Maximizing Profit: how high will our campus store price its goods?

Maximizing Profit: how high will our campus store price its goods?

Alice, Congyi, Isha and Linda

We all know that the MHC campus store is expensive. It is a monopoly on MHC apparels such as sweatshirts and (weirdly enough) bandeaus and can thus self-determine the prices of these goods. As a monopoly, facing downward sloping demand curve, how does our campus store determine the prices of everyday goods? Also at what price and quantity does it maximize profit?

With changing seasons, people are becoming sick more often. Since DayQuil is one of the few options on campus to combat a cold or the flu and Mount Holyoke students can rarely afford taking time off to fully nurse their illness. Lets look at an example of how the Campus store may set price to maximize profits. Let the inverse aggregate demand function for DayQuil from the campus store be P = 24 - 4Q, and the cost function as C (Q) =Q²-2Q. Since the Store is situated on campus, it does not have to worry about paying rent; thus, for now, the fixed cost is zero. So the question is at what price and quantity would the Campus Store maximize their profit?

We know that the campus store is a monopoly. If the campus store wants profit maximization, the optimal price and quantity would be where their Marginal Revenue (MR) equals to their Marginal Cost (MC.)
 (As demonstrated in the graph)

So, let’s do profit maximization for the Campus Store, this way we can get the price and quantity

We know, P=24-4*Q and C (Q) = Q^2-2*Q

Total Revenue = (24-4Q)*Q = 24Q-4Q^2

Marginal Revenue = 24-8Q.

                      

Max (Q) = P*Q- C(Q) = 24Q-4Q^2 - (Q^2-2*Q)                                                      

FOC : 24-8Q-2Q+2 = 0

                     24-8Q = 2Q-2                                             

                            Q = 2.6                                                                                              

So P = 24-4Q = 13.6                       

Now the Profit (π)= TR-TC

                               = P*Q – C (Q) = (13.6*2.6 ) - ( 2.6²-- 2*2.6)

                              = 23.4

From this example of the Campus Store and the product DayQuil, we maximized the profit and got profit of 23.4, Price as 13.6 and Quantity as 2.6. At this quantity the marginal revenue is equal to the marginal cost. Therefore this would be the optimum price at which Campus store could maximize its profits.

Shopping for Pareto Efficiency

Shopping for Pareto Efficiency

Group members: Shelley, Xianger, Lady, Delia

Public goods are goods that must be provided in the same amount to all members of a society. Economists refer to these types of goods as “non-excludable” and “non-rival”. “Non-excludable” means there is no way to prevent another person from using and benefiting from the same public good. Public goods cannot even be withheld from those who do not pay for them. “Non-rival” means that one’s usage of the good will not decrease the amount that is available for others to use. The availability of the good is never reduced. National security, street lights, and lighthouses are all examples of public goods.

One downside is the free-rider problem. Public goods can not exclude anyone from benefiting from them. A problem that arises is that members of a society do not have the incentive to provide public goods. Instead, they have the incentive to be free riders - those who get the benefit of the the public good but do not pay for the provision of that good. A rational person would not pay for a service that s/he could benefit from without paying. However, if a free rider problem exists, public goods are not provided at their Pareto efficiency level. The following story shows an example in which public goods are provided at the Pareto efficiency level.

           

In the Mount Holyoke community, public goods can be shared among roommates.

We have four women who chose to live in an apartment in Buckland Hall.The apartment comes with a kitchen and a bathroom that they can share. In order to pay for their apartment’s public goods, the roommates all decided to chip in money for the additional utensils. Each person chipped in with $3 that will go towards buying an additional utensil for the public spaces. This amount of money is the value that roommates place individually on an additional utensil, which goes to the marginal utility of using the utensil. Assuming the equation for the cost of the amount they use the utensils is C(G)=G^2, we take the first derivative of the equation and get the marginal cost of 2G. Provided that the equation for MRS1+MRS2+MRS3+MRS4=Marginal Cost, where MRS1 is equal to the marginal utility (MU) of using the utensils divided by marginal utility of using other goods except for utensils for person 1. The same logic is applied to MRS2 which is the MU of using the utensils divided by MU of using other goods except for utensils for person 2. Similarly, MRS3 is the MU of using the utensils divided by MU of using other goods except for utensils for person 3, and MRS4 is the MU of using the utensils divided by MU of using other goods except for utensil for person 4. Since income has been spent on only one good (e.g., utensils) and the MU of using other goods except for utensils is 1, the sum of marginal utility of each person equals to the marginal cost. Therefore, the sum of the total marginal utility equals the marginal cost. This makes sense in this case when finding out the pareto efficiency level because if the sum of MU of the four students is greater than the marginal cost of buying an additional plate, then the students will keep buying the utensils. Thus, making the equation sum of MU=MC allows us to find the pareto efficiency level of the number of utensils to be bought. Since the MU for each person is $3, the total marginal rate of substitution for these four women is 3*4=2G. Solving the equation, we get  G=6. Therefore, the Pareto efficiency of the number of utensils is 6.

Similarly, this example can apply to the purchasing of additional ceramic plates. Each person chipped in $4 for buying the additional plate. Using the same equation as above, the cost of the amount they use the plates is C(G)=G^2 and the marginal cost is still 2G. Marginal cost remains MRS1+MRS2+MRS3+MRS4 and the only thing that changes is that the MRS for each person is now $4. This makes the total marginal rate of substitution 4*4=2G, resulting in G=8. In this scenario, the Pareto efficiency of the number of plates is 8. This is how the Pareto efficiency is calculated for these Buckland residents paying for additional utensils and ceramic plates.

However, sharing public goods do not always work out ideally. Most of the time, having free riders is unavoidable. One possible way to solve this problem among roommates is have all of them take a Microeconomic Theory class and learn how to maximize their utilities by studying the marginal cost equation above.

Amtrak: Price Discrimination in the Pioneer Valley

Amtrak: Price Discrimination in the Pioneer Valley

Edmee, Marilyn, Yuzhi, Jenni 

We all have benefitted from the Peter Pan buses services. What a great opportunity to go to NY or Boston for the week-end! Of course if the tickets are sold out, you can go to Springfield and catch a train. But most of us prefer to take the bus!

Imagine if one day Peter Pan exit the market. What would you do? What would your options be to go home or to visit a friend? You could take a taxi but to go to Boston it would cost you around $180/$200 and it is too expensive for college students like us.

Therefore, we would be left with only the train option. In this situation, Amtrak becomes a monopoly in the transportation services market. With this situation, students began to worry about what prices would be and how they would be fixed. So Amtrak decided to work with price discrimination to try to satisfy all types of consumers.

The company began with what is called: the first degree price discrimination. Prices were settled in order that each individual were charged their exact willingness to pay. For example, Lucie a Mount Holyoke student wanted to go to Boston for the week-end but wanted to spend only $5 on her train tickets, and this amount became what she paid.

Unfortunately we would all want to go everywhere for free, we would lie to Amtrak about our willingness to pay and there would be no way for Amtrak to verify our actual willingness to pay.  Therefore this first-degree price discrimination is impractical and Amtrak started to review their method to set prices.

Thus, Amtrak considered using the second degree price discrimination. Here, the company tries to charge different prices for different quantities of goods. For instance during holidays, the company quantity discounts for bulk purchases, cheap early bird tickets and even high prices for last minute purchases (consumers will definitely buy the tickets as they have no choice). Since the Pioneer Valley has a large population of students, using this price strategy will be beneficial for Amtrak especially in seasons where students want to buy group tickets to see a concert in Boston or just to visit a museum as a class. As people have no choice, using discounts for quantity purchases may even help Amtrak increase the number of hours of their services as they can cater for more customers while increasing their profits.  

As monopolist make various decisions to increase profits, they also think about how they can satisfy other groups while maximizing profits. Another interesting decision that Amtrak can take is to use the third degree price discrimination. Noticing the different groups of people living in the community (students, senior citizens, workers, etc.), they divide the market into segments and created slightly different prices for each group. This will help them to maximize their profits in the future as they continue to remain a monopoly because they continue to satisfy the needs of each and every individual. Students and senior citizens may pay fewer prices compared to professors and workers alike. These market segmentations are linked to consumers’ willingness and ability to pay and thus more customers are attracted to Amtrak as they gain the trust of the producer.

This is how Amtrak will be able to stay as the only monopoly in the pioneer valley as they are able to use price discrimination strategies to satisfy different consumers in the market while maximizing profits for themselves.

Rao’s and Uncommon Grounds – Location Model

Rao’s and Uncommon Grounds – Location Model

By Liz, Paula, and Weiding

Oligopoly refers to market with a small number of firms. Each firms behavior is interdependent of the others meaning one firms choices affect the other firms choices. Consider Coke and Pepsi, the price Pepsi charges affects not only their sales but the sales of coke as well. Game theory analyses the strategic behavior of firms whose choices are interdependent. Each game has a player (firms), strategy (the choice the players have e.g. where I should locate the firm) and payoffs (what the player obtains as a result of playing the game). Below is an illustration of location model between Rao’s and Uncommon Grounds.

 Both Rao’s and Uncommon Grounds sell beverages, cookies and cakes .The differences between them are the quality of their products and their locations. Rao’s is located in the library while Uncommon Grounds is in Blanchard and Uncommon Grounds has higher quality of goods. Rao’s attracts students who like to study in the library and who live near the building. Those students are willing to give up the pleasure that they can get from Uncommon Grounds’ more delicious milkshakes, smoothies cupcakes for the convenience of a closer location. They choose to go to Rao’s because they value their time more than food or drink and don’t want to waste it on transportation. The same conclusion applies to Uncommon Grounds. 

            In a case where the two firms are differed only by locations, as we covered in class, the two firms will move toward the middle, as they are able to have more customers and increase their market share as well as their profits.  But in this case where two cafes are also differed by quality of foods, this model is distorted.

            Suppose Rao’s moves to a location closer to the Blanchard, let’s say, in the common room of Brigham. Then, Rao’s is supposed to attract some customers who previously went to Uncommon Grounds e.g. students who live in Brigham are more likely to go to Rao’s. However, as the locations of two cafés are much closer, people who used to consume at Rao’s may have second thoughts because Uncommon Grounds obviously has more delicious foods. Therefore, people will make their choices based on their preferences. Those who live close to Rao’s and value time more will still consume at Rao’s while those who value tasty foods more will go to Uncommon Grounds instead even though it is farther from them. Since people have different preferences, it is hard to calculate whether changing the location will attract more consumers or not. Therefore, it is not likely for Rao’s to move toward the middle.

            The same analysis can apply to the case of Uncommon Grounds’ change of location. On the contrary though, the conclusion is different. If Uncommon Grounds moves closer to the library, because it has higher quality of foods, it is able to attract customers from Rao’s. So Uncommon Grounds has the incentive to move closer to Rao’s!

HOW DO WE GET THAT EXPENSIVE TEXTBOOK?

HOW DO WE GET THAT EXPENSIVE TEXTBOOK?

by Jackie, Shijia, Van, Yixuan

            Life is never easy for a college student, isn’t it?

            When approaching the time for thorough packing at the end of the semester, we will find the most troublesome stuff is BOOK. Staring at these textbooks, do you recall the scene of hesitating in Odyssey? After careful comparison with copies online, we still walked away because of the ridiculously un-affordable price.

            Why are textbooks so expensive? Even though it does not cost hugely to enter the publishing industry and the U.S. has antitrust laws, a relatively small number of powerful publishers are still perceived to have monopoly power over textbook pricing. When our professors decide the materials for their courses, they will place orders at prospective bookstores, in our case the Odyssey. Odyssey will then contact publishers to notify them what books to order. Once the deal is set, the retailer like the Odyssey has the right to increase the price of each copy a little bit for its own profits. Unfortunately, if our professors happen to choose books whose copyrights owned by certain publishers, then it is quite usual for us to spend over $200 for the latest edition of a hard cover, colored, used textbooks. Sadly, since publishers only make money when new books are sold, they also buy up the old books and force the used book market to raise price, which makes used books less appealing to students.

            In this case, some of us tend to seek for digital forms of textbooks instead. This option generally costs less and is suitable for students’ tiny budgets. Not surprisingly, as we can see, Amazon dominates vast marketplace of e-book retailing and provides with only kindle edition to limit the use of resources. Compared to physical books, e-books are more accessible. You can read e-books on multiple devices such as PCs in the library, your MacBook, or even the smartphones that you carry everywhere. However, e-books also bring about inconvenience that keeps majority readers from using, such as difficulty in looking up specific part of the book, distraction from redundant features like embedded quizzes and electronic flashcards. You will find another disadvantage of e-books when you read through this blog.

            Luckily, we can go to our beloved library and borrow a hard copy of textbook for free. From the economics we learned, we know that each decision has an opportunity cost. Most textbooks are on reserve and each student can only borrow one at a time for three hours. We need to well plan this limited time period and use the book to the fullest. Don’t be too optimistic! You are risking not getting the book and re-plan your time, because someone might have already checked it out! Well, “If only I had bought my own book!”

            After the semester is done, you are offered several ways to sell back your books. Odyssey only buys back books that have been ordered from professors for the new semester at no more than half of the original price. You can try bigger marketplace like Amazon.com, Half.ebay.com, Textbookrush.com, where you will find a pool of potential buyers. Compared to Odyssey, in the latter option, you will see listed prices of different sellers and then set your own price. It sounds like perfect competitive market where you have perfect information, competitors perceive same prices as you do, and it is easy to enter and exit. Faced with this elastic demand, however, you may realize that the older edition that you possess, the less likely you are able to sell it back. Besides, you wouldn’t be able to sell if it is an e-book! Rationally speaking, you want to adjust your preference for purchasing textbook next time by thinking of how will you be better off. As a supplier, your cost is the original price you paid, the depreciation of the book, the transaction fee charged by Amazon, and the shipping fee you paid. You need to balance the original price you pay for and the chance of getting potential return.

            In a nutshell, we are facing unaffordable prices for textbooks. Many of students still prefer using physical books. We cannot change the fact that we need books to do homework, which contributes to a fairly inelastic demand for textbooks. Thus, we do wish that the textbooks could be less expensive. We hope there would be more open source. However, it seems that the price adjustment won’t come soon, so why don’t we think about it in a more optimistic way: The cost we pay for books will gradually pay off and become our very own intangible asset, something called “Knowledge”.

Apple as a monopolistic industry

Apple as a monopolistic industry

Yixi, Gabriela, Jessica, and Tahlia

A monopoly is a market structure involving only one firm that sets both price and quantity and has a downward sloping demand curve. The graph below shows that the quantity in a monopoly is at MC=MR. It would be maximizing for Y. The price is the demand curve. The consumer surplus is located below the demand curve above the price. The producer surplus, is found between the price and marginal cost.

The first Apple ipad was released in 2010 and, at the time, dominated the hand held tablet industry. According to an ABI Research report, the ipad held 85 percent market share. For the purposes of this example, we will assume Apple is still a monopoly. What does this exactly mean? Apple has no other competitors, they created a product without substitutes and therefore face no competition. Because of this they set the price and quantity of their product regardless of the market equilibrium (as mentioned in class they now are the market). Quantity is lower than that of a perfect competition scenario and profits are much greater as well. More details on the price effects are explained below. Monopoly power is regulated in the United States by antitrust laws which promote fair competition. On the other hand, patents give a firm the right to produce an exclusive design of the product, for example. This means that, at least for some time, the firm is the only one who is able to produce and sell the exact product for which it was given a patent. This is done as an incentive for innovation and change.

By creating the new category of device, iPad dominated the tablet industry. Apple as a monopolist had the power over setting the market price of iPad. Recall the quantity effect and price effect in influencing Apple’s decision in setting the price. Aiming at attracting more potential consumers to its first generation iPad, which was innovative and advancing, Apple set the price of base model at $499, which was much lower than the pre-release estimates by Wall Street analysts. Therefore, Apple sold more than 15 million first-generation iPads before its release of the iPad 2. As price decreases on all iPad that Apple sell, the marginal revenue of iPad 1 is less than the slope of consumers’ demand curve. However, since Apple was acting as a monopoly in selling iPad, the market price is still much higher than the one in a perfectly competitive market.

**How apple uses price discrimination to increase their revenue.

During the fall of 2011, Apple introduced and sold their MacBook Pro laptop computers with 13-inch screen on its website and in its retail stores for $1, 499. Yet, college students and faculty members could buy the same computer from Apple for $1,399. Why would Apple charge different prices for the same computer, depending on whether the buyer is an customer that studies in an educational institution? It makes sense for Apple to charge different prices because students that are customers have a different price elasticity of demand than other customers. So, Apple will charge the market segment with the less elastic demand a higher price and the market segment with the higher elastic demand a lower price. This suggests that Apple charges customers a lower price because they have a more elastic demand than some customers.

Here, the graph shows that in the education customers segment of the market, the marginal revenue equals marginal cost at 20,000 computers sold. This shows, Apple should charge a price of $1,399 to maximize their profits. Yet, if Apple charges $1,399 to the general public segment of the market, shown in (b) then it will sell 32,500 computers which is more than the profit-maximizing quantity. By charging $1,499 to the general public, Apple will sell 30,500 computers, which is the profit-maximizing quantity. We have shown that Apple will maximize their profits by charging students in educational institutions with a lower price than it charges the general public. You would notice the demand curve in graph (a) that is more elastic and steeper.

Math example :)

Apple wants to maximize its profits. An output and price must be found that allows the company to make as much as it can. The profit maximization function is given for a monopoly:

    Max y, P(y)*y - C(y)

As an example (not using actual data) let us say that Apple has a demand curve of P=400-3yand a total cost function of C(y)=y2+ 4

In order to find optimal output we must use the profit maximization equation.

Max y, (400-3y)*y - y^2- 4

Here we use First Order Conditions and solve for y

400-8y=0

y=50

Now that we have found y, we plug it into the demand curve to find the price

p=400-3(50)

p=250

Lastly, we want to know the profits that this monopoly will receive. Here we plug our newly found quantity and price into the profit equation

profit =(50)(250) - (50)2-4

profit = 10,004

This is how one would calculate the profit of a monopoly.

Resources:

http://www.tuaw.com/2011/04/20/ipad-held-85-market-share-in-2010-according-to-abi-research/

http://www.law.cornell.edu/wex/patent

Sunny Island Coffee: A Mount Holyoke Coffee Supplier

Sunny Island Coffee: A Mount Holyoke Coffee Supplier

By Dorothy, Kate, Niole, Thu

Sunny Island Coffee is the main supplier of coffee beans to Mount Holyoke College. The school recently had to reevaluate Sunny Island’s ability to fulfill the school’s demand for coffee in light of bad weather affecting coffee bean crops. In 2012, the plantation became a victim of flood damage. In years previous, Sunny Island Coffee broke even in terms of their net profit. The equilibrium price in the coffee market was p = $8per lb. In 2012, the Island’s crops were severely damaged. The firm decided to prevent further issues by investing in a drainage system, but they will have to incur the cost of laborers to maintain this system which they considered a variable cost.

This has also increased the cost of running the plantation. The cost per lb of coffee produced became: C(y)=,y-2.+5y. The supply function looked like this: p=2y+5

Mount Holyoke College’s Economist decided to investigate further and found the the profit equation,π=py-5y-,y-2.=8y-5y-,y-2..

As P=8, ATC=y+5, the firm can easily produce the right amount of coffee so that P>AVC (8>y+5, 3>y) and make profits. Therefore the firm can continue to produce in the short run.

For now, because Sunny Island Coffee is able to continue production in the short run, Mount Holyoke College decided to continue giving Sunny Island their business. But will need to evaluate other options, as it is unclear whether or not they will be able to continue business in the long run. However, as we all know, Mount Holyoke students need their coffee, and Sunny Island is able to produce it.