# Visualizing the Production Function and Cost Curves

Single, static images of data trends aren’t the most effective way to communicate the ways the different elements of an equation or formula contribute to a trend.  This is especially true for introductory economics concepts such as cost curves or the production function. Dynamic, interactive visualizations that allow users to manipulate the variables contributing to a relationship which enables the audience to better understand how equations express trends.

Krit Petrachaianan ‘17 of DASIL programmed a visualization using R that illustrates cost curves and the production function, two core concepts of introductory economics.  DASIL’s visualization allows users to manipulate the different parts of the equations that define cost curves and the production function. For instance, users can manipulate the costs per input (denoted r and w) and the amount of a particular input (denoted K for capital and L for labor). Users can also define the productivity of the firm’s inputs.

Cost curves visualize the costs of producing different levels of output. The total cost of production for a business can be subdivided into fixed and variable costs.  Some costs, such as raw materials and production supplies, change proportionally as more or less of the good or service is produced and are known as variable costs.  Other costs, such as the annual rent or salary of workers, are independent of the level of goods or services a business produces and are known as fixed costs.

The production function shows the relationship between the output produced by a firm from a given amount of inputs (i.e. labor and capital). The productivity of inputs in producing output can vary in three ways: 1) with constant productivity, the additional output produced by a given amount of input is constant as more of the input is used, 2) with diminishing productivity, the additional output produced by a given amount of input declines as more of the input is used, and 3) with increasing productivity, the additional output produced by a given amount of input increases as more of the input is used.

Explore DASIL’s latest R visualization below, as well as in the Graphs section of the Data Visualizations page and in the Economics tab of the DASIL website.

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# The Common Mistakes Made in Creating a Data Visualization

Oftentimes the best way to learn about how to do something right is by learning what not to do, especially for how to make good data visualizations. WTF Visualizations is a website that compiles poorly crafted data visualizations from across the web and media. Below is a sampling of some of the visualizations featured that illustrate some of the most common data visualization mistakes:

• Absence of Proper Scaling

Including proper scaling is essential in accurately representing your data. In the example below, the differentiation between values is misrepresented due to the absence of a clear scaling measure. The 52% measure does not appear to be as large as it should be in comparison to the other bars, and the 13% figure appears to be much larger than 3% when compared to the two 10% figures.

• Too Much Information

While the inclination is to include as much information in visualizations as possible, oftentimes including too much information detracts from the clarity and concision that is essential to good data visualization. The example below perfectly illustrates how including a myriad of different categories can muddle your visualization, as well as the importance of clear axis labels and descriptive titles.

Ensure that the data that you do decide to visualize is comprehensible to your audience: recode categories when there are too many; don’t include measures that illustrate the same phenomenon; don’t include 10 different variables when 3 will do. If need be, include more than one visualization to highlight different sub categories or variables.

Always double check your math before sharing your visualization to the public. You may run the risk of misrepresenting your data, as well as appearing as though you are not capable of simple arithmetic. The example below illustrates this point perfectly: while the creator uses a pie chart, the sections do not add up to 100%, but rather, 128%. The sections of the pie chart also do not accurately reflect the values they supposedly represent: The “51% Today” section, for instance, should be taking up a little more than half of the pie chart.

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# Journalists and Maps: The Need for Teaching Quantitative Literacy to Everyone

In recent years programs like ArcGIS and Tableau have made it very easy to produce maps. Journalists have responded by richly illustrating their articles with quantitative data displayed as maps.  Maps are both attractive and easier to explore visually than the same data provided in tabular form, so in many ways they are ideal illustrations. For the average reader information transmitted as quantitative data appears authoritative and these maps are no exception.  On the surface they seem real and informative. Unfortunately, just as with any data-driven information maps can inadvertently be misleading.

In a recent example, NBC news illustrates an article about the Supreme Court consideration of a Texas law that would force the closure of a high percentage of existing abortion clinics across the country were similar laws to be enforced or enacted more broadly with a map of the U.S. showing the number of abortions per state in 2012, using data from the CDC (Center for Disease Control).

A quick perusal of this map seems to show why Texas is so concerned about abortions.  After all it is one of the states with the most abortions.  After a moment’s examination, the viewer might (or might not) note that the states with the highest populations also seem to have the largest numbers of abortions.

Thus, this map really tells us little about which states have the biggest problem with abortions.  Some kind of standardization by population is needed.  One option would be to just use population size. Since the number of women of women who might potentially become pregnant and secure an abortion (usually defined as the number of women between 15 and 44) does not necessarily vary by state in direct proportion to the population size, this statistic may be a better measure for standardization than simple population size.  In terms of the number of abortions per 1,000 women ages 15-44 Florida and New York have high rates of abortions, but Texas no longer looks unusual.

But this still might not be the most revealing measure to use, since there is state to state variation in the birth rate.  In 2012 the average birth rate for the U.S. was 1.88, but Texas had a birth rate of 2.08.  The highest birth rate in the 50 states was 2.37 in Utah and the lowest 1.59 in Rhode Island. An option that takes into account the differential birth rates is to examine the ratio between the number of births and the number of abortions.  Using this measure, New York remains very high, but due to its relatively high birth rate Texas is even lower.

The CDC provides all of these statistics, but the journalist chose the least revealing of the possible measures to display.  Journalists are generally both well-educated and, we assume, well-meaning.  Why not pick a better measure to map when it would have been equally easy to do so?  I suspect that the answer lies firmly in the laps of educators like myself.  While we prioritize skills like writing and speaking well, we do not mandate that all students graduate statistically or even quantitatively literate, but we should.

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# Data Across the Curriculum: Teaching Data Skills in Sociology

Casey Oberlin, Assistant Professor of Sociology, understands the importance of using data in the classroom, especially in such a discipline as Sociology, which is commonly viewed by others outside the discipline as a field with less real-life application of hard skills (e.g. data analysis). This conception is far from the truth, and Oberlin’s approach with data in the classroom gives her students a very holistic and interactive view of data analysis in the field that shows how data is part and parcel to the discipline.
Oberlin uses both her introductory Sociology courses and Research Methods courses as opportunities for students to get deeply entrenched with the data-rich, multi-tiered research process of the field. Data in Sociology is very diverse, as it involves both quantitative and qualitative measures, so Oberlin’s approach focuses on getting students exposed to the vast array of data types, as well as the techniques, technologies, and methods used to interpreting each type.

At the introductory level, Oberlin focuses on data consumption as a first step to data concepts. Students study infographics (see Figure 1) and other data visualizations to learn how to present data and interpret the data being presented. Oberlin’s Research Methods courses are reserved for her experiential-based approach with data that teaches students two data software programs throughout the semester, one quantitative (SPSS) and the other qualitative (Nvivo), shows students the wide range of data utilized by Sociology, and has students grapple with the entire research process for themselves. In Research Methods, students create research questions, hypotheses/expectations, clean or assess the dataset, analyze their results, and present their work in a professional manner. Her heavy guidance through the research process helps to mitigate understandable anxiety about trying new techniques and presenting their ongoing work, setting her students up to then develop their own sustained research project throughout the semester. Oberlin states this immersive method is beneficial to and enthusiastically received by students, as the practice in research opens doors to internships, jobs, and grad schools.

All in all, Casey Oberlin’s utilization of data in the class gives students exposure to the intensive research process that is integral to Sociology and teaches important data skills and concepts that are applicable both in the real-world and in a classroom setting.

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# 10 Suggestions for Making an Effective Poster

Written papers are the traditional way to share research results at professional meetings, but poster sessions have been gaining popularity in many fields. Posters are particularly effective for sharing quantitative data, as they provide a good format for presenting data visualizations and allow readers to peruse the information at leisure.  For students they are a great teaching tool, as preparing a good poster also requires clear and concise writing.

Making a poster is easy, but making a really good poster is hard.  I have found the guidelines below helpful to students.  The most important piece of advice, however, is the one true for all writing—write, read and revise; write, read and revise; write, read and revise!

1. Make your poster using PowerPoint. This will allow you to put in text via text boxes as well as to paste in charts, graphs, tables, maps, and pictures.  It is easy! To get your pictures and text boxes to line up consistently, use snap to grid.  In the Format tab choose Arrange>>Align and then Grid Setting. Select to view the grid and to snap to the grid.  You can set the grid size here as well.
1. Use a single slide. In the Design Tab pick Page Setup, select custom, and then set the width and height to maximize your slide, given the locally-available paper size. At Grinnell the paper width available is 36”, so we set the width to 45” and the height to 36”.  Use “landscape” for your orientation.
1. As in a written paper, have a descriptive title. Put the title (in 68 point type or larger) at the top of the poster.  Place your name and college affiliation in slightly smaller type immediately below it.
1. The exact sections of the poster will vary some depending on the project, but include an abstract placed either under the title or in the upper left column.
1. As in a written paper, be sure you have a good thesis and present it early in the poster, support it with evidence, then remind your audience of it as you conclude. Finish with a minimum of citations and acknowledgements in the lower right hand corner.
1. Posters should read sequentially from the upper left, down the left column, then down the central column (if you have one) and finally down the right column. Alternative layouts are possible, but the order in which the poster is read must be obvious.
1. Use a large font–a minimum of 28 point.
1. Limit the number of words. Be concise and think of much of your text as captions for illustrations.
1. Use lots of charts, graphs, maps, and other pictures. Be sure to label your figures and refer to them in the text.
1. Make your poster attractive. Use color.  Pay attention to layout.  Do not have large empty areas.

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