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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