaws are glaring, let’s not throw the baby out with the bathwater. There are valuable lessons we can adapt from the school system: 1. Consistency Is Key. Showing up at the same time every day, whether you feel like it or not, builds discipline. Professionalism isn’t about motivation; it’s about consistency. Think of an untidy room: cleaning after one day is easy, but waiting weeks or months makes it exponentially harder. The same applies to creativity—more entropy equals more effort to create order. Destroy chaos with consistency and build momentum. Making your work easier and faster. 2. Structure Enables Freedom. Deadlines, schedules, and systems help you focus your energy. Structure creates the freedom to be creative within constraints. 3. Collaboration Matters. Group projects teach you how to work with others, even when it’s frustrating. The ability to collaborate is essential in the creative economy. Build Your Own Curriculum The most valuable education is the one you design for yourself. Here’s how: Define Your Goals. What do you want to achieve? Clarity is the foundation of progress.
Learn What Can’t Be Replaced. Everything can be learned but not everything can be taught. As Naval Ravikant suggests, focus on skills that are so unique and personal that no one can compete with you. You will be unbeatable when it feels like play to you but feels like work to others.
Use High-Leverage Tools. Leverage books, mentors, and tools that multiply your efforts. AI, automation, and modern tech aren’t crutches—they’re accelerators.
Act. Study less, practice more. Theory without application is waste. Reading or consuming information before doing the thing doesn't work. You'll end up consuming useless things, and yes, knowledge can waste. It's easier to fix a leaking bucket when you find out where it's leaking first. Doing the thing and failing gives you a clear picture of the knowledge gaps you have and will help you know the right questions to ask.
Iterate. Learning isn’t linear; it’s cyclical. Experiment, reflect, and adapt. Your Future Is in Your Hands When you design your own curriculum, you take full responsibility for your growth. You can’t blame the system for your failures—or your lack of progress. The creative economy rewards those who think for themselves, adapt, and create value. Be the architect of your education, and you’ll thrive in a world that celebrates the exceptional. Final Thought: To thrive, you need to think like a professional, create like an artist, and learn like a lifelong student. Merge work with play. Focus on creativity over conformity. Build your curriculum with intention—and become irreplaceable. I’m rooting for you. Subscribe to my newsletter here, or simply click the Hackernoon subscribe button to improve your creativity, productivity and becoming the best at what you do. Enjoy the rest of your day. “If someone teaches it to you, they can teach someone else [or robot] and replace you.” — Naval Ravikant The traditional education system is suboptimal. It teaches memorization over understanding, conformity over curiosity, and compartmentalization over synthesis. It prepares us for a world that no longer exists while punishing the very skills life demands. Here’s the good news: You don’t need to follow that broken script. The key to success lies in designing your own curriculum. A learning system tailored to your unique goals and interests. This is how you become irreplaceable. The Flaws of Traditional Education Schools reward conformity, obedience, and rote memorization. The real world doesn’t. Here’s how traditional education sets us up for failure: 1. One Correct Answer One Correct Answer Schools teach convergent thinking: one problem, one solution. Real life demands divergent thinking: one problem, infinite solutions. Creativity thrives not in finding the "correct" answer but in exploring new possibilities. For example, convergent thinking insists 1 + 1 = 2, and there’s only one method to solve it. If you solve it another way, you’re “wrong.” This rigidity is absurd. Alex Hormozi, in his book $100M Offers , asks, “How many ways can you use a brick?” You could build a wall, create a paperweight, design art, or even invent something new. These are abundant examples of divergent thinking. There are several “right” answers, and some are more right than others. That's how the real world works. $100M Offers When solutions are convergent, they’re easier to teach and easier to replace. If someone can teach you, they can teach someone else—or program a computer or robot to do the same thing. Divergent thinking happens with creativity, making it irreplaceable. 2. No Shortcuts No Shortcuts Have you ever solved a math problem your way, only to fail because it wasn’t the way your teacher wanted? Me too. Traditional schools discourage shortcuts. They insist on “doing it the hard way” under the false pretense that you’ll learn more. But you don’t need to learn everything —you only need to learn what’s useful. everything useful. The truth is, no one succeeds alone. A pencil is the product of thousands of people working together. Woodcutters, miners, rubber producers, and manufacturers who’ve never met. Schools lament that younger generations use calculators, computers, and now AI tools. But isn’t that the point of progress? Every generation should make life easier for the next. I don’t want to memorize faster or calculate quicker than a computer. That’s a race I’ll never win. Instead, I want to improve my creativity, the one skill computers can’t replicate. Tools like AI aren’t competition—they’re collaborators. They free us to think bigger and focus on what matters most: creating solutions that didn’t exist before. 3. Punishes for Copying Smart People. Punishes for Copying Smart People. Copying isn’t only natural—it’s essential. You learned to speak, walk, and survive by imitating others. Copying smart people is how you speed up success. Want what someone has? Repeat their habits. Avoid what others regret? Study their mistakes and do the opposite. Copying with intelligence saves you decades of trial and error. There’s no point in wasting 40 years of your life trying to do the same things others have done before you. Copy what they’ve figured out Get the outcomes faster Figure new stuff out and make things easier for the next generations. Simple. Copy what they’ve figured out Get the outcomes faster Figure new stuff out and make things easier for the next generations. Simple. If you don’t seek to create your own curriculum, you will receive one. You’ll be living a life that has been lived millions of times by millions of people. 4. Questioning Authority. Questioning Authority. In school, asking “Why?” can land you in detention. In life, it’s how you innovate. Questioning assumptions saves time, money, and energy. Rushing through tasks without asking why can cause rework and wasted effort. why Take time to pause, reflect, and question the process for better, faster outcomes. 5. Effort Isn’t Rewarded; Results Are. Effort Isn’t Rewarded; Results Are. School rewards effort—turn in your homework, and you’ll get points. Life doesn’t care how hard you try. If you miss the one crucial detail, your entire effort wastes. The market rewards outcomes, not inputs. Grind doesn’t matter; results do. 6. Memorization Is Useless. Memorization Is Useless. “School rewards you for what you can remember. The market rewards you for what you can predict. The latter pays more.” — Alex Hormozi Memorizing is storing data. Understanding is seeing how the data connects. It’s the difference between repeating a script and improvising a masterpiece. Think about it: Memorization is fragile. Forget one step in a process, and you’re stuck. Understanding is robust—it adapts and improvises. Memorization is limited. Your brain has finite storage. Understanding compounds, connecting concepts across disciplines. Memorization is replaceable. Why memorize the periodic table when Google can recall it in seconds? Understanding makes you irreplaceable. Memorization feels like progress, but it’s fragile. Remember math class? Everything clicked until the pace picked up. You were suddenly memorizing formulas instead of understanding them. That didn’t end well. School rewards what you can remember. The real world pays for what you can predict. Memorization is fragile. Forget one step in a process, and you’re stuck. Understanding is robust—it adapts and improvises. Memorization is fragile. Memorization is limited. Your brain has finite storage. Understanding compounds, connecting concepts across disciplines. Memorization is limited. Memorization is replaceable. Why memorize the periodic table when Google can recall it in seconds? Understanding makes you irreplaceable. Memorization is replaceable. Memorization feels like progress, but it’s fragile. Remember math class? Everything clicked until the pace picked up. You were suddenly memorizing formulas instead of understanding them. That didn’t end well. School rewards what you can remember. The real world pays for what you can predict. Memorization feels like progress, but it’s fragile. School rewards what you can remember. The real world pays for what you can predict. What Schools Got Right While the flaws are glaring, let’s not throw the baby out with the bathwater. There are valuable lessons we can adapt from the school system: 1. Consistency Is Key. Consistency Is Key. Showing up at the same time every day, whether you feel like it or not, builds discipline. Professionalism isn’t about motivation; it’s about consistency. Think of an untidy room: cleaning after one day is easy, but waiting weeks or months makes it exponentially harder. The same applies to creativity—more entropy equals more effort to create order. Destroy chaos with consistency and build momentum. Making your work easier and faster. 2. Structure Enables Freedom. Structure Enables Freedom. Deadlines, schedules, and systems help you focus your energy. Structure creates the freedom to be creative within constraints. 3. Collaboration Matters. Collaboration Matters. Group projects teach you how to work with others, even when it’s frustrating. The ability to collaborate is essential in the creative economy. Build Your Own Curriculum The most valuable education is the one you design for yourself. Here’s how: Define Your Goals. What do you want to achieve? Clarity is the foundation of progress. Learn What Can’t Be Replaced. Everything can be learned but not everything can be taught. As Naval Ravikant suggests, focus on skills that are so unique and personal that no one can compete with you. You will be unbeatable when it feels like play to you but feels like work to others. Use High-Leverage Tools. Leverage books, mentors, and tools that multiply your efforts. AI, automation, and modern tech aren’t crutches—they’re accelerators. Act. Study less, practice more. Theory without application is waste. Reading or consuming information before doing the thing doesn't work. You'll end up consuming useless things, and yes, knowledge can waste. It's easier to fix a leaking bucket when you find out where it's leaking first. Doing the thing and failing gives you a clear picture of the knowledge gaps you have and will help you know the right questions to ask. Iterate. Learning isn’t linear; it’s cyclical. Experiment, reflect, and adapt. Define Your Goals. What do you want to achieve? Clarity is the foundation of progress. Define Your Goals. Learn What Can’t Be Replaced. Everything can be learned but not everything can be taught. As Naval Ravikant suggests, focus on skills that are so unique and personal that no one can compete with you. You will be unbeatable when it feels like play to you but feels like work to others. Learn What Can’t Be Replaced. Use High-Leverage Tools. Leverage books, mentors, and tools that multiply your efforts. AI, automation, and modern tech aren’t crutches—they’re accelerators. Use High-Leverage Tools. Act. Study less, practice more. Theory without application is waste. Reading or consuming information before doing the thing doesn't work. You'll end up consuming useless things, and yes, knowledge can waste. It's easier to fix a leaking bucket when you find out where it's leaking first. Doing the thing and failing gives you a clear picture of the knowledge gaps you have and will help you know the right questions to ask. Act. Iterate. Learning isn’t linear; it’s cyclical. Experiment, reflect, and adapt. Iterate. Your Future Is in Your Hands When you design your own curriculum, you take full responsibility for your growth. You can’t blame the system for your failures—or your lack of progress. The creative economy rewards those who think for themselves, adapt, and create value. Be the architect of your education, and you’ll thrive in a world that celebrates the exceptional. Final Thought: Final Thought: To thrive, you need to think like a professional, create like an artist, and learn like a lifelong student. Merge work with play. Focus on creativity over conformity. Build your curriculum with intention—and become irreplaceable. I’m rooting for you. Subscribe to my newsletter here , or simply click the Hackernoon subscribe button to improve your creativity, productivity and becoming the best at what you do. here Enjoy the rest of your day.

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