Assignment 1 (application focused) Problem Definition and Model Conceptualization Designing and evaluating high-leverage policies demands a long-term, dynamic perspective. The analyst or manager must be able to characterize the strategic problem, including its current symptoms and history. The time horizon should be explicit and must be long enough to include possible side effects, delayed responses to policies, and other feedbacks. This assignment cultivates your ability to develop a reference mode, a graphical characterization of the patterns of problem behavior over time in various situations. The assignment also develops your skill in constructing causal loop diagrams that capture the feedback structure of the system, and your ability to relate the structure in a causal map to the problem behavior in the reference mode. Problem definition involves both textual and graphical statements of problematic behavior. Conceptualization entails identifying feedback loops hypothesized to underlie observed patterns of system behavior. Model formulation entails moving from a theory of underlying structure to a fully specified mathematical model so that the theory can be tested. This assignment focuses on problem definition and initial model formulation. Later assignments will bring these skills together with those of formulation and analysis to focus on a variety of strategic and operational problems. Assignment Guidelines While your graphs and diagrams should be clear and legible, DO NOT spend your time creating artist-quality presentation graphics. Use your time to think about the issues and develop your ideas. A legible handwritten diagram you had time to think about is preferable to a beautiful computer-generated diagram that took so much time to render you didn’t have time to think deeply about its content. Before starting, review the readings covering causal-loop diagrams as noted in the syllabus, particularly chapters 4 and 5 of Business Dynamics. 2 Each of your diagrams must fit comfortably and legibly on a single sheet of 8.5 x 11 paper. Diagrams should include the loops essential in explaining the dynamics, but be simple enough to understand. Your client will not understand a diagram that includes everything. Be sure to follow the conventions and rules for causal diagrams and reference modes described in chapters 4 and 5. These include: ­ Show the time horizon of graphs explicitly; provide units of measure and scales for all variables. ­ Label the polarity of every link in your causal diagrams. ­ Identify the polarity of the important loops. ­ Give each important loop a meaningful name. ­ Use variables with a clear sense of direction. ­ Clearly label your graphs, especially if you’re printing in black and white. Operational thinking and dimensional consistency Formulate your causal diagrams so they capture operational realities—the physics and decision making procedures—of the processes you seek to represent. The units of measure for the variables should be obvious and conform to standard practice. In many cases, the equation for a key concept should be readily inferred from the causal diagram and units. For example, consider a model of a work process. A key formulation shows how the amount of work completed each day is determined. The following diagram states that work completion rises with resources, effort and skill: However, the definitions and units of measure for the inputs to the completion rate are unclear and ambiguous. Are resources measured in people or dollars? What is “effort” and how do we measure “skill”? A much better diagram is: Task Completion Rate Workers Workweek Productivity + + + Task Completion Rate Resources Effort Skill + + + 3 Each variable has a clear sense of direction and obvious units of measure. From this information a reader can easily infer the equation for the Task Completion Rate: Task Completion Rate = Workers * Workweek * Productivity (Tasks/week) (People) (Hours/Week) (Tasks/Hour/Person) Defining variables  When it comes to choosing names for variables, there is no right or wrong answer. Choosing a boundary for your analysis is a central part of problem definition; the model boundary should always be chosen to be broad enough to encompass the issues that may be relevant to understanding the problem and designing effective policies. Submitting your work: Please submit your write-up as a single Word or PDF document. Please do not submit more than 4 pages (font 12, 1 inch margins) – brevity is a virtue! A. Identifying Feedback Structure of Growth and its Limits (5 points: 1/2 of total)  A1. Uber is a private company offering car-for-hire services globally through an online app. Since its launch the company has grown exponentially to become one of the most valuable private companies worldwide, with a hotly anticipated public offering. Their most recent fundraising round values the company at more than $68 billion. However, analysts disagree on how much Uber is really worth and whether or not they can sustain their impressive run. The articles below are just a few of those available that provide a window into these discussions and the relevant mechanisms. https://www.zacks.com/stock/news/255900/will-uber-be-the-hottest-ipo-of-2017 http://investorplace.com/ipo-playbook/uber-ipo-valuation/#.VxfpiWOqF90 • https://www.bloomberg.com/features/2017-uber-airbnb-99-billion-idea/ Using this material, any other public resource, and your own insights, identify at least four reinforcing loops you believe are contributing to Uber’s exponential growth. Develop a causal loop diagram capturing the most important reinforcing feedbacks you believe to be responsible for the astounding growth of Uber and its revenue, and those relevant for its future growth. In your write-up, provide a one-sentence explanation of each loop.  A2. No real quantity can grow forever. Identify some of the balancing feedbacks that might eventually stop the growth of Uber. Identify at least four balancing feedbacks. Add them to your causal diagram. Provide a one-sentence explanation of each loop. 4  A3. What is likely to happen to the number of Uber customers in the future? Specifically, use your diagram to suggest what the pattern of development for active Uber customers might be in the future. Draw a graph showing possible futures for the number of active users. Select an appropriate time horizon, and explain your choice briefly. Provide at least two possible future paths for subscribers. Name your scenarios.  Use the feedback structure and other features of your causal diagram (such as delays) to assess what the likely behavior of the customer base might be. Chapter 4 of Business Dynamics discusses different feedback structures and the various patterns of behavior they can generate. A good answer here will explain how the structure you hypothesize generates the behavior you anticipate. B. Exploring causes of Market Instability (5 points, 1/2 of total) The Boston real estate market is booming. A recent article in the Boston Globe reports the price of luxury condominiums hit a record high in the first three months of 2016, with prices in the city reaching an average of $1,380 per square foot and an average sale price of 2.3 million dollars.1 If you look at the Case-Shiller housing index reported below, you will see that this isn’t first time the city has been through this cycle. Previously real estate cycles peaked in 2005 and then fell by almost 25% before the current rise started in 2012. And, real estate cycles are by no means unique to Boston. The next graphs show that the real estate markets have been notoriously volatile for over 100 years. Your task in this question is to develop a simple causal loop diagram that explains the dynamics of real estate markets. Conventional economic theory would predict stable prices as builders and home buyers adjust their decisions to match supply and demand, but in real estate and many other markets this doesn’t seem to happen. Why?  B1. Make a list of the most important variables or concepts characterizing the real estate market. Keep your list as short as possible (eight or fewer). Aggregate similar concepts where possible (e.g., it is not necessary to represent different types of housing separately, nor do you need to differentiate between commercial and residential).  B2. Use the description presented here and your own knowledge to sketch graphs of the behavior of the key variables you identified. First, identify the time horizon over which the dynamics unfold. Select a time period long enough to capture the dynamics of the critical variables throughout the cycle, including the past development and enough of the future for the dynamics to play out. Next, sketch a graph showing the behavior for each variable over the time horizon you identified. If two or more variables have the same units of measure, plot them on the same scale (for example, in a model of a business one would show revenue and cost on the same graph so that the difference between them (profit) can be easily seen). Qualitative patterns are more important than numerical 1. Logan, Tim, “Boston’s Luxury Real Estate; price and getting pricier,” Boston Globe, 14 April 2016. https://www.bostonglobe.com/business/2016/04/14/boston-luxury-real-estate-pricey-and-gettingpricier/d9zAvLF7bwhRnUKNxPeTLM/story.html 5 precision in the early stages of problem definition. You do not need to go to the web or other sources to find data. Include the reference modes in your write up.  B3. Develop a causal diagram that captures the feedbacks you believe are responsible for the instability. Your diagram should have, at its core, the basic feedback structure regulating demand and supply in markets (Business Dynamics, p. 170). You should add the most important feedbacks and delays that you believe to be critical to explaining why prices are not stable in real estate markets.  To get your causal diagram started it is useful to ask yourself “what is the rationale for the decisions of each actor in the system?” That is, what is the intended rationality or intended outcome of the decision to buy a home? To sell? To build? For example, one motivation for buyers is to provide a roof over one’s head, but a house can also be viewed as an investment with the potential for capital gains.  Be sure to show important time delays, including delays in physical processes, in the measurement and reporting of information, and in the change in perceptions and beliefs.  Selecting an appropriate boundary is a critical skill in modeling. You need a boundary broad enough to include the key feedbacks but not so broad that your model becomes overwhelming. For example, while the effects of the housing bubble and crash in the early 2000s rippled out to affect world financial markets and contributed to the global economic downturn known as the Great Recession, including the nearbankruptcy of Greece and other nations, the possible breakup of the Eurozone, the bailouts of US banks, and so on, you should not attempt to develop a global macroeconomic model. Keep your model focused on the core dynamics responsible for real estate cycles and bubbles. Remember that while the specifics of the housing market may have differed in recent episodes compared to previous bubbles, the feedback structure underlying all speculative bubbles is the same.  B4. Using your diagram, briefly explain the genesis of the instability. What causes prices to rise and what causes them to eventually fall? What policies might mitigate these dynamics? And, most importantly, what do you think is going to happen in Boston? 6 US Real National Home Prices 1890-2010-II, with Associated Variables Prof. Robert J. Shiller S&P Web Conference on S&P/Case Shiller Home Price Indices, August 31, 20102 August 2010 US National home price index, from 1988. The Case-Shiller home price index is based on repeat sales of the same properties. To get a sense of the extent of the rise and fall in home prices, note that in some cities home price appreciation reached 15-25%/year by 2004-2005, then consider these data on peak to trough performance. 2 Source: http://www.standardandpoors.com/servlet/BlobServer?blobheadername3=MDTType&blobcol=urldata&blobtable=MungoBlobs&blobheadervalue2=inline%3B+filename%3DCaseShiller_Presentation_20100831.ppt&blobheadername2=ContentDisposition&blobheadervalue1=application%2Fpowerpoint&blobkey=id&blobheadername1=contenttype&blobwhere=1243746968251&blobheadervalue3=UTF-8 7 Case-Shiller home price index city by city Peaks, Troughs and Current Data as of August 2010 From the Standard and Poor’s presentation, S&P Web Conference on S&P/Case Shiller Home Price Indices, August 31, 2010; URL above. For more information, see www.homeprice.standardandpoors.com