Teaching production theory through simulation

Abstract

The authors present a Web application they designed in the R programming language as an experiential learning tool for teaching production theory. The app simulates production decisions where a manager is tasked to find the optimal mixture of inputs through experimentation. Users of the application are instructed to use calculations and intuitions from production theory to improve profitability quickly. The underlying parameters and starting points are randomized to allow for additional practice. Variations of the exercise correspond to cost-minimization and profit-maximization problems with and without market power in the output market. Also, the app provides dynamic, interactive visualizations in 3D in order to assist in a better understanding of standard production theory graphs. The app is located at https://bit.ly/387HsHL.

Keywords:

• Experiential learning
• production theory
• simulation

JEL codes:

• A22
• A23
• D24

Acknowledgments

The authors are grateful to two anonymous referees for their invaluable comments. They also thank many former students who were unafraid to express feedback, positive and negative, during the conception and development of this application, and they also thank the grrr R Slack group for help in developing the tools to make this happen.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Marginal products and related measures are only estimated when just one input is changed from one period to the next.

2 See Hawtrey (2007) and Sheridan, Hoyt, and Imazeki (2014) for further motivation for and examples of experiential learning techniques.

3 For example, a standard problem in traditional approaches is to give students a Cobb-Douglas function with input prices and target quantity, and the students mathematically solve for the cost-minimizing set of inputs. Our app helps students intuitively understand what the marginal rate of technical substitution means and why it should equal the wage ratio in the optimum.

4 The online appendix can be found at bit.ly/41lO0fu.

5 If the user chooses to have the simulation provide the marginal products, this is akin to having a production team that provides this information. The default setting is to not provide these because our MBA students have asked where information on marginal products could be obtained in a business setting and were not satisfied with the suggestion of consulting a production team. Also, finding marginal products through input choice reinforces what marginal products mean.

6 We chose the notation in this article to be consistent with the application. There were some typesetting limitations in designing the application, so the best notation we could choose might still differ from standard.

7 The number of variable inputs is decided on the first page of the application.

8 This application is designed so that even the least mathematically sophisticated economics student can gain a working understanding of the major concepts of production theory. But, more advanced courses could use this application to demonstrate deeper connections between the mathematics and the application of production theory, for example, because the Cobb-Douglas production function (1) is log-linear. $\mathrm{\text{ln}}\hspace{0.17em}\left(Q_t\right)=\mathrm{\text{ln}}\hspace{0.17em}\left(A\right)+{\alpha }_u\mathrm{\text{ln}}\left(u_t\right)+{\alpha }_s\mathrm{\text{ln}}\left(s_t\right)+{\alpha }_r\mathrm{\text{ln}}\hspace{0.17em}\left(r_t\right)$. After at least four periods of choosing a variety of inputs, the underlying parameters can be calculated using mathematical tools such as linear algebra or regression analysis. Once these model parameters are found, the students can solve for the optimal mix of inputs and immediately reach the profit-maximization point.

9 One might think of other penalties for missing production targets, such as excessive overtime costs, delays in production, storage costs, etc. This particular mechanism seems most tractable and still be fairly realistic.

10 If the display marginal products option was selected in the Welcome Screen, the VMPs are already available. The user can go right to analyzing them.