# Pricing Decision and Nash Equilibrium Price Questions

Q #1You have just been hired as the manager for a Fortune 500 company. In your new role you have three primary tasks that are due within the next two weeks. The first task is to determine pricing for a new product that directly competes with another company’s product. A group of market analysts have run several models to determine the profitability of each pricing decision made by you and the competing company. Below are their results (profits are in millions).CompetitorPrice LowSame PricePrice HighYour FirmPrice Low2, 24, 15, 0Same Price1, 43, 33, 1Price High0, 51, 43, 31. Which pricing strategy do you choose?2. Why did you choose this pricing strategy?3. Was there a better strategy to choose? If so, why didn’t you choose it?Your second task is the renegotiation of contracts. You have learned that negotiations had stalled between the prior management and you want make sure that the current negotiations are completed, as production needs to ramp up for the upcoming holiday season. The production crew wants a raise, whereas you want to keep costs at a minimum but also improve worker morale—which may lead to more productivity. Below are the most likely scenarios (payoffs are in thousands).CompetitorBargain HardAccommodateYouBargain Hard0, 05, 2Accommodate2, 54, 44. What is the most likely outcome and why?5. As the manager, what can you do to change the disagreement value of those you are bargaining with or your own disagreement value?Your last task is to hire a new employee for the data analytics department. You have several résumés on your desk and one catches your eye. The applicant has graduated summa cum laude from a top 20 institution, they held an internship at another Fortune 500 company, and have been involved in the local community.6. Why did this résumé catch your eye as compared to the other résumés?7. You want to hire the applicant, but are risk averse. List two ways you can be assured that the applicant is a good choice.8. Even though the new hire looked great on paper, they have quickly become a problem (due to lack of effort) in their department. You need to act, as you don’t want turmoil throughout the department and company. List two ways to improve the employee’s work effort and productivity.9. After a long week, you’ve finally had the chance to look over the data. You’ve found that the new hire generates $1,000 of additional productivity per week. You also know that the new hire earns $30/hour. Thinking about this, you’re unsure if hiring the new data analyst was a wise decision. What amount of hours should the analyst work for this new hire to be a prosperous one?Q #2You are conducting market research on the largest firms in the video game industry. You have found out each firm’s sales and the industry sales. Below are your results.FirmSales (millions)1$5002$6003$3004$9005$7506$800Industry$5,5001. Based on your research you determine that the four firm concentration ratio is _____ and you can classify this industry as a(n) _____?2. There are 10 other firms in this industry and they evenly split the remaining industry sales. What is the Herfindahl-Hirschman Index for this industry?3. Will the Department of Justice allow a merger to take place between firms 4 and 6? Why or why not?As luck would have it, you are able to collect data on two of the firms you have been researching. The products they sell are homogenous. Below is the estimated demand function for each firm and their marginal costs:Q = 80 – 4PA + 4PBMC = 24. What is the price response curve for each firm?5. What is the Nash Equilibrium price that each firm should charge?Being satisfied with the results you found, you happen upon a new set of data for two other firms in the industry who have been fiercely competing. You analyze the data and come up with the following:Firm BLower PriceRaise PriceFirm ALower Price1, 13, 0Raise Price0, 32, 26. The payouts represent profits for each firm given a pair of strategies. You think the firms will make this a one-shot promotion. What is the likely outcome and why?7. You’ve reconsidered what each firm is doing. Now, you believe the firms will act in a behavior that seeks long-run profits instead of short-run profits. What is the most likely outcome now? Why?You’ve researched many aspects of this industry and have a good understanding of how it works. However, in a recent change, the firms find themselves switching to a new technology that increases their productivity. There has also been an increase in the incomes from those who buy video games.8. Draw a supply and demand diagram showing the before and after effects of the changes. Use the price you found in question 5 as your starting market price. Be sure to label all parts of the graph.Q #3Two firms currently comprise the market for chicken sandwiches. One firm has been in the market for 50 years and has considerable market share. The other firm has been in the market for 25 years and is trying to erode the market share of the first firm. Below is the inverse demand function for the market. Each firm also faces marginal costs of $1.P(Q) = $8 – 0.25QMC = $11. How many chicken sandwiches will each firm produce (assume this is thousands)?2. What price will each firm charge?3. How much in profit will each firm earn? How much will the industry earn in profit?4. Draw a supply and demand diagram for this market. Be sure to appropriately label all parts on the diagram. Use the price and quantity you found in questions 1 and 2. (Hint: the supply curve is found by multiplying MC times Q).5. How much is consumer and producer surplus in this market?6. A new study shows that chicken sandwiches are delicious. At the same time, each firm faces rising wages as the “Fight for $15” becomes a reality. Show these changes on your graph from question 4.Each firm is not thrilled that the “Fight for $15” became a reality. They are now back to the drawing board to determine how to enhance profitability. The graph below shows the results of the first firm’s research.Popeye’sLower PriceRaise PriceChick-fil-ALower Price3, 34, 1Raise Price1, 42, 27. If the other firm has the same results, what is the most likely strategy of each firm?8. In an effort to surpass Chick-fil-A, Popeye’s is considering placing drive-thru kiosks to create more efficient lines and reduce costs. The investment is expected to cost $20 million. Over the next 5 years, the kiosks are expected to generate income flows of $9 million, $7.5 million, $5million, $3 million and $1 million, at which time the kiosks will need to be replaced. If the average interest rate is 8%, should Popeye’s invest in the new kiosks? Why?Q #4You have crunched the numbers and found your business has the following demand and cost functions:Q = $150 – 5PTC = $1,000 – 3Q + 0.05Q21. What is your business’ marginal revenue function and marginal cost function?2. What is the profit maximizing price and quantity?You have found your profit maximizing price and quantity, but a little market research determined that there were five other firms with similar marginal revenues and marginal costs. When you combined the output of all firms (under the assumption they chose their profit maximizing quantity as well) you came up with the following table:Price ($)Quantity Demanded Quantity Supplied 0750046507585501501245022516350350202504253. Draw the appropriate supply and demand graph.a) What is the equilibrium price and quantity in this market?b) At a price of $8, will there be a shortage or surplus in this market?c) At a price of $20, will there be a shortage or surplus in this market?You don’t think this market is as competitive as you originally assumed. Instead, you think there are enough quality differences in your product over your competitors that you can increase the price. Being cautious, you first decided to find the current price elasticity of demand.4. Using the demand function above:a) What is the price elasticity of demand when price is set to equilibrium price and quantity?b) Is your product price elastic or price inelastic? How do you know?5. You experiment with a 5% decrease in price. What is your new price and quantity (hint: be sure to use your demand and inverse demand functions)?As it turns out, you do have a competitor whose product closely matches yours. This leads to a predicament, as you have already raised your product price. Assume the numbers below represent the change in profit you will receive if you keep your price as is or if you decide to lower it (positive numbers increase profit; negative numbers decrease profit)CompetitorKeep PriceLower PriceYouKeep Price-50, -50-100, 100Lower Price100, -10050, 506. Based on your analysis, what should you do? Why should you do this?7. Suppose we are operating in the short-run. If market conditions change and more consumers enter the market and your resource costs (and competitors) increase; what are the likely effects on the supply and demand curves you drew in question 3? Show this in your graph, be sure to label the changes, if any.Q #5Over the past few decades, Boeing’s chief competitor was Airbus. Recently, smaller firms have entered the market. One of these firms is Embraer. Embraer recently had one of the best-selling business jets, the Phenom 300. Though, there are competitors, Boeing has led the market in terms of pricing.1. What type of market structure is this and what model might we use to analyze it?These companies have the following total cost functions with A = Airbus, E = Embraer and B = Boeing:TCA = $1,500,000 + $30,000,000QA + $500,000QA2TCE = $484,000,000 + $10,000,000QE + $250,000QE2TCB = $3,000,000,000 + $2,000,000QB + $55,000QB2The industry demand curve for this type of jet aircraft is:Q = 950 – 0.000015P2. What are the supply functions for Airbus and Embraer? (Hint: these firms operate as price takers) 3. What is Boeing’s demand function? (Hint: Boeing’s demand function is the industry demand curve minus the following firms’ supply or QB = Q – QA – QE. Use the answers you found in question 2)4. What is Boeing’s profit-maximizing price and output.5. What are Airbus’ and Embraer’s profit-maximizing output levels?6. Is the industry in short-run equilibrium, i.e. does firm supply equal total demand?7. Which firms are earning an economic profit? Which ones are earning a normal rate of return? How do you know?8. Is the industry in a long-run equilibrium? Why or why not?Q #6You’ve been hired as a consultant by a local company to help them determine what course of action they should take regarding future investment in capital. The firm is currently profitable and has the ability to acquire a loan at a 6% interest rate. They are looking to expand their current operations, but are unsure if the investment will be profitable. The market looks to be in a long-run equilibrium (i.e. the marginal entrant is making a normal rate of return), so you are unsure if the firm should make the investment. You crunch the numbers anyway.1. The investment will cost $500,000 and is expected to provide income of $275,000 in year 1, $200,000 in year 2, and $100,000 in year 3 after which the piece of capital will need to be replaced. Is the investment profitable? Why or why not?2. You are unsure that the answer you found is reliable, so you ask for more information. The owner tells you that previous experience ensures an 80% success rate and that they can scrap the capital for one-fifth its value. With this new information do you find the project to be successful? Why or why not?Satisfied with your analysis, the owner asks you to conduct further analysis. The owner is interested in changing market conditions and how that will affect business. She thinks there has been a change in demand, but wants to be sure. You ask for her sales so that you can run a regression to determine her demand. You get the following:QD = 500 – 0.25P + 0.2Iwhere P is the price of the own good and I is income.3. Using the demand function above, draw a demand curve and label the graph appropriately. Assume that income is held constant4. You analyzed the local market and have found that average income is expected to increase from $45,000 to $45,500. Show this change in your graph. Label all parts appropriately. What change in demand have you found?Digging further into the business, you want to give the owner a full set of information to help her better understand her pricing decisions going forward. You find that the business’ marginal cost is $1,200.5. What is the profit-maximizing quantity the business should pursue?6. What is the business’ price elasticity of demand?7. If the business is currently producing 50 units, at a price of $1,200, should they increase production to increase profit? Using the optimal price formula, what is the price the business should charge?Lastly, you assess the entry of a new competitor into the local business’ market. You make a few calculations to determine what the profit per unit will be if the entrant comes into the market or stays out. Below is part of your analysis.8. Looking at your game tree, what would you advise the owner to do and why?Q #7 The instructor for the course has caught several students cheating. He asks the students to come to his office on separate days. He confronts each student about their actions and shows them proof that directly ties them to their misdeeds. He asks the students to either confess to the misdeed or stay silent. As the instructor is benevolent, he is only considering filing academic misconduct charges if the students become hostile. The following is a set of potential outcomes (final assigned grades):Student 2Stay QuietConfessStudent 1ConfessD, FD, DStay QuietF, FF, D1. What is the most likely outcome? Why/?2. Is this a Pareto optimal outcome? Why or why not?3. What can the instructor do to ensure that students do not cheat in the course?4. Why is it in the best interest of the instructor to be benevolent towards his students early in the term, i.e. why would the instructor be forgiving of an early term late assignment? (Note: if you get this question then you have a strong grasp of game theory concepts). 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