24 Jun HOW TO EXPLORE BEFORE STARTING TO EXPLORE A CLASS OF FUNCTIONS IN MATHEMATICA, CONDUCT TWO TYPES OF SEARCHES.
Issues to explore In exploring these basic standard cost functions using Mathematica, consider the following issues: 1. What class of functions can allow for the relationships illustrated above? 2. Are there any restrictions on the relevant parameters of the class of functions? 3. What issues, if any, might arise in trying to estimate such cost functions? 4. Can the class of functions for given parameter values re×ect the following phenomenon?If so, how? (a) high or low Öxed cost industries (b) long run versus short run costs 5. Can the class of functions handle the following observed long run phenomenon? many industries have an output range over which they experience decreasing average costs, but then at some output (minimum efÖcient scale), average costs become relatively constant for large ranges of output How to explore Before starting to explore a class of functions in Mathematica, conduct two types of searches. Your most productive search route will be a general search via Google. Youll Önd many results; focus on the academic materials by faculty using cost functions in research and teaching. A second avenue is to search the EconLit database available at the Miami University Libraries databases page, http://www.lib.mi- amioh. edu/databases/ for a professional economics journal article (or professional economics book) about cost functions (some may be from older articles). Use Mathematica to computationally explore the class of functions you selected: what shapes of average total cost, average variable cost, marginal cost can be generated by the class of functions? how do the shapes vary with parameters speciÖed in the function? can all the issues raised above “be addressed” with varying parameters ranges and restrictions on the parameters? It is advisable that you conduct all your explorations in a separate notebook from the notebook you use to write up the results.
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