Economics Research International

Volume 2015, Article ID 875301, 10 pages

http://dx.doi.org/10.1155/2015/875301

## Monopoly Profit Maximization: Success and Economic Principles

^{1}Ostwestfalen-Lippe University of Applied Sciences, Liebigstraße 87, 32657 Lemgo, Germany^{2}Johannes Gutenberg University of Mainz, Jakob-Welder-Weg 9, 55128 Mainz, Germany

Received 14 October 2014; Accepted 15 March 2015

Academic Editor: Udo Broll

Copyright © 2015 Korbinian von Blanckenburg and Milena Neubert. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper presents a classroom experiment on pricing strategies available to monopolists. Each student makes production decisions as a monopolist during the experiment, learning from his/her own experiences what it means to be a price searcher. Full information is provided on cost conditions, while the demand function remains unknown to the participants. Given a sufficient number of periods, students will in principle be able to maximise their profits by applying a simple trial and error strategy. However, one of the objectives of the experiment is to demonstrate to students that search strategies based on economic principles are more efficient.

#### 1. Introduction

It might be provocative to state that a typical student in an introductory course in economics would “memorize a few facts, diagrams, and policy recommendations, and then ten years later [⋯] be as untutored in economics as the day he entered in class” [1]. Surprisingly, few empirical studies have been published on this serious indictment of the sustainability and pedagogical effectiveness of economic teaching [2–6]. The results of these studies, however, indeed consistently indicate minimal or even no lasting effects of introductory economic courses. Given these considerations, academic economists have continued to develop new teaching approaches over the past decades in order to improve the way in which economic principles can be taught. In this regard, a number of educators have highlighted the advantages of experimental learning in the classroom [7–11]. Classroom experiments enable students to learn from their own experience, which may greatly improve their understanding of theoretical concepts [12]. Accordingly, interest in using classroom experiments to teach economics is increasing [13, 14]. Over the past three decades, teaching tools have been designed for several theoretical concepts, including price discovery mechanisms [8], Coasian bargaining [15], monopolies [16], voting paradoxes [17], public goods [18], oligopolies [19], and cartel behaviour [20]. We add to this range by proposing a classroom experiment on monopoly profit maximization.

The classroom experiment described in this paper is based on a game developed by Nelson and Beil [21], which demonstrates to undergraduate economic students what it is like to be a monopolist and enables them to investigate and consider pricing strategies first-hand.

The paper begins with theoretical background on the basic concept and learning goals. We explain the experimental design and the similarities, differences and enhancements with respect to Nelson and Beil [21]. To demonstrate the feasibility of concepts and to provide teachers with examples of results, we show the results of our classroom experiment, which was conducted in 2012 during a seminar at the University of Kassel, Germany. Afterwards, instructions for teachers are provided, demonstrating how the monopoly experiment may be used as a teaching tool in economic classes. In order to ensure that even novice experimenters will be able to apply the experimental procedures in their own classroom, sufficient detail is provided on experiment administration and on postexperimental discussion. The paper ends with a summary of the major insights.

#### 2. The Monopoly Experiment

##### 2.1. Experimental Design

The monopoly experiment enables students to develop through first-hand experience a cognitive understanding of pricing strategies available to the monopolist. To achieve this, each student acts as a separate, independent monopolist during the experiment. Each participant is provided with a cost function, but the demand function remains unknown. In fact, locating the shape, slope, and position of the demand function is one of the fundamental tasks during the experiment. The teaching tool is designed to proceed over multiple classroom periods. During each period, all students must submit a price at which they are willing to sell the product in the corresponding period, and a quantity that they will produce and offer for sale. However, there is no guarantee for the monopolist that all units can be sold. Assuming production in advance, under- as well as overproduction is possible. Consequently, only in the next period does the monopolist learn from the instructor, whether and how many of units were bought at the asking price. Given that each unit offered by the monopolist is produced, production costs will be incurred in any case—even if the goods remain unsold. Participants should aim to maximise their (cumulated) profits across all experiment periods.

Given a sufficient number of periods in which to search, most students will be able to find the profit-maximising combination of price and quantity by trial and error alone. However, it becomes evident through the course of the experiment that strategies based on economic theory are more efficient than trial and error. Furthermore, the experiment highlights that in, the “real world,” demand functions are typically unknown, which hampers monopolists wishing to apply the strategies proposed by standard economic textbooks. Consequently, students discover personally that companies which are able to accurately assess the real market demand for their products should benefit accordingly.

We use the basic framework of Nelson and Beil [21] in our experiment but provide some relevant and important enhancements. Their article and ours demonstrate to students the effectiveness of the economic principle of an optimal profit maximizing monopoly (MC = MR approach). Full information about the cost function is provided, participants know nothing about the constant demand function, and the monopoly is a price searcher. In both articles, there is no guarantee that all units produced can be sold. Underproduction and overproduction are possible and unsold units cannot be carried over as inventory. Also similar to the experiment of Nelson and Beil [21] is that bonus points are awarded for successful playing and based on profits.

However, there are notable differences to Nelson and Beil [21]. We assume that the product is not perishable and that units are divisible. We allow for fractional prices and quantities, and a cost function is given, but the demand curve is linear instead of a step function. This means that the exact profit-maximizing quantity can only be calculated by using the MC = MR approach. In Nelson and Beil [21], the exact profit-maximizing quantity can be calculated accidently both by using the MC = MR approach and by trial and error, which is, however, not the best way. To make this clear, in our experiment the optimal quantity was 4.398,27567 (rounded to five digits). A “trial and error” students may find 4.398 after 15–20 rounds, but a “calculation” student who estimates demand and calculates the quantity with an MR = MC approach will determine the quantity more precisely. Without fractional prices (as in Nelson and Beil) we would be unable to differentiate between such strategies. By allowing the participants to choose fractional prices and quantities (instead of whole numbers), our approach is closer to reality and able to give the students a more realistic picture of what markets look like and how they function. Only the right approach leads to the optimum, so that students who are able to determine the optimal level of production must have used the MR = MC approach. Students who try to estimate the optimal production by minimizing marginal costs and/or merely by trial and error do not obtain the profit-maximum. The changed parameters thus differentiate between students who used the wrong approach and those who used the right one.

Secondly, our incentive structure contains three elements, that is, an additional incentive for the applied strategy. Students who adopt the economic approach obtain extra points. Nelson and Beil [21] also offer bonus points, but only based on accumulated profits. We extend the practice of awarding bonus points based on profits into the final period and to the applied strategy during the experiment. We believe this to be important, because students should have an incentive to find the best strategy and not to stumble upon a good result by trial and error only. There is some evidence that bonus points have a positive impact on learning success (e.g., [22]). However, we can identify successful students particularly in the final phase of the experiment. Additionally, the student report on the applied strategy enables us to analyse their behaviour more precisely. Moreover, we present a method for collecting and using experimental data in an Excel framework and provide all the files needed by teachers free of charge.

Furthermore we do not include a line-of-credit to cover losses, because this is not necessary.

##### 2.2. Sample Experimental Procedure

In order to demonstrate the practical feasibility of the theoretical concept, in 2012, a sample experiment was conducted at the University of Kassel, Germany. Accordingly, 21 students of the seminar “Basic Concepts of Competition Policy” were asked to take part in the monopoly experiment. Given that the seminar was designed for advanced Bachelor students in economics or related subjects, it can be assumed that all participants had already attended introductory microeconomic courses before participating in this experiment. During the first classroom session, students were told that each of them would act as a monopolist, selling seven-league boots. Furthermore, they were provided with a cost function (TC), which was identical for all participants and read as follows:where is the total quantity in thousands. The constant demand was given by the following linear and decreasing function, which was, however, not known to the students:where is the price in Euros.

We used a profit calculator which generates the subject’s payoff when provided with his or her own selected quantity. Experiments that use a profit calculator are characterized by the fact that some investigators include a “best-response option,” which provides the quantity that maximizes the subject’s payoff. The design of the experiment cannot fully prevent collusion between students, so that how exactly the information is given to them is particularly important. Requate and Waichman [23] observe that less collusion occurs in the treatment with best-response options. In particular, there are only a few markets in this treatment that collude successfully. In our case, however, collusive behaviour was not observed at all. In fact, collusion in a cartel situation was not possible in our experiment, as each student operated in a separate market. However, we were using identical demand functions for all students. Through exchanging their experiences during the course of the experiment, students could therefore have discovered that they were all facing the same demand conditions and collude. We used identical demand functions for the sake of simplicity in our experiment. Nonetheless, our design does also allows for using differing functions. Teachers who wish to implement this in their own classroom should be aware that using multiple demand functions requires additional effort in the preparation and analysis of results. The experiment continued over a period of ten (weekly) classroom sessions. Each week, each participant submitted a bid for the quantity of seven-league boots that he was bringing to the market and the price he was asking on the university’s student online platform. Before students had to submit their next bid one week later, they were individually informed how many of their units had been sold at their asking price. To increase the probability that participants would be able to figure out the optimum combination within the given time frame, students were allocated a constraint, indicating that the profit-maximising quantity of seven-league boots would lie between 1000 and 5000 pieces per week (so: ) and the profit-maximising price would lie between 50 and 350. In the last period of the game, students were asked to provide feedback on the strategy which they had pursued during the experiment. Furthermore, participants were able to evaluate the classroom experiment.

To motivate students to take part in the experiment and to ensure that they provide the appropriate level of effort, participants were provided with bonus grade points for being successful in the experiment, which were based upon the following criteria: level of cumulative profits over all ten periods (40%), level of profit in the last period (40%), and strategy applied during the experiment (20%). We awarded bonus grade points for the “strategy applied,” firstly by considering students’ self-reports and secondly by aligning observed behavior with these reports. As discussed in Section 2.1, allowing for fractional prices and quantities enabled us to differentiate between student strategies with relative certainty. Students who had calculated the optimum by using economic principles and presented a convincing process of calculation in their reports obtained the best score. Students who used trial and error but showed an awareness in their reports that they should have used economic principles and explain why this is the case, as well as how they should have proceeded to calculate the optimum, obtained the second-best score. Participants who simply stated that they had used trial and error were awarded the lowest score. Students who did not explain clearly how they approached the experiment or whose explanations were not in line with their actual behavior during the experiment did not receive any bonus grade points in this category. A maximum of up to ten bonus points (ca. 20% of the final grade) could be earned by the students, which were added to the result of the written exam at the end of the seminar.

##### 2.3. Theoretical Solution

One of the first things which undergraduate students learn in microeconomics classes is that, having no rivals by definition, the monopolist has a unique position in the market. If he decides to raise the price he does not have to worry about potential competitors [24]. However, this does not imply that the monopolist is able to charge any price he wants for his goods—at least not if he aims at profit maximisation. Rather, to maximise profits, the monopolist needs to define his costs, analyse the market demand, and decide accordingly. In the classroom, this is typically illustrated graphically by establishing the profit-maximising quantity at the intersection of the marginal cost (MC) and marginal revenue (MR) curves, and finally determining the price from the demand function [24].

However, as in real-world situations, the demand function is unknown to the students participating in the monopoly experiment. Consequently, in order to maximise profits, participants basically have two options. The one is to approach the profit-maximising and by trial and error, exploring various combinations of total revenue and total costs until they have established the combination that constitutes a global maximum. The other option is to access their knowledge of basic microeconomic principles to locate the demand function and apply the MC = MR approach. In fact, students who have not attended microeconomic classes or do not know how to operationalize it are likely to use a trial and error strategy [21].

Table 1 and Figure 1 demonstrate how students can estimate the profit-maximising combination using economic principles. Applying economic principles would theoretically enable a student to find the profit-maximising combination in week three of the classroom experiment. Students have complete information about the cost curve. However, to identify the profit-maximising combination by applying marginal principles they first need to estimate the prevailing demand function. To achieve this, participants must choose combinations of price and quantity, which lead to overproduction in the first two weeks, bringing them back to the band defining the demand frontier after the instructor has informed them how many of the units offered had been sold at their asking price.