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Comprehensive case study

COMPREHENSIVE CASE IN MANAGERIAL ECONOMICS

Journal of Business Cases and Applications

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Rent-A-Car: An integrated team-based case study for managerial economics

ABSTRACT

Dmitriy Chulkov Indiana University Kokomo

Dmitri Nizovtsev Washburn University

The case study covers multiple learning outcomes and consists of several assignments designed to enhance understanding of both theoretical concepts and quantitative methods featured in the course over a semester. This case is particularly appropriate for a team-based learning curriculum.

Keywords: Managerial economics, case study method, team-based learning, M.B.A. curriculum

CASE INTRODUCTION

Rent-a-Car is one of the two car rental agencies serving a small regional airport in the U.S. Midwest. Forty percent of its customers are airline passengers and the remaining sixty percent are dwellers of the nearby college town who use rental cars for business and leisure trips. The airport is within two miles from campus and approximately six miles from the city center. It is easy to reach by car, taxi, or city bus.

You are a manager of Rent-a-Car. Your fleet consists of 72 cars, of which 47 fall into the ‘economy’ class and 25 in the ‘luxury’ class. Whenever demand for cars in some class exceeds the number of cars available, additional vehicles can be delivered from the nearest company hub in the state capital located 70 miles away. Alternatively, some customers unable to rent an economy-class car may be upgraded to a luxury-class car at no extra cost to them.

Your only competitor at this location has a more sophisticated system of car category tiers, which consist of Compact, Economy, Mid-size, and Large cars. More detailed data will be provided to you at a later stage. Upon receiving the data, you will be asked to examine various ways to improve the performance of this enterprise.

Journal of Business Cases and Applications

CASE ASSIGNMENTS – PART 1

In order to better understand your unit’s operating environment, you are asked to provide your estimate of the demand equation that would account for various factors that affect your customer traffic. This will be done by using regression techniques. Estimating the demand equation is useful for future analysis of your unit performance.

You need to request the data for your empirical study.

Specifically,

(1) What are you planning to use as the dependent variable in your regression? What units of measurement for that variable are you going to adopt?

(2) What other data would you need and can realistically get? You may request information about up to five independent variables.

For each variable you request, provide reasons why you expect it to be important for your analysis and explain the expected sign of the relationship between the proposed independent variable and the dependent one.

Teaching Notes

This assignment requires familiarity with demand and supply analysis, demand and supply functions, and regression analysis. The assignment forces students to think critically about the design of their empirical study instead of including every possible variable in a non- discriminatory “kitchen-sink” fashion.

In the process of working on this assignment, students will:

(1) explain the difference between dependent and independent variables;

(2) support their variable selection and explain why the variables are expected to be significant and relevant;

(3) justify the expected sign of each variable’s relationship with the dependent variable;

(4) use their creativity in selecting appropriate proxy variables if desired data is not available;

(5) examine the limitations of linear regressions which tend to work best on monotonic relationships;

(6) recognize that there has to exist a sufficiently large variation in a variable in order for it to play a meaningful role in a regression (such metrics as the population of the town/county are not likely to be particularly helpful in explaining week-to-week changes in customer traffic);

(7) use their common sense and understanding of causal, economic, and functional relationships between variables.

This exercise provides an opportunity to remind students that revenue or profit are not good choices for dependent variables, due to the complexity of factors involved in deriving those metrics and their resulting non-monotonic relationship with the price charged. A superior approach is to focus on clear-cut, easy-to-understand relationships whenever possible. In this case, the best candidate for the dependent variable would be some proxy for quantity demanded.

Assignment – PART 2

Is there any way to use last year’s data to forecast the demand for our “economy” vehicles in a specific week? (Week number is selected by the instructor as appropriate.) It would be even better if you could suggest a specific rate that we should charge for the “economy” category to maximize revenue.

How many vehicles do you expect to be rented at the rate you are suggesting?

Do we need to worry about increasing our fleet if we follow your demand forecast?

Teaching Notes

This assignment requires familiarity with demand equations, the concepts of elasticity, total and marginal revenue, and revenue maximization techniques.

In the process of working on this assignment, students get an opportunity to:

(1) Practice regression analysis techniques;

(2) Recognize and interpret the economic and statistical significance of regression variables;

(3) Evaluate regression results and present them in the form of a demand equation;

(4) Practice the relevant course material by performing revenue maximization.

Students are expected to select appropriate dependent and independent variables, use correct procedures for step-by-step elimination of insignificant variables, and select the best regression model from many possibilities, using such metrics as adjusted R-squared and p- values. Students are also expected to formulate the demand equation and present it in the form appropriate for forecasting. The demand equation may include variables that are exogenous and not controlled by the manager. The students have to develop their judgment on the appropriate assumptions about these variables in forecasting demand, and perform revenue maximization correctly. The data set described in Table 2 provides the choice between the two proxies for quantity demanded – the number of rental agreements initiated (*QE*) and the total number of rental days (*Q_length*). Students face the need to choose the most appropriate data variable among these. A possible conclusion here is that there is lack of correlation between a consumer decision about the length of rental and their decision to rent from a specific firm. There are numerous ways to demonstrate this idea, which helps the instructor to encourage student creativity and at the same time provide a basic introduction to alternative data-analysis techniques and approaches.

Provided the analysis is done correctly, the resulting demand equations and revenue- maximizing prices obtained by different teams are usually similar, even when they start with slightly different subsets of variables selected in Assignment 1. The advantage of this approach is that students are made aware of suspicious discrepancies in their results and therefore possible mistakes in their analysis not via the instructor’s verdict but by comparing their results including demand equations and revenue-maximizing prices with those of other teams.

(1) Show how “data visualization” may reveal striking patterns in the data;

(2) Demonstrate how breaking a composite variable down into simpler ones makes the analysis cleaner, produces more intuitively clear results, and helps with understanding complex relationships;

(3) Discuss correlation analysis and potential multi-collinearity problems.

Another possible follow-up to this assignment involves the following questions:

*While making the recommendation to adjust our own price, what assumptions did you make regarding **the competitor’s pricing?*

*How realistic **are those assumptions?*

*Can you suggest a better way to perform the analysis?*

In answering these questions, the students are expected to realize that changes in own pricing may induce a response from a competitor. Ideally, this response needs to be incorporated into forecasts. Allowing the teams to share their thoughts on the issue may serve as a good opener for the discussion of game theory.

Assignment – PART 3

We’ve been going back and forth on our philosophy regarding local advertising. As you know, each branch currently gets a $20,000/month advertising allowance but not everyone uses it completely.

Does it make sense for us to spend money on advertising locally? Why or why not?

Teaching Notes

Students are expected to be familiar with regression analysis and be able to read and interpret regression results.

In the process of working on this assignment, students will:

(1) Review regression analysis techniques;

(2) Derive the demand specification from the regression model;

(3) Interpret the economic and statistical significance of the estimated coefficients;

(4) Apply cost-benefit analysis to business decision-making.

Assignment 3 requires the students to examine and interpret the effect of a single variable – advertising – on quantity demanded. The students are expected to rely on quantitative analysis while developing their recommendations. For this case study’s data set, the estimated coefficient for the *TotalAd *variable in a multiple regression has low statistical and economic significance. This leads to a discussion of the optimality of advertising spending. Students are expected to relate the advertising expenses to the increase in revenue it brings about.

Students should not follow the stereotypical notion that advertising is always a good idea are led to think about advertising critically. When their preconceived notion is not supported by the data, the students either accept the empirical result or are forced to look for alternative explanations and missing variables. One potential explanation for the lack of significance is that advertising has a lagged effect. Another possible explanation is missing information on competitors’ advertising expenses. It is possible that competitors’ advertising actually negates the positive effect of own ads. Once again, this discussion may help the instructor transition to game-theoretic topics.

An extension to the problem requires the parts of the data set that describe advertising spending on various media:

*If advertising looks like a good idea, then what media would work the best for our advertising needs and what aspects of our product offering should we highlight the most?*

Assignment – PART 4

Previously, we established our revenue-maximizing price.

What if we want to maximize not revenue, but profit?

Would the revenue-maximizing price do the trick, or should we raise or lower it?

What additional information do we need to answer that question accurately?

Teaching Notes

This assignment offers an opportunity to show the effectiveness of the marginal approach in obtaining intuitive answers.

In the process of working on this assignment, students will:

(1) Review the concept of marginal revenue;

(2) Recognize the relationship between marginal revenue and price for an imperfectly competitive firm;

(3) Identify relevant components of marginal cost for a business unit;

(4) Analyze and contrast revenue and profit maximization in a graphical format.

For a firm that operates in an imperfectly competitive market, the marginal revenue (MR) is decreasing in quantity produced and sold. Total revenue is maximized when MR=0, whereas the profit maximizing quantity corresponds to MR=MC. Since the marginal cost (MC) of renting the vehicle is always positive, a firm facing a smooth demand curve will always maximize its profit at a smaller quantity (and therefore higher price) compared with revenue maximization. Therefore, students are expected to recommend a price increase, the exact size of which is open for discussion.

Initiates the discussion of what the marginal cost of renting a vehicle out includes. Students should not incorrectly claim that, since the vehicle has already been purchased by the company, its cost is sunk and MC=0. This is incorrect and allows the instructor to review the concept of opportunity cost. The vast majority of rental vehicles are later resold in the secondary market, and the resale value of a vehicle depends heavily on the mileage. Additionally, every vehicle has to be serviced periodically and re-conditioned for each new customer. Coming up with an all- encompassing estimate for the marginal cost of each rental is a useful exercise in data mining.

Assignment – PART 5

When we develop our pricing recommendations, do you think we should focus on maximizing revenue or profit?

Please provide your thoughts and argumentation for which approach is better and make recommendations for pricing our economy vehicles in these weeks of the year (weeks are selected by the instructor as appropriate).

Our accounting department estimated that the cost of a rental is $16.37/day for an economy vehicle and $24.34/day for a luxury vehicle, plus $8.70 per rental contract for re- conditioning, for either type of vehicle. Delivering an additional vehicle from our state capital hub costs the company $35 on top of all of the above.

Teaching Notes

In the process of working on this assignment, students are expected to:

(1) Use the demand equation obtained from Assignment 2 above to derive the analytical expression for marginal revenue as a function of quantity;

(2) Analyze unstructured data to quantify marginal cost;

(3) Use the marginal revenue to marginal cost comparison to arrive at the profit- maximizing price-quantity combination.

Students should exercise care in distinguishing between average and marginal costs. Either use the estimates for the marginal cost of each day of rental they obtained for Assignment 4, or rely on data provided by the accounting department. In the latter case they should be reminded that reliance on average costs can produce misleading results in terms of profit maximization. First, the average cost figures may include fixed costs independent of the decision to rent the vehicle out. Second, they are often based on aggregate historical data and therefore fail to accurately reflect the cost to the firm of the decision to rent out an additional vehicle, which should be the focus of cost-benefit analysis.

Assignment – PART 6

Currently, all our customers are charged the same daily rate. (The only exception is customers under 25 years of age who have to pay the $12.50 daily surcharge according to the company policy.)

What are your thoughts on our chances to increase our revenue and profit charging different prices to different groups of customers?

If you think we should explore such a possibility, make sure to include the details of the implementation plan.

Teaching Notes

This assignment follows the discussion of pricing strategies and requires familiarity with the concept of consumer surplus, as well as various pricing strategies, including price discrimination, volume discounts, and tiered pricing.

The following pedagogical objectives are achieved by this assignment. Students will:

(1) Recognize the necessary conditions for successful price discrimination;

(2) Compare and contrast cost-based and value-based pricing approaches;

(3) Apply theoretical foundations to forecast the expected outcomes of various pricing strategies.

Additional discussion question is: *Is the ‘under**–**25’ surcharge an example of **price discrimination?*

For this question, students are expected to recognize the fact that younger customers are likely to have lower income than general population, which may affect the elasticity of their demand. The instructor may facilitate a discussion of the optimal number of pricing tiers in this context.

Assignment – PART 7

Our customers who choose to keep a car for an extra day are currently paying the same base daily rate. Do you see any potential in exploring alternative schemes? If so, what changes should we implement – price those extra days at a higher rate? Lower rate? What considerations are involved in this decision? Provide your thoughts on this issue.

Teaching Notes

This assignment builds further on the topic of pricing strategies.

Learning outcomes for this assignment include the following. Students will:

(1) Explain the reasoning behind volume discounts;

(2) Recognize the impact of increasing marginal cost on supply;

(3) Describe the negative impact of uncertainty on firm’s operations.

Students are expected to contrast the volume discount philosophy with the need to account for increasing marginal cost due

to uncertainty resulting from customers keeping a car for an extra day. The former consideration suggests the optimality of charging a lower rate for additional days whereas the latter one calls for an increasing rate to cover the rising inventory costs. Both considerations are valid and need to be weighed against each other. Students may also be able to reflect on the possibility of moral hazard created by consumers who would take advantage of the lower-extra-day-rate scheme by renting a vehicle for a short term at the base rate and then extending the length of the rental as needed, reducing the company profit potential. The best answers would recognize and explore the distinction between attracting customers willing to rent a car for a longer term and spontaneous decision to extend the lease. The discussion of uncertainty issues serves as a preamble to an in-depth coverage of the economics of uncertainty and information typically done later in the course.

Assignment – PART 8

Our competitor has launched an aggressive ad campaign, advertising the $24.99/day rate for an economy car starting next week. This is a sharp $8 decrease from their average price over the last four months. Based on their prior pricing patterns, we expect the same price reduction to occur in their other vehicle categories.

How strong of an effect, if at all, do we expect this announcement to have on our weekly revenues if we maintain the price you have recommended previously?

Should we try to respond to their price reduction with one of our own, or should we ignore it and proceed doing business as usual?

If we decide to reduce the price, how deep should our discount be?

Teaching Notes

In this assignment students will:

(1) Reinforce the understanding of the demand function and revenue maximization methodology;

(2) Apply the best-response technique and other game- theoretic concepts.

In order to answer this question properly, students are expected to go back to the demand equation that included the competitor’s price (*Pcomp*) as one of the independent variables. The procedure is no different from the one used in assignment 2. In both cases, students have to pick a value for *Pcomp *to plug into the demand equation before they proceed to revenue maximization. In the present assignment, the lower value of *Pcomp *will result in a smaller vertical intercept of the demand curve for Rent-A-Car vehicles and consequently in the lower optimal price it should charge.

Additional questions :

*(1) Estimate the maximum attainable revenue we can achieve if the competitor offers a discou**nt and if they don’t**.*

This question required students to carry out the revenue maximization

procedure.

*(2) Would your answer differ if the forthcoming week is expected to be heavy in the volume of rentals?*

This is an intentionally ‘tricky’ question. Students need to realize that an increase in demand would be reflected in the demand equation. Therefore, this question de facto overrides the preceding quantitative analysis done for the ‘regular’ demand conditions. While students should be able to answer the question based on intuition, a quantitative approach based on a modification of the demand equation is also possible and preferred.

Assignment – PART 9

Trying to avoid the need to assemble our think tank every time our competitor alters their price, could we possibly come up with some sort of a magic formula than would help us quickly pick our price in response to theirs?

Teaching Notes

This assignment works well as a follow-up to an in-class discussion of Assignment 8. It utilizes a more general approach to revenue maximization, suitable for more quantitatively inclined students. Student will:

(1) Practice the best-response technique on a general-form demand function;

(2) Apply quantitative analysis skills.

It is possible to carry out the entire revenue maximization procedure while keeping the competitor’s price (*Pcomp*) in the equation as an unknown parameter. The resulting own optimal price will then be a function of *Pcomp*. Another possibility is to try several levels of *Pcomp *and find corresponding optimal own prices using a spreadsheet. This method is more labor intensive but some less advanced students may find it easier to understand. The utilization of this approach also provides the instructor with an opportunity to demonstrate that the formula obtained through the use of the more general approach produces the same result as a spreadsheet but does it in a more concise way.

Note that Assignments 8 and 9 are stated in the context of revenue maximization. If the students’ quantitative proficiency allows, both assignments can be easily modified to include profit-maximization.

Assignment – PART 10

One of the board members inquired about the use of a “price match guarantee” which would mean we promise to match our competitor’s price for a certain vehicle category if their price happens to be lower than ours. I need your opinion about the viability of such a policy in our case – would it be a good idea? Separately, how widely should we advertise such a policy if we decide to adopt it?

Teaching Notes

In this assignment students will:

(1) Recognize the theoretical basis for price matching;

(2) Apply game-theoretic concepts to pricing decisions.

Two themes tend to prevail in the discussion of price-matching policies. On one hand, a price-matching policy can serve as a tool for price discrimination between informed and uninformed customers. The rationale is that price-sensitive customers put more effort into searching for discounts and are more likely to receive the reduced price matching that of a competitor. Groups with less elastic demand continue to pay the price that may exceed that of the competitor. According to this logic, the availability of information should be limited.

On the other hand, price-matching guarantees may help facilitate implicit price collusion and avert price wars in concentrated markets. This is because once a merchant adopts this marketing tactic, its rivals can no longer lure away its customers by charging a lower price, and therefore have little incentive to initiate a price cut. According to this logic, it is better to make the price-matching policy widely known. Once advertised, it effectively places the responsibility for pricing policy onto the competitor. An important caveat to this approach is that it is effective only if the firm offering the price-matching guarantee has a cost advantage over the competitor. Otherwise, commitment to such a policy can be self-destructive in the case of a price war.

Current theoretical and empirical research on the issue recognizes both sides of the argument and is inconclusive on this issue. Students would benefit from a discussion involving both points of view. For best results, the assignment should follow a discussion of repeated prisoners’ dilemma type pricing games.

Table 1. Description of the variables in the data set

PownE |
Average daily rate Rent-A-Car charged for its economy cars in a given week |

PownL |
Average daily rate Rent-A-Car charged for its luxury vehicles in a given week |

Pcomp |
Average daily rate of the only competitor across all vehicle categories |

Session |
Binary variable with 1 indicating weeks when college is in session |

Weather |
Number of days in a week with severe weather |

Unemployment |
Number of unemployed workers in the county as of Tuesday each week |

FlghtWk |
Number of flights (in- and outbound) serving the local airport that week |

CancWk |
Total number of flights cancelled that week |

Holiday |
Binary variable with 1 indicating weeks of national holidays (long weekends) |

Wrecks |
Number of major accidents that week |

Discount |
Number of customers in a given week using the 15 percent discount off the base rate offered through our affiliate partner, a credit card company |

Upgrade |
Number of customers who received a free upgrade to a luxury vehicle due to the unavailability of economy vehicles |

TotalAd |
Amount spent on local advertising each week |

AdBlbd |
Weekly spending on billboard ads |

AdPaper |
Weekly spending on ads in local newspapers, including the online version |

AdTV |
Weekly spending on ads placed with local TV |

QE |
Number of rental contracts initiated each week in the economy category |

Q_length |
Number of paid days of rentals, grouped by the agreement starting date |

Age<25 |
Number of rental agreements in a given week for which the person listed as the primary driver on the rental agreement was less than 25 years old |

Age25_50 |
Number of rental agreements for which the person listed as the primary driver on the rental agreement was between 25 and 50 years of age |

Age51+ |
Number of rental agreements in a given week for which the person listed as the primary driver on the rental agreement was 51 years of age or older |

FleetAge |
Average age of our fleet measured in weeks |

BedTax |
Amounts collected from the 1% local hospitality tax in the county – this information is reported only on a monthly basis |