Playing Game Theory for an Exam: Large Classes and Small Classes

Playing Game Theory for an Exam: Large Classes and Small Classes

Zehra, Adaora, and Anna

            For some classes at Mount Holyoke, grades are given on a curve, often so the averages is a B or B+, to reflect the average grade of all of Mount Holyoke. In Macroeconomic Theory, a grade doesn’t mean anything by itself, it only means something compared to the other students.  Since the average grade is a B+ every year, it means that every year, the number of questions needed to make a B+ changes. Some years, if almost every student gets every question right on every exam, getting one more question wrong than the class average may put a student at a B-, even though if another year, if a class wasn’t as bright, the same number of questions right on the exam may be an A. This also gives the class has control, in theory, of how what a B+ should be. If everyone in the class makes sure to do poorly on an exam, the B+ would not be only a few questions answered correctly. However, this means if one person did ignore the class’s plan and answered a few more questions correctly than the original plan, they would get an A without doing particularly well, presenting a form of Prisoner’s Dilemma, with the Nash Equilibrium of always doing well, or at least trying to do well, in an exam or paper.

            Even in small classes, a curve on an exam sometimes arises. Though the teacher may not mean to, but if everyone in a six or seven person class didn’t do well on an exam or paper, the professor may deem the topic or exam questions too hard, trusting her students to have tried their best, and add bonus points if it is an exam, or reading papers with a lower standard. Therefore, students also have the Nash Equilibrium of doing their best, no matter what the other students may have decided.   

The Economics of College Tuition Fees

                                        

The Economics of College Tuition Fees

Lina, Olivia, Xinyang and Yang

If you are sensitive to price changes and the money you (or your family to be more specific) spent, it’s not too hard to notice that the tuition fee of Mount Holyoke College is increasing through your staying here and that everybody’s bill has a different number on it. Why is that?

In the 2011-2012 school year, Mount Holyoke’s tuition is $41,270. Room and board cost $12,140. Including student activities fee of $186, the total amount is $53,596. ( Type in the following website address to check the latest tuition fee number: http://www.mtholyoke.edu/admission/tuition_finaid.html. ) According to an online ranker website DMVFollowers, this year Mount Holyoke ranks #66 among the top 100 most expensive colleges in U.S. (http://www.dmvfollowers.com/?p=3631) Taking into account the quality of education that has been offered here, this ranking doesn’t look too unreasonable. However, it should not prevent us from exploring the economics behind college tuition fees either.

According to the College Board, the average cost of tuition and fees (including costs for books, transportations etc.) for the 2011-2012 school year is $42,224 at private colleges, $21,447 for state residents at public colleges, and $33,973 for out-of-state residents attending public universities, while the U.S. median total household income is only $49,445. This partly explained why the amount of student loans taken out exceeded $100 billion last year.

How does economic theory explain the expensive and constantly increasing college tuitions fees?

One obvious reason could be resulted from the development of new knowledge and programs. However, William Bowen has proposed a theory in 1967 attributing the constant increase in college tuition fees to the fact that higher education institutions were not sharing in the productivity gains that applied to the rest of the economy. For example, in a college like Mount Holyoke where student vs. faculty ratio is almost fixed, faculty productivity doesn’t increase over time (because they always teach fixed number of students). While in other industries, increasing productivities push wages to go up. Therefore, if the college administrators restrict tuition growth rate to inflation rate, faculty salaries would fall behind the earnings of other professionals, which is not beneficial for colleges in the long run.

In terms of profit maximization, it’s hard to judge whether high prices are optimal for colleges because the demand curve for college admission is downward sloping. The higher the tuition fee, the fewer the people who would be willing to pay.  Thus theoretically, all colleges would eventually reach a point where increasing tuition fee causes shrinking profits.

Then what do colleges do to improve the situation and enhance their profits?

Unlike pure monopolies, colleges have a tool that doesn’t exist in most other industries: colleges can charge different prices for each individual student by granting different amount of financial aid!

In a monopolistic model without financial aid, the college can only pick one price (p_1, p_2 or p_3):

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In the graph, revenues are areas of the rectangles.

However, if we include financial aid into the model, each one extra unit can take a different price. For example, if we just want to limit our price to be below p_1 and above p_3, we can get the whole area below p=p_1 and the demand curve, and left to q=Q_3.

PVTA Buses: To Run or Not to Run, That Is The Question!

PVTA Buses: To Run or Not to Run, That Is The Question!

by Linda, Rudmila, Alina, Taniko

Who stayed on campus during Thanksgiving break?  Not a lot of people.  Many students were able to leave campus to celebrate the holiday.  Thus, there was a huge decrease in the number of students who stayed on campus.  There were, however, students who stayed on campus to catch up on school work, complete internship application, study abroad paperwork, and even visit friends in the neighboring five colleges, such as Smith, Amherst, Hampshire, and UMass Amherst.  However, for the students who stayed on campus, how could they visit their friends at the neighboring colleges if the Pioneer Valley Transit Authority (PVTA) buses were not running?

PVTA buses run throughout the five colleges as well as the pioneer valley.  Students at the five colleges can ride on it without paying for it themselves.  PVTA buses are a public good.  They have a positive externality for college students, but have a negative externality (air pollution) for the environment.  They are non-excludable and non-rival.  For example, it is not possible to prevent anyone who has not paid, from having access to it.  Anyone who wants to ride the bus, can.  Also, just because Linda is getting onto the bus does not mean that Taniko can’t.

When thinking of running the PVTA buses, one needs to analyze the cost of doing so.  For example, the fix cost (FC) is the bus itself and the lot to house the buses when they are not running.  The variable costs (VC) are gas, employees, maintenance costs, cost of insurance, etc.  Every semester, there is a range of possible variable costs that the five colleges (Mt. Holyoke, Smith, Hampshire, Amherst, and UMass Amherst) contribute to, in return for offering the public good on campuses.  All five colleges must pay for the PVTA buses, but UMass Amherst runs it.

Depending on which time of year it is, the PVTA runs on different schedules. For instance, during J-Term and summer, the PVTA buses run less frequently, on a minimized schedule and it may only run every half an hour or every hour in order to minimize cost due to fewer students and less demand on campuses.  During spring, fall, Thanksgiving, and December break, when the PVTA buses do not run at all, there is an opportunity for extra revenue by PVTA from the few students who decide to stay on campus.

With this new opportunity for revenue, the PVTA needs to analyze the cost of providing such good during those breaks.  Before PVTA can make this decision, they need to be sure that the revenue generated from this period will be greater than the cost to run it during this period.

The Confessional

The Confessional

by Regina, Auste, Gabriela, and Jenna

The Confessional. The name itself is steeped in controversy. Is it a platform for free expression or a festering pit of inanity? It is unknown if Wilder Bowl LLC makes a profit from the notorious forum. When reaching out to the Confessional community for an answer the only response we received was “It’s … entertaining, duh.” (profanity omitted).  The current owner Shibo Xu bought the website for $750 in 2007, but the motive of this purchase is unclear as in many ways the Confessional serves as a public good to the Mountain Holyoke community. It is non excludable and once used it does not diminish other individuals potential use. And as noted, public goods are not profitable. The Confessional’s Facebook page states it’s mission as such: “A space to share thoughts, debate ideas and communicate...anonymously.” But has this mission been successful?

As a public good, the Confessional is in high demand with almost 3,500 pages filled with posts. Students will go on when they are off campus and access it from their cell phone if the internet is down. In some ways the Confessional has become more than a forum for debate. Amongst the numerous crush posts and angry rants a sort of free market has arisen. Towards the end of the semester numerous posts are dedicated to the sale of unwanted items. Graduating students looking to unload no longer need mini fridges and storage bins abound, as do students looking for a perhaps slightly more generous offer on their used textbooks. In this way the Confessional enables commerce that would be more difficult to facilitate in it’s absence and it has the convenience of advertising to the target market. Without the Confessional students would have to place advertisements in local papers, increasing their operational costs and diminishing their profitability.

The Confessional also facilitates another type of exchange: information. During October alone, there were over fifty posts about Mountain Day. While the President is the only one with complete information regarding Mountain Day, the information exchange facilitated by the Confessional is able to level the information inequality. On the other hand, as the number of posts increases regarding Mountain Day, the responses tend to be more agitated and obnoxious. Thus, the law of diminishing marginal utility holds true.

Also, students use the Confessional to seek advice, which can benefit some socially. However, in the anonymous nature of this forum asking for help can lead to responses that are malicious. This cyber bullying has a high social cost. Specific students may feel singled out for ridicule on the Confessional. There have been posts demanding the Confessional be deleted, as it is too costly to society in the eyes of some. Moreover, the Confessional has a high cost to students’ productivity in regards to their schoolwork. It is commonly used as a distraction, drastically decreasing a student’s utility.

Despite the high social costs that the Confessional creates, it is debatable whether or not taking down the website is a solution. If the website is removed, the likely hood of it popping up on a different domain is high, as many colleges have a Confessional equivalent. Because the Confessional and websites alike are the norm for campus’ it’s absence at Mount Holyoke would dually felt by the student populous.

The price strategies of Blanchard café

The price strategies of Blanchard café

by Mindan, Yanni, Syeda, and Jiayi

How many times have you been to Blanchard Café this semester? Have you ever felt frustrated that your meals kept exceeding the meal plan dollars—$7.25? Have you ever thought about the sales strategies of Blanchard café?

In fact, foods and beverages at Blanchard are very well calculated. The items at Blanchard, except for the special and classic salads which are exactly priced at $7.25, can be grouped basically into the following categories: soup($1.99), snacks (mostly $1.09 with some $1.29), dishes ($3.25 to $4.25), fruit ($0.65), burgers ($2.65 to 5.75), pizza (mostly $2.5 with some $3.5), ice cream (starting at $0.5), hot drinks (small coffee at $1.99, small tea at $1.65, coco at $0.65), regular salad ($4.25), cold drinks and snacks (yogurt $1.75, fruit $2.25, beverages ranging from $1.25 to 3.99).

In most cases, if one wants to order her meal among the various above-mentioned options, she may choose one item from group A (burgers, salad, pizza, dishes), one from group B (soup, fruit, cold food), one from group C (coffee, coco, drinks), and perhaps additional one from group D (snacks, ice cream). Now let’s do a brief analysis of the prices of items from each group. For group A, the items’ prices vary from $2.65 to $5.75, but most of them are priced at between $4.75 and $5.25. Hence, the price average is around $5. For group B, the prices vary from $0.65 to $2.25. However, based on my observation, most people won’t choose the item that costs$2.25. Instead, they would like to have a soup or one to two fruits, so the average price goes around $1.5 to $1.99. According to all the information above, if one chooses two items, each of $1.5, from group A and B, subtracting the costs from $7.25, she would only have $0.75 left! Now one can only choose coco from group C. It is worth noting that there is not a single item that is priced at exactly $0.75 in Blanchard Café and the cheapest one still costs $0.65 with the exception of a small bag of frozen carrot. It then follows naturally that one would either waste $0.1 of her meal plan or have to pay for the extra. Assume that there are 300 students on average who waste $0.1 in Blanchard Café per day, it will generate a considerable profit of $6000 for the college per year.

If one choose her daily meal following the exact pattern of the one mentioned above, the maximum price of $7.25 may be reasonable. Bearing this limit in mind, one can enjoy a very simple meal with a main dish, a soup or some fruit, and a drink. However, if different individuals’ preference are taken into consideration, then this proposed pattern will no longer hold. For the main dishes, the preference’s effect on prices is almost insignificant. However, for most students, a coffee is usually preferred over a coco for drinks, especially during the cold seasons. As for Massachusetts, cold weather lasts much longer than warm weather during a school year. If one adds a coffee and a main dish to her meal, then the price will go up to $6.5, leaving only $0.75 to spare. But since no item costs exactly $1 at Blanchard, there are only two choices available. One could get a fruit for $0.65 and waste $0.1 (Case 1), or she could get a snack for $1.09 and pay extra $0.44 (Case 2). In either way, you are indeed worse off.

From the perspective of profit maximization, the price ceiling of the mean plan for Blanchard Café is better to be $7.5 than $7.25. As mentioned above, if a student chooses a coffee and a main dish as her meal, then she will have additional unused $0.5 left. She might then decide to buy a fruit and pay the extra $0.15. In addition, she could choose pay for the cheapest carrot for $0.3, in which case she would lose $0.25. In case 2, one can have a main dish and a coffee with $1.01 left. She may go on to get a snack and pay extra $0.08 instead of wasting $0.46, which would happens if she buy a fruit. Thus, Blanchard’s profit is increased. Furthermore, if the price limit is raised to $7.6, then students can easily purchase foods with total costs of exactly $7.6. As a consequence, Blanchard’s profits will not be maximized.

It’s very interesting to analyze these price strategies. All in all, since profit is the primary concern for business, it is not surprising that Blanchard Café would have set such a price limit for student’s meal plan.

Student Parking: Economic Rationing at Mount Holyoke

Student Parking: Economic Rationing at Mount Holyoke

By Auste, Gabriela, Jenna and Regina

While studying for Microeconomics midterm in the library, we have heard someone complaining that it is so hard to find a space to park a car on campus. And this is not the first time we hear such complaints... Many people say that even though they are required to pay a lot for a parking space (150 dollars a year), they are never able to find a spot quickly. When they finally succeed, they realize that their residence hall is so far away from the parking lot. Yet, when you come back the next day, you find a parking ticket, because you accidentally parked you car in a wrong parking lot…

At Mount Holyoke we are given a lot of free, more precisely included in the tuition, goods, such as a room, a bed, a closet, a table, a chair, three meals a day, activities in the residence halls, public lectures, art museum, gym… But what about a very important thing for a student – a parking space? Generally, if you have a car, you are likely to use a parking space many more times than you visit the museum. It is so convenient to bring your car to the campus and go to the other towns or colleges with your friends since PVTA buses are never on schedule or do not arrive when you need to catch it before your final exam at another college.

Well, if you are an economist, you quickly see that the parking fee is just the economic rationing. Rationing is used in order to have a relatively stable level of consumption of some good, because when a fee is imposed, the demand for the good decreases. Sometimes, this method is also used to discourage bad behavior, such as high taxes on the cigarettes to prevent people from smoking.

There are a few possible reasons why we have a parking fee (tax). One reason is that Mount Holyoke is trying to be green. It is trying to reduce consumption of water, electricity, to-go containers, and probably the number of vehicles on campus. Reducing the cars reduces the pollution, so we will have cleaner air. The other, more likely, reason is that there is a limited amount of parking places available for students, so in order to have a sufficient amount without a need for expansion, we need to have a fee, which would decrease the demand for having a car on campus. A quite old (2003-2006) statistical data table on Mount Holyoke website suggests, that the amount of student cars on campus has already slightly decreased. This may have happened due to the parking fee since the number of students increases every year.

In conclusion, this example shows that not only the government uses rationing to control undesirable behavior, but also the college practices such methods to control students’ behavior on campus.

But the reality is: bring your car, pay the fee, and you will have a lot of friends (who will use your car as a public good to go to the mall).