(5) For each situation, solve for the Bertrand-Nash Equilibrium (differentiated Product). 5a) Suppose Sarah’s constant marginal cost is $5 but Joe's is $8 Recall that in a Bertrand model with differentiated product, each supplier faces his/her own demand: = 100 – 10 Pjoe + 5 Psarah Qsarah = 100 - 10 Psarah + 5 Pjoe 5b) Suppose Joe and Sarah have the same cost functions as earlier (constant MC of $5) but asymmetric demand functions Qjoe = 100 – 10 Pjoe + 5 Psarah Qsarah = 160 – 10 Psarah + 5 Pjoe
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- Suppose Tasty Cakes is deciding its pricing strategy: it is debating whether to offer a single linear price for its sheet cakes or to offer non-linear pricing. Suppose on any day, it gets 2 customers–who are of Type A and TypeB with the following maximum willingness-to-pay for the cakes: Units Type A Type B 1 $100 $90 2 $75 $40 Suppose it costs $10 to bake each of the cakes. (a) If Tasty Cakes decides to pick a linear pricing strategy, what will be the profit-maximizing price it should choose? How many cakes will it end up selling and what will be its total profit? (b) If Tasty Cakes decides to pick a non-linear pricing strategy where it may offer a different price depending on the number of cakes purchased, what should be the profit-maximizing set of prices? How many cakes will it sell and what will be its total profit? (c)Comparing Tasty Cakes’profits in (a) and (b), explain IN WORDS why we see this difference in profitsIt takes 3,000 households having average annual income of $50,000 within a 3-mile radius to support a grocerystore. There are actually 6,000 households within 3-miles of the Shop-Rite Grocery that have $50,000 per yearaverage incomes. Today, Shop-Rite is the only grocery store in this area. Using the concept of Nash Equilibrium inlocation, explain what the likely outcome will be for this area, given those conditionsGary's Gas and Frank's Fuel are the only two providers of gasoline in their town. Below is the demand schedule for the market of gasoline. Assume that the cost of producing gasoline is 3 per gallon (AC=3, FC-D0). Suppose that the two producers collude (split production and profits evenly), what are the joint profits of these two firms? Q demanded (in gallons) 10 12 4 Market price (in dollar) $22 $20 $18 $16 $14 $12 $10 $8 $6 $0 O $27 O None of these options is correct. $55 O $72 O $36 50 00 3)
- There are two firms in the market (duopoly). These two firms are competingsimultaneously. The first firm chooses its output level (x) by predicting the second firm’soutput (y). Let c denote the total cost function c(x) = x and c(y) = y. Also, let’s assumethat the inverse demand function is p(Y) = 7 - Y where Y = x + y. (1) Obtain the reactionfunction of the first firm. (2) Find the equilibrium (output and profit of each firm) whentwo firms simultaneously competethe set of Fationalizable strategies will be the same for party R.) Explain your reasoning. ve Intel and AMD, the primary producers of computer central processing units (CPUS), compete with one another in the mid-range chip category (among other categories). Assume that global demand for mid-range chips depends on the quantity that the two firms make, so that the price (in dollars) for mid-range chips is given by P = 210 – Q, where Q = qin- || GAMD and where the quantities are measured in millions. Each mid- + 9AMD tel range chip costs Intel $60 to produce. AMD's production process is more streamlined; each chip costs them only $48 to produce. (a) Write the profit function for each firm in terms of qintel and qAMD- Find each firm's best-response rule. (b) Find the Nash equilibrium price, quantity, and profit for each firm. (c) (Optional) Suppose Intel acquires AMD, so that it now has two sep- arate divisions with two different production costs. The merged firm wishes to maximize total…Two firms produce identical products at zero cost, and theycompete by setting prices. If each firm charges a low price,then both firms earn profits of zero. If each firm charges ahigh price, then each firm earns profits of £30. If one firmcharges a high price and the other firm charges a low price,the firm that charges the lower price earns profits of £50, andthe firm charging the higher price earns profits of zero. (a) Which oligopoly model best describes this situation?(b) Write this game in normal form.(c) Suppose the game is infinitely repeated. Can theplayers sustain the "collusive outcome" as a Nashequilibrium if the interest rate is 50 percent? Explain. Please answer the a, b and c parts.
- 1. The market (inverse) demand function for a homogeneous good is P(Q) = 10 - Q. There are two firms: firm 1 has a constant marginal cost of 2 for producing each unit of the good, and firm 2 has a constant marginal cost of 1. The two firms compete by setting their quantities of production, and the price of the good is determined by the market demand function given the total quantity. a. Calculate the Nash equilibrium in this game and the corresponding market price when firms simultaneously choose quantities. b. Now suppose firml moves earlier than firm 2 and firm 2 observes firm 1 quantity choice before choosing its quantity find optimal choices of firm 1 and firm 2.The Tampa Tribune and the St. Petersburg Times compete for readers in the Tampa Bay market for newspapers. Recently, both newspapers considered changing the prices they charge for their Sunday editions. Suppose they considered the following payoff table for making a simultaneous decision to charge either a low price of $0.50 or a high price of $1.00. Tampa’s profits are shown in regular type. St. Petersburg’s profits are shown in bold. 5. This newspaper pricing decision ________ (is, is not) a Prisoners' Dilemma.Exercise A.5 Consider a company with market power that sells its product to two distinct consumer groups (type 1 consumers and type 2 consumers). Graphically illustrate the following situation: "if you charge a single price only consumers of type 1 will be able to buy the product but, if you charge differentiated prices, the two types of consumers will be able to buy it"
- 9: Suppose there are two restaurants on an island, Ace's (A) and Betty's (B). They both have to decide how many meals, qa and qB, to sell per day. For Q = qA + ¶B, the market demand function for meals is p = 120 – Q || Both restaurants face a marginal cost per meal of $30. (1) Find the Cournot equilibrium quantities and prices. (2) What if the restaurants decide to form a cartel and split the production and profits evenly. How much will each firm produce and what price do they charge? (3) Suppose they competed with prices instead of quantities. Find the Bertrand equilibrium quantities and prices. (4) Find the deadweight loss of Cournot competition, Bertrand competition, and of the cartel outcome. Then rank each of these from least deadweight loss to most deadweight loss. For the rest of the problem, assume firms compete in quantities (Cournot) and there is no cartel. (5) Suppose Betty's marginal cost per meal increases to $60. Ace's marginal cost remains at $30. What are the new…At a busy intersection on Route 309 in Quakertown, Pennsylvania, the convenience store and gasoline station, Wawa, competes with the service and gasoline station, Fred's Sunoco. In the Nash-Bertrand equilibrium with product differentiation competition for gasoline sales, the demand for Wawa's gas is qw=740-400pw + 400ps and the demand for Fred's gas is as = 740-400ps + 400pw. Assume that the marginal cost of each gallon of gasoline is m = $6. The gasoline retailers simultaneously set their prices. What is the Bertrand-Nash equilibrium? The Bertrand-Nash equilibrium is where pw = $ 7.85 and Ps =$7.85. (Enter your responses rounded to two decimal places.) Suppose that for each gallon of gasoline sold, Wawa earns a profit of $1.00 from its sale of salty snacks to its gasoline customers. Fred sells no products that are related to the consumption of his gasoline. What is the Nash equilibrium? The Bertrand-Nash equilibrium is where Pw = $ and Ps = $ (Enter your responses rounded to…As the new general manager of the Grand Palladium Jamaica luxury all-inclusive resort, youare assessing your pricing policies. Currently, the price of a weekend stay is $2,000 perguest. You estimate the marginal cost of serving a guest at $1,600, and while yourpredecessor unfortunately did not leave you data from the pricing experiments and testmarketing she performed, you do know that such experiments were done, and that yourpredecessor was competent.a. What is your best estimate of the elasticity of demand for a weekend stay at the GrandPalladium?b. Your learned that at the current price, the resort is only 80% full on the weekends.Remembering the sense of belonging that you experienced in a crowded subway duringthe rush hour, you contemplate lowering the price so the resort is completely full. What isyour back-of-the-envelope calculation for how much you need to lower the price?c. After some thought you cooled to the idea of full occupancy. Instead, you focused yourenergy and…